Relativity and Cosmology

Nice explanation Jorrie.

Given that the expansion of the universe wasn't linear, how comfortable are we with the 13-14 billion years estimate. I ask because as I understand it, the age is taken by exploiting a linear relationship between distance and redshift. It seems like the further you go in distance, the less reliable the redshift measure might be, but that may not be true until you're within hours of big bang for all I know.

Also, would there be matter beyond our observable universe? It seems likely that inflating space would drag matter along with it. That would make the size of the universe staggering in volume.

Another thought. Is it possible that the galaxies that we say are moving away from us are actually moving in the same direction as us but at a slower speed so that relative to us they appear to be moving away? Is that question meaningless being mired in classical thinking (not joking, I suspect this might actually be the case)?

Hi Roger.

The 13.7±0.2 Gy age of the universe comes from using the best-fit observational parameters in the non-linear λCDM model. A linear extrapolation would give an age of roughly 9 Gy.

Yes there appears to be a lot more beyond the limits of our observation, which is purely constrained by the age of the cosmos and the time light had to travel up to now. The behaviour of the farthest observable galaxies appears to be consistent with this view, i.e., they appear to feel the gravitational effect equally from all sides, hence also from 'over the horizon'.

On your final thought: everything we know moves through space, meaning it is moving relative to the CMB radiation (so-called peculiar movement). However, the distant galaxies 'move' so much faster due to the expansion of the space between them and us that we cannot really measure their peculiar movement.

Expansion of space makes everything moving away from everything, unless gravitationally bound. This 'movement' is isotropic on the large scales and cannot be explained by peculiar movements or spatial movements relative to us.

-Jorrie

Given the solar system's age at 4.5b, and given that Sol is roughly about it's mid-age now (Mid of main P-P sequence) and given that Sol is thought to be a third generation star, taken into account that it's predecessors were bigger and therefore with shorter life-span, both in the sum of third of Sol's, which is about 9b+3b, and there you are with this current estimation.

Only first-generation stars didn't just pop, following the initial Big Bang;

It should take some time for first-generation stars to condense and ignite from local irregularities of accumulated matter, so this should be added to the time.

So I hear it's estimated around 15b to 18b.

Does it make sense that the initial accumulation to first generation took about 5b following the Big Bang?

Hi Yuval, you asked: "Does it make sense that the initial accumulation to first generation took about 5b following the Big Bang?"

I believe they found a quasar at a redshift of around 6.8,^[1] which when plugged into the current best model^[2] gives a distance of around 12.9 Gly (based on light-travel-time). That same model gives the age of the universe as 13.7±0.2 Gy, leaving at most 1 Gy for the first galaxies to have formed up to the point of having an active galactic nucleus.

Jorrie

[1] http://www.universetoday.com/2006/09/15/subaru-finds-the-most-distant-galaxy/

[2] The distances and ages are somewhat model dependant though. Presently, the ΛCDM model with Ω_Λ ~ 0.7 looks like the 'best-buy'.

Thanks

Jorrie,

You stated that "Since they were not moving through space, there is no relativistic problem with that." Here is where you loose me. I get the concept that space was expanding, not matter moving "through" it, but you still have to accept the fact that the matter was traveling "away from a point" at >3c in order for it to be that far away now.

Also, do you know exactly how they calculate the 90 billion light year distance or where I might find it?

Hi Guest.

Another way to wrap one's head around it is to consider a subsonic aircraft flying with a stratospheric jet-stream. The ground speed of the aircraft may far exceed Mach 1. OK, expanding space is not a jet-stream, but it takes matter with it all the same.

The short answer to the 90 billion ly is that that is what the cosmological models say if they plug in the best measured parameters.

For the long answer read http://en.wikipedia.org/wiki/Size_of_the_universe, especially the subsection "Size".

I have described the basic modelling of the cosmic expansion in a miniseries on CR4 before. See http://cr4.globalspec.com/blogentry/456/Cosmology-Equations-Part-4.

-Jorrie

Probably a grammatical, rather than a physics, note, but you say in the para "The best models... 45 billion ly each way, with us in the center." Isn't this prohibited by the erroneous Earth-centered view of the Universe? Also, are there any "photons passing thru space" vs. the outward expansion of space that might negate the arguement that early photons were actually receding from us, due to spatial expansion? We see space being curved or warped by massive bodies (stars, star clusters), and photons following that curvature. Is it possible that mass concentration could act as a "gravitational pathway" to allow shortcuts across the expanding space? I'd appreciate any additional thoughts on topics such as What borders the edges of the Universe, if there are edges. It would seem that if space is (or was) expanding, then there must be "edges" to the space envelope, and what are these boundaries expanding into? Thanks for lighting a glow in an old brain!

Hi Cardio07, on your problem with "... 45 billion ly each way, with us in the center."

We are always in the center of the observable universe. The Universe does not have a center, because it is thought to be either infinite or hyper-spherical.

On photons taking 'shortcuts': actually, the warping of space make them take 'long-cuts' - photons are slightly delayed by massive galaxies that they pass on their way to us. This happens due to gravitational lensing^[1] and also the so-called 'Shapiro time delay'.^[2]

Whats beyond the "edge"? Even if our Universe is perhaps flat, but finite, we observe only a small portion of it, as is clear from the behaviour of galaxies near our observational horizon. What borders a (possibly) flat, finite Universe no one knows, or has any chance of ever knowing. One can speculate, but that's not for me...

Jorrie

[1] See http://cr4.globalspec.com/blogentry/1847/Gravitational-Lensing-Einstein-Rings

[2] See this page from Relativity 4 Engineers and pdf download offered there.

Hi Jorrie and you other cosmic-minded individuals. Here's a question I have always had since my recreational drug use days: Is it possible that the universe is not expanding but all matter and energy is actually shrinking? How could we know the difference? Sounds as plausible as the concept of a holographic universe. Am I hallucinating?

Hi guitarhunter.

The answer to a 'shrinking' universe is quite simple: the red-shift that we observe in light from distant galaxies would have been blue-shift.

Jorrie

Hi Jorrie. I didn't mean the universe was shrinking. Let's say it is one uniform, stable size, but 14B years ago what is now the volume of the observable universe contained one atom. the universe volume stayed the same but the atom has shrunk to the size it is now (and continues to do so). Take that dots-on-a balloon example of how the universe expands and dots on the surface recede from each other. Instead of the baloon expanding, the dots themselves are shrinking and seem to be seperating from each other.

I should have taken the blue pill.

Hi guitarhunter.

I'll bet my bottom dollar that the redshift would not work the way we observe it, unless all the constants of nature (including c) changes in step with our 'shrinking'.

I think it might be better to take that pill...

Jorrie

Jorrie, I want to weigh in on the side of guitarhunter on this one. His question does not seem trivial to me. Like him I have pondered it for years and have wondered why I have been unable to find any serious response to this question in the literature of cosmology.

The basic concept of relativity tells us that perception of momentum depends on the "inertial frame" of the observer. Newtonian physics holds that there is no "preferred" inertial frame from which from which to gauge the motion of objects.

Instead of postulating the size of cosmological objects to be "fixed" and space to be "expanding", it seems perfectly as valid to consider the size of "space" to be fixed and the size of the objects (matter) within it to be shrinking. For that matter, "space" and "objects" could also be expanding and shrinking at a range of different rates, as long as the relative degree of expansion as between them remains consistent with observed measurements. The key question here is why it is even reasonable to postulate a "preferred" size frame of reference to choose between a (relatively) expanding universe and a (relatively) shrinking set of contained objects.

It is interesting to contemplate a Big Bang event in this alternative model, where the universe was the same gross "size" as it is today, but matter or its predecessor was (relatively speaking) cumulatively so "large" that it entirely filled the initial physical universe. No room for empty space at all, until the contents of the universe subsequently shrank over time.

In this model, Redshift and Blueshift might be explained as a subjective perception resulting from the "shrinking" size of the eyes and instruments of observers. This assumes that, while matter is continuously shrinking, energy (e.g., light or electromagnetic fields) once released do not shrink. The relative perception in the shrinking matter model is "conserved" (mirror image) compared to the Expanding Space Model.

The Shrinking Matter Model seems to me to require that the speed of light decreases over time in proportion to the shrinkage of matter. Otherwise we would perceive that the speed of (contemporaneously emitted) light is increasing relative to the distance measurements we make (relative to the size of atoms and other matter).

It sounds weird to say that something substantial and well, "massive", like matter could experience enormous "shrinkage" over time. But is it any weirder than saying that "space" (whatever it is made of) is expanding? In my book, space seems like a more fundamental substance than matter, and therefore if we are going to prefer any frame of reference we should prefer the constancy of space. (Not that we have any basis for actually preferring either frame).

At first blush, I don't see that the Shrinking Matter Model helps explain any of the current mysteries of cosmological physics any better, or indeed any differently, than the Expanding Universe Model. Things like the uneven rate of expansion/shrinkage, the distribution of matter at cosmological scales, or the oddities of quantum physics. But perhaps our insight will be improved in some respect if we keep an open mind on the subject of spatial frame of reference.

And, it's not as though the classic theory of the expansion of the universe doesn't have its own open switches. I am intrigued by the work of Erhad Sholz with respect to the Pioneer Anomoly involving redshift. See http://arxiv.org/abs/astro-ph/0701132v4. His theoretical model is quite different from the shrinking matter model, but perhaps it leaves the door open a notch...

Jon

Considering your shrinking universe theory for a second, how would it account for cosmic background radiation?

Hi Jon.

First a diversion: You wrote: "The basic concept of relativity tells us that perception of momentum depends on the "inertial frame" of the observer. Newtonian physics holds that there is no "preferred" inertial frame from which from which to gauge the motion of objects."

I can't agree here: Newton specifically viewed light as travelling through an aether at a constant speed and thought that one can measure your own velocity through the aether by observing the non-isotropy of the speed of light in various directions. This implied a preferred reference frame and was the standard view until the Michelson-Morley experiment in the 1880s.

Back to the issue at hand. Do you think all the observations around the cosmological redshift, structure formation, etc. can be explained in this 'shrinking matter' hypothesis? A good starting point would be to write down Hubble's law in this 'theory' and show a mechanism for the changing redshift over distance and time. Good luck with that - I think it's impossible.

Erhad Sholz ideas are surely interesting and will be valuable unless the Pioneer anomaly vanishes due to an acceleration caused by the nuclear power plants. We will probably only know when a mission specifically designed to check for such an anomaly is flow in the future.

Jorrie

Jorrie:

Well, of course I'm several levels below an amateur at cosmology so I will ask for forebearance on my technical gaffs while I try to hypothesize the incredible Shrinking Matter model. I'm incapable of doing Lorentz Transformations or any of the other necessary math!

Actually, I need help from a trained expert such as yourself to briefly explore how this model could be described in its most defensible form, and then in (hopefully) developing a concrete "knock-off" proof or logic to disprove it.

Regarding your aside, I didn't mean to imply that Newton himself articulated the principle that no particular position or direction in space can be preferred as a frame of reference over other possible frames. However, I had understood that concept was fleshed out over time, as you say including by the wonderful Michelson-Morley experiment, but nevertheless became an established principle of Classical physics predating, and not relying upon, Einstein's Special Relativity theory. Even if that's not the case, I think Relativistic physics fully supports the absense of any universally fundamental reference frame. It seems a fair question to ask why modern physics is entitled to adopt as the universal reference frame (for physical measurement) the observed local size of matter, in preference to alternative frames, such as one based on a fixed size of "space" or of the total universe.

I recognize that it may ultimately be impossible to actually measure the fixed size of "space" or the total universe, such that my postulated reference frane remains physically "unavailable" for direct use. But in any event we still can calculate the relative change in physical size between matter and space, which in this model is simply the inverse of the accepted model's rate of expansion of the universe.

Here are some additional questions and thoughts about the Shrinking Matter model:

1. Obviously the Shrinking Matter model would be easier to contemplate if the speed of light could remain a constant. I postulated in my first note that the speed of light logically must be decreasing proportional to the shrinkage in our physical "measuring sticks", because otherwise we would have observed an apparent increase in the measured speed of light. However, I do not know for a fact that the speed of light has actually been measured over a long enough period of time and to a sufficient degree of accuracy to rule out the possibility that the locally measured speed of light might be "increasing" at the rate of universal expansion (or matter shrinkage). Are the facts on that are readily available?

2. Hubble's Law says that redshift increases as a function of increasing regression speed between an emitter and receiver. For the Expanding Universe model, observed redshift is used to estimate regression speeds of cosmological objects at the historical instant when the light was first emitted, and thereby to infer the distances and ages of the objects. In the Shrinking Matter model, however, I don't see any mechanism that would cause the redshift to occur at the instant of emission. The emitting object is undergoing continuous physical shrinkage, including at that instant, but at such a miniscule rate that it seems unlikely to account for substantial redshift. And if redshift did occur at the instant of emission there would be no explanation for the observed variation in redshift among different cosmic objects.

So in this model I will assume that redshift is not an artifact of the emission process, but instead it is an artifact either of an in-transit transformation, or of the final reception process. My sense is that in-transit redshift has been fairly discredited in the context of "tired light" hypotheses. Would the same disproofs of "tired light" apply here, even though the redshift is tied to a fundamental shrinkage of matter (and maybe energy)? I don't know. Erhad Sholz isn't dissuaded by it, but for different reasons.

Perhaps it is more promising to postulate the redshift as an artifact of the final reception process. The causation mechanism could be as simple as the physical shrinkage of our "measuring sticks" (eyes and instruments) relative to a "non-shrunken" electromagnetic field. To our shrunken retinal cells and photon detectors, older incoming waves would look relatively "large" (because the historic emitter was relatively large) which could mean more physically spread out, i.e. lower frequency, i.e. redshifted. It would be nice if this function were geometrically proportional, but I'm not sure that must be the case. In this approach, a theoretical observer who herself somehow managed to avoid shrinking along with all the other matter, would perceive no redshift at any distance.

In any event, I am postulating that the mathematical formula of Hubble's Constant remain the same in the Shrinking Matter model, for all observable purposes.

3. As I understand it, in current physics the Cosmic Background Radiation (CMB) represents the free energy (photons) which filled the universe and became de-coupled from matter and "visible" at a certain time shortly after the Big Bang. We now observe that energy as redshifted, as a direct result of the expansion of space. That stays the same in the Shrinking Matter model, up to the last step. The Big Bang remains the same, except that, if the size of the universe is presumed to be fixed, then the same matter and energy which are the contents of the universe today were so much "larger" at the time of the Big Bang that they completely filled the universe. The CMB still would be generated upon the de-coupling of the universal sea of free photons from the VERY large matter. Subsequently the CMB would have been redshifted in the manner I outlined above. An interesting question is whether the primordial photons would have been VERY enormous, or whether in a general sense the shrinkage affects only fermions and not bosons. Full-rate shrinkage of energy (by which I mean decreasing energe density) is implied in this model in order to retain a proportionality between the absolute amount of matter and energy in the universe throughout its history. Otherwise the CMB doesn't seem to work.

I would invite more thought on a mechanism to corellate the shrinkage of matter with a corresponding decrease in energy density.

Jon

In my last post I said at the end:

"Full-rate shrinkage of energy (by which I mean decreasing energe density) is implied in this model in order to retain a proportionality between the absolute amount of matter and energy in the universe throughout its history. Otherwise the CMB doesn't seem to work."

Alternatively, I suppose one could postulate that the total energy density of the universe shortly after the Big Bang was not "nearly infinite" but instead was substantially the same as the energy density of the universe today. In which case, the incredible Shrinking Matter model would not need a mechanism to explain decreasing energy density over time.

Would a low energy density shortly after the Big Bang run afoul of other observations or calculations about the CMB (Cosmic Microwave Background) and subsequent distribution of matter and energy across the universe?

Hi jonmtkisco.

This 'theory' has so many flaws that I do not know where to start! I will just comment on some errors or apparent lack of understanding or knowledge.

You wrote: "However, I do not know for a fact that the speed of light has actually been measured over a long enough period of time and to a sufficient degree of accuracy to rule out the possibility that the locally measured speed of light might be "increasing" at the rate of universal expansion (or matter shrinkage)."

From distant supernovae observations, the speed of light has been measured as pretty constant over the last few billion years. And that was not done by timing the light as it came from the supernova (an impossibility), but by timing transverse light-travel phenomena in real time.

You said: "For the Expanding Universe model, observed redshift is used to estimate regression speeds of cosmological objects at the historical instant when the light was first emitted, and thereby to infer the distances and ages of the objects."

Not so. Observed cosmological redshifts indicate the amount of spatial expansion that has happened since the light has left the object and has nothing to do with receding speed at any time. It is not a Doppler shift.

The fact that the Hubble constant is expressed as speed per distance (km/s/Mpc) is just historical 'baggage' from the time Hubble discovered the effect. It is true that a redshift can be converted into an apparent recession speed for convenience of expression (as Hubble did), but that does not mean that cosmological redshifts are recession speeds.

Finally, have you given a thought how fast we must be shrinking in order to give the CMB an observed redshift of over 1000? What will happen when we hit the Planck size?

Regards, Jorrie

PS: I'm an engineer, not a physicist who can refute alternative theories on first principles. My aim is to make engineers and the like understand mainstream relativity and cosmology better, nothing more.

I fail to understand why you push an 'alternative theory' when, by the looks of it, you do not know mainstream cosmology very well. It is usually just a waste of time and energy.

My advice: use your curiosity to first understand mainstream theories; then think about alternatives that solve some problems with them.

Fair enough, thanks for correcting my technical blunders Jorrie. That's what I was hoping for.

You're right, redshift due to the expansion of space is different from the Doppler Effect. However, my proposition remains the same, that from the perspective of the Shrinking Matter model, redshift is simply a reception artifact caused by the ongoing contraction of our local "measuring sticks".

I don't think I'm posing an "alternative theory" at all. I just want to perform a simple mathematical conversion where the size of "space" is fixed as a constant and the (non-relativistic) length of matter is treated as a constant. In that sense it becomes just another "coordinate system" for examining exactly the same physical phenomena and dynamics as the accepted model. (Analagous, for example, the different coordinate systems used to analyse the event horizon of black holes). In general, all observed relationships and algorithms should remain the same. But... maybe testing the data using alternative coordinate systems can provide interesting new perspectives.

Also, I looked into the question I asked you about whether science has ruled out the possibility that the speed of light could be "decreasing" at the rate of local expansion of space. Ironically, as it turns out, since 1983 the definition of the speed of light has been fixed as the length of the path traveled by light in a vacuum over in 1 second, which is 299,972,458 meters. This re-definition had the effect of fixing the speed of light as a constant, such that it can never be more accurately defined. In effect, the measurement uncertainty was shifted to the definition of the length of the meter. Most recently, a meter is defined based on the iodine-stabilised Helium-Neon laser. Today's best determination of the wavelength of this laser is 632.991 398 22 nm with an estimated relative standard uncertainty of +/- 2.5 x 10 to the -11. That uncertainty is the limiting factor in defining the accuracy of a meter. According to Wikipedia it is several orders of magnitude poorer than the current measurement accuracy of a second.

My estimation is that the current uncertainty in the measurement of the local speed of the light is considerably larger than the velocity of the local expansion of the space. I don't have the math readily at hand, but if my intuition about the math is correct, it is reasonable to conclude that current measurement techniques cannot rule out the possibility that the locally measured speed of light might be decreasing at precisely the same rate (and opposite sign) as the local expansion of space.

Jon

I guess I really am brain dead. In this posting, I said:

I just want to perform a simple mathematical conversion where the size of "space" is fixed as a constant and the (non-relativistic) length of matter is treated as a constant.

What I meant to say is:

I just want to perform a simple mathematical conversion where the size of "space" is fixed as the constant and the (non-relativistic) length of matter is treated as the variable.

Hi again, Jon. You wrote: "I just want to perform a simple mathematical conversion where the size of "space" is fixed as the constant and the (non-relativistic) length of matter is treated as the variable."

Why do you want to make such a mathematical conversion? It is possible to do, but then you will have extreme difficulties in trying to couple any physical cause to the phenomenon. The way cosmological equations work today at least give a plausible cause.

Jorrie

Jorrie, first let me point to my reply to guitarhunter where I proposed naming this new coordinate system as "ECC" (Expansion Co-moving Coordinates). That simplifies the terminology.

I don't know how useful ECC will be in shedding light on any phenomena. However, I think it holds out some interesting possibilities for doing so.

The underlying motivation for ECC is that it normalizes measurements around the expansion of space, which filters out the wiggly, complex curves of historic cosmic expansion into a fixed metric. It will prove useful if it illuminates relationships between things that don't stand out in the classic coordinate system.

For an analogy, I cite your description of the utility of using 3 different metrics for studying black hole event horizons:

• "The Schwarzschild vacuum of the isolated static black hole was shown on two charts so far: the Schwarzschild chart and the Painlevé chart. Both have their place and utility, but one of the easiest charts to work with is the so-called ingoing Eddington-Finkelstein chart. (There is also an outgoing Eddington-Finkelstein chart, but we will leave it alone for now).... Eddington discovered this technique way back in the 1920s, but it took decades before Finkelstein rediscovered it and realized that it has a very special utility.… Unlike the Schwarzschild and the Painlevé charts, which have curved spacetime trajectories (or world lines) for infalling photons, the Ingoing Eddington-Finkelstein chart sports straight world lines for infalling photons (the yellow lines).… This looks just like flat spacetime, at least for infalling photons. It may appear like 'cheating', but it's no different from plotting power law relationships on a log scale, giving straight lines."

"Black Holes Part 3 - Eddington-Finkelstein Charts", posted January 28, 2007 11:00 PM by Jorrie (underlining added).

Jorrie, is it reasonable to interpret that the inverse-square effect of gravity does not literally retard the expansion of space itself, but instead actually accelerates all of the matter "against the current" of spacial expansion? Which should inevitably cause all of the matter in the universe to be somewhat "bunched up" in a larger surrounding space? If so, then it seems like we should be explicit in stating that the size of the universe (whatever that really means) must be physically larger than the outermost expansion of matter (which is NOT the definition of the universe), by some readily calculatable margin equal to the cumulative effects of the inward pull of gravity. In other words, matter and space may be co-expanding but they cannot be co-extensive at any point in time after the Big Bang.

Which raises a straightforward question: By what percentage has the effect of gravity over the age of the universe caused the total size of the universe to exceed the outermost extent of matter?

Jorrie, your non-response to this question makes me worry that I've committed another blog faux pas. I hope not, because I really appreciate the dialogue!

In the interest of clarity, I will restate my question, starting with some proposed definitions:

(a) "Space Cosmos" = ("initial size" of universe) + (average rate of space expansion)(age of universe).

(b) "Matter Cosmos" = Space Cosmos - (mass of contents of universe)(average rate of matter self-gravitational de-acceleration)

(c) "CMB Cosmos" - (size of universe at "time of last scattering") + average rate of space expansion since then)(age of universe - time of last scattering) - (mass of contents of universe)(average rate of photon de-acceleration due to mass contents of universe)

Would it be correct to surmise that (a) > (c) > (b)? That would occur because matter is de-accelerated (swims upstream) compared to cosmic expansion, and the CMB is similarly de-accelerated but to a lesser degree because it has no mass itself.

I recognize that we can't measure the "initial size of universe" at the BB and that it may be infinite. The question here is a relative one, not absolute.

The point is that intuitively it seems that by definition there must be "expanded space" in the cosmos that extends well beyond the de facto boundaries of the most voluminous extent of radiation and matter. Perhaps that extra margin of expansion could be calculated using current science.

However, the above proposition wouldn't be true if the gravitational effect (of all matter in the universe) acted to retard the expansion of the fabric of space itself. I know that gravity will curve space, but I don't recall hearing any description of how gravity could retard the ongoing expansion of the fabric of space itself.

In Wikipedia, the definition of "cosmos" or "universe" is unclear and doesn't seem to capture the distinctions I'm describing.

I appreciate your indulgence!

Jon

Hi Jon, you wrote: "Jorrie, your non-response to this question makes me worry that I've committed another blog faux pas."

As I mentioned before, I'm not keen on debunking off-mainstream theories. A few comments on your definitions in relation to mainstream cosmology are in order though.

I'm afraid your a) to c) show ignorance of what physical cosmology theory says. There are only two possibilities for the size of the cosmos: it is flat or open and hence infinite, or it is closed and finite, but without bounds, like the surface of a sphere in four dimensions instead of three. The latter one looks like the more probable case at the moment.

There is no difference between a 'space cosmos', a 'matter cosmos' and a 'CMB cosmos' in cosmology. All of space is filled with the energy of radiation and/or matter. There is also no space 'outside the radiation and matter' - in fact, there cannot be an 'outside' in the best models that fits observational data.

You wrote: "However, the above proposition wouldn't be true if the gravitational effect (of all matter in the universe) acted to retard the expansion of the fabric of space itself."

Present physical cosmology observations tell us that spatial expansion was originally decelerated by the energy density of matter, radiation and (perhaps) curvature. During the last 5 billion years or so, it is indicated that the expansion is accelerating due to some form of dark energy (with positive pressure). Expansion of space is controlled by the energy density inside it, be it matter density, radiation density or whatever...

I know this is a mouthful, but you will have to read a lot more cosmology than Wikipedia to understand the principles behind it.

Hope this helps!

Jorrie

Thanks for the answers Jorrie. The combination of direct dialogue and book learning definitely is quicker than book learning alone, so please be patient!

Here are some aspects of gravity and the expansion of space that confuse me:

1. The gravitational attraction of mass operates on the fabric of space itself, literally decreasing the amount of space between things. Does that mean that when two masses move towards each other due to mutual gravitation, the fabric of space between them contracts accordingly (and ultimately is entirely eliminated at the point when the two masses touch)? As opposed to the two masses moving through space towards each other? General relativity speaks of gravity causing "curvature of spacetime", but it seems to me that eliminating the intervening fabric of space is different from "curvature of spacetime". For example, the converse doesn't seem to be true -- general relativity doesn't speak about the expansion of the cosmos as constituting merely a "(negative) curvature of spacetime".

2. Since energy and mass are related by E = mc², general relativity predicts that radiation (e.g., the CMB) also exerts the same kind of gravitational effect.

3. The energy density of all the mass and radiation in the cosmos is said to operate on the fabric of space to reduce the rate of spatial expansion. Does the term "energy density" equate to the term "gravitation", or are they different aspects?

4. In the following formula, I would expect the effect of both the mass and radiation components to be negative. Which means that the 3rd component, dark energy, must contribute not only 100% of the pro-expansionary vector, but also an additional amount to offset the anti-expansionary contributions of mass and radiation. Is that correct?

5. Dark energy is postulated to have positive energy density as well as strong negative pressure. The negative pressure is what (somewhat non-intuitively) causes the anti-gravitational, pro-expansionary effect of dark energy. The positive energy density of dark matter contributes gravitational attraction (anti-expansionary), but this is more than offset by the pro-expansionary contribution of its negative pressure. The overall effect is that at the cosmological scale dark energy's pro-expansionary contribution overwhelms all other forms of gravitational attraction, resulting in the net accelerating expansion of the universe.

6. Since gravitation is subject to the inverse-square law, its effects tend to be relatively local, diminishing rapidly at great distances. This suggest that net rate of expansion of the universe occurs at highly differential rates locally depending on how much mass and radiation is present locally. Large empty spaces of vacuum expand much more rapidly than local areas containing dense masses. For example, space must be contracting rapidly in the local vicinity of a black hole.

7. Given the highly differential rates of expansion/contraction of space in various locations, more than 100% of the total net expansion of the universe should be be occurring in locations where no matter is found, ie empty space. The fraction of the total universe that contains no matter whatsoever inherently is increasing rapidly over time.

8. If originally matter was equally distributed across the universe, will that distribution change over time? It seems plausible to me that at the scale of the largest super-galactic structures, gravitation might pull matter into more compact bundles, leaving proportionately larger and "empty" voids. Those voids in turn will expand at an accelerating rate. Have calculations been done on whether, at various times in the future, matter might become more bunched up overall, or is the general view that entropy will drive matter to smoother and smoother distribution across space over time? Certainly individual black holes represent a dramatic form of local clumping. Will the mutual gravitation of groups of black holes cause additional higher-level clumping structures to form, or conversely will the expansion of empty space between them inevitably spread them ever further apart such that gravity can no longer further clump them? At a gross level one could compare the estimated overall formation and mass accumulation rate of black holes with the acceleration rate of spatial expansion.

9. If one can imagine a hypothetical journey to the very outermost "boundary" of the universe, one might expect to find the same distribution of mass and empty space as in the central parts of the universe. But the regions of empty space on the very "edge" would be less affected by gravitation because there is no mass "outward" from them. Therefore, it seems to me that empty space should be accelerating the most rapidly at the very outer edge of the universe. Which implies that over time, the part of the universe containing the "normal" distribution of matter will be constrained into an increasingly smaller subset of the total universe. This seems like a phenomenon that would accelerate quickly, maybe geometrically, resulting in a significant distinction between the "matter universe" and the "space universe".

I fully recognize that the concept of an outer boundary of the universe is beyond our knowledge, and so it could be considered meaningless. But at least I'm constraining this discussion to only that which occurs within that boundary, not outside. If the universe is and always has been infinite, then of course #9 doesn't apply. I'm not going to worry much about the possibility that the universe is curved, since the observational data continues to be consistent with a very flat universe. And I'm not going to spend any time worrying that it might be dodecahedron shaped!

For clarification, I am not suggesting in #1 that the contraction of the fabric of space accounts for the actual movement of the two masses towards each other. I recognize that the contraction of space is a very tiny effect compared to the movement of the masses through space. So my reference to the general relativity's curvature of spacetime doesn't make any sense. Although it wouldn't surprise me if there is a causal connection between the contraction and curvature.

Hi again Jon.

I suggest you read what I recommended in my previous post. Brief comments on your questions:

1. Not so, as I think you realized after posting question 1.

2. Correct.

3. Yes and no. Energy density is not quite equivalent to 'gravitation', but plays a role in how the expansion slows down.

4. No, all energy density is positive in our universe. The negative pressure of vacuum energy works on the 'speed side' of the proper expansion equation.

5. Correct.

6. No. On large scales, the expansion is equal everywhere in the universe. Black holes are local phenomena, almost like extremely tiny ripples on a very large expanding space.

7. Yes and no. Just like inside matter, there is overwhelmingly more space than their is matter in the cosmos. Matter that is gravitationally bound does not expand, but that does not influence the overall expansion rate one bit.

8. Yes on all but your "At a gross level one could compare the estimated overall formation and mass accumulation rate of black holes with the acceleration rate of spatial expansion." Black holes do accumulate mass, but the expansion is vasly larger than what they can muster, I think.

9. Yes and no. In an infinite or finite, closed universe there is no edge. There is a cosmological horizon over which we cannot observe, but from the observations near the horizon, it looks like there is just more of the same over the horizon. Space near the horizon does not expand faster today. However, when the light left that region, some 13 billion years ago, space was expanding about 60% faster than today. Remember that our own region was also expanding 60% faster then...

Jorrie

Jorrie, you said:

6. No. On large scales, the expansion is equal everywhere in the universe. Black holes are local phenomena, almost like extremely tiny ripples on a very large expanding space.

7. Yes and no. Just like inside matter, there is overwhelmingly more space than their is matter in the cosmos. Matter that is gravitationally bound does not expand, but that does not influence the overall expansion rate one bit.

I would really appreciate further explanation as to why the expansion of the fabric of space is equal everywhere in the universe. The pro-expansion vector of space is driven entirely by dark energy, which is spread uniformly throughout the cosmos. However, that pro-expansion vector is offset to a significant degree by (and must overcome) the anti-expansion vector caused by the gravitation of matter and radiation. The total amount of mass in the universe has the effect of substantially reducing the average rate of expansion of the universe, as compared to a hypothetical universe that contains only dark energy and no mass at all.

Since the effect of gravitation is very localized due to the inverse-square law, while dark matter is not localized, how can the expansion of space be equal everywhere in the cosmos? A large mass can "work against" the pro-expansive effects of dark energy only locally, not at cosmic distances.

If we divide the universe into a large number of "mini-universes" (or bubbles) by drawing arbitrary boundaries in space, we can divide it in such of the way that some of the bubbles contain virtually all the mass, and others contain virtually all empty space. Assume that the bubbles are large enough that the "mass-bearing" bubbles don't exert significant gravitation into the "empty space" bubbles. It seems to me that straightforward application of the math to each such bubble will calculate a differential rate of spatial expansion between the "mass-bearing" bubbles and the "empty space" bubbles.

If mass at one "end" of the universe could have an (instantanious?) effect on the rate of spatial expansion at the other "end" of the universe, then it seems that information is being communicated across the universe at speeds far exceeding the speed of light.

Hi Jon.

I'm just going to comment on your final paragraph for now: "If mass at one "end" of the universe could have an (instantaneous?) effect on the rate of spatial expansion at the other "end" of the universe, then it seems that information is being communicated across the universe at speeds far exceeding the speed of light."

In the big bang with inflation model,^[1] this is not a problem. Our observable universe was once very small and not really expanding in the first 10^-35 seconds or so. During that time, a gravitational field was present and reaching all corners of our observable universe..

Then inflation happened and the expansion got kick-started. Every piece of our observable universe still feels the gravitational field of every other piece. It's as simple as that.

Jorrie

[1] Read the Cosmic Inflation chapter in Relativity 4 Engineers, or if you do not have it yet, download the chapter by right-clicking here => Cosmic Inflation.

Jorrie, I was hoping you would answer the main part of my question... Or could point me to some reading that would answer it.

Jon

Hi Jon.

Right, now for the main part of your question. "Since the effect of gravitation is very localized due to the inverse-square law, while dark matter is not localized, how can the expansion of space be equal everywhere in the cosmos? A large mass can "work against" the pro-expansive effects of dark energy only locally, not at cosmic distances."

Yes, the expansion is only noticeable on large scales. Gravitationally bound areas are too small to for us to notice. It may also be that gravitationally bound systems do not expand at all. Think about the old balloon analogy with coins 'spot-glued' to the surface. The balloon expands everywhere but the coins just drift apart, without expanding.

This is so because cosmological expansion is not matter that moves through space - matters is just dragged with space. Any local gravitational effects make the matter move through space and hence do not hinder the expansion of space.

In the balloon analogy one can also say that the gravitational 'resistance' to expansion works towards the center of the balloon while the gravitational effects on galaxies works only along the surface, hence they are decoupled.

I acknowledge that the balloon analogy has its limitations, but it clearly shows the correct idea of how expansion of space and the contraction of matter under local gravity are two different things. This also shows why taking the universe as homogeneous on the larger scales is a reasonably valid premises.

"If we divide the universe into a large number of "mini-universes" (or bubbles) by drawing arbitrary boundaries in space, we can divide it in such of the way that some of the bubbles contain virtually all the mass, and others contain virtually all empty space."

I think the balloon analogy answers this to some extent. According to standard theory, the circles will all expand at the same rate, while the matter in the populated bubbles will move closer to each other, without affecting the expansion of space. How one would measure the size of the circles in a practical cosmos, I don't know...

Hope it is clearer now!

Jorrie

Jorrie, I understand what you are saying with your balloon analogy. But it is an analogy that makes it more difficult for me to understand your conclusion.

Again, the starting point is that the analogy must reflect that gravitation in is a very significant factor in retarding the rate of inflation of the universe at large scales.

Normal balloons resist inflating outward from the center primarily because the rubber resists stretching along the balloon's surface dimensions. The isotropic nature of the stretch-resistance of the rubber makes the balloon's surface look smooth at small scales.

In the balloon analogy, the glued coins prevent the balloon surface from expanding along the surface dimension in the areas where the coin faces are glued. The areas between the coins remain free to stretch at the normal rate. The cumulative effect of the glued coins is to reduce the total amount of "stretchable" balloon surface, which in turn increases the balloon's overall resistance to stretching from the center.

If the "rubber" is relatively stretchy, the surface of the balloon will "bulge out" very significantly between the glued coins. Just as a normal balloon will tend to bulge in one area if it develops a weak spot there. The glued coins cause the balloon's surface stretchiness to become non-isotropic at small scales.

To smooth out the bulges, one could construct the balloon out of a very rigid, stretch-resistant rubber. That would reduce the local bulges but never eliminate them. Also, the more stretch-resistant the rubber, the more force is required to inflate the balloon. It is apparent that the balloon's surface cannot remain bulge-free between the coins unless the stretch-resistance of the rubber is increased to the point where the glued-coin areas become a negligible factor in the balloon's overall rate of expansion.

Yet our starting point requires that gravitation is not a negligible factor in the expansion rate of the universe.

Obviously, the 2-dimensional surface of the balloon prevents it from being a complete analogy to the 3-dimensional expansion of space. In 3-dimensional space, the stretch-resistance needed to smooth the expansion of space on small scales would need to be some sort of 3-dimensional effect.

If anything, the balloon analogy is useful in demonstrating that the ability of space to resist significant local bulging in non-gravitationally bound areas is incompatible with gravitation being a significant factor in the large-scale expansion of the universe. The balloon analogy does not suggest any mechanism to de-couple the two factors, nor can I readily imagine such a mechanism.

I can accept that there may be no observational evidence for significant small-scale distortions in space. But to me that represents a potential weakness in the current standard theory, and the actual mechanism for achieving local smoothness remains to be explained.

Here's a 3-dimensional analogy to replace the 2-dimensional balloon analogy. Imagine that a lot of pennies are mixed in with raw bread dough. Then the bread is left to rise. The expansionary force of the yeast will more than offset the 3-dimensional stretch-resistance of the dough, which therefore will "rise".

Clearly, freely floating pennies will not prevent the dough from expanding at the same rate as if the pennies had been absent, and very little local distortion will occur in the expanding dough. (Let's disregard any minor anti-expansionary effect caused by the weight of the pennies, since the earth's gravity is an artificial "externality" in this analogy).

Logically, rigid pennies floating freely in 3-dimensional dough do not contribute any significant anti-expansionary vector to the dough as a whole.

On the other hand, if all the pennies were linked together with very thin, non-stretching wire, then either (a) the pennies collectively would impede the overall rising of the dough (if the dough is very thick), or more likely (b) the dough would expand around the pennies at nearly the same rate as if there were no pennies, and at small scales the dough would be forced to expand in very distorted angular directions.

Even in this 3-dimensional model, any constraints the pennies place on the free expansion of the dough at the largest scale (the loaf) cannot be de-coupled from the angular distortion of the dough that the expansion-resistant pennies cause at small scales.

In honor of the Simpsons movie, we can refer to this as the "D'oh!" analogy.

Hi again Jon.

Your "D'oh!" analogy is interesting (known in the literature as the 'raisin bread' analogy and others), but it too has its limitations. If the cosmos works like you described the interaction between the pennies and the dough, then how would orbits be stable?

As in the balloon analogy, one must be careful when viewing cosmic properties as the sum of of local properties. The cosmic D'oh is apparently near infinitely large (or larger) and our observable D'oh is but a tiny speck somewhere in that vastness.

As time goes on, the influence of matter will be completely dwarfed by the elusive dark energy that speeds up the expansion - it already makes up 70% of the cosmic energy density and it is apparently spread evenly.

Finding what dark energy is, is at the cutting edge of cosmology today. It's perhaps more important than the 'quantum cosmology' research about what happened at or before the big bang.

Jorrie

Hi Jon.

You wrote: "... the glued coins prevent the balloon surface from expanding along the surface dimension in the areas where the coin faces are glued." Remember I said 'spot-glued', meaning at one singular point per coin. This allows the fabric of spacetime to expand without being influenced by the local aberration of the coin.

Actually, if the balloon was in free space and expanding at a constant (or accelerating) rate, you did not have to glue the coins at all. They would have stayed where they were relative to the balloon, yet drifted apart due to the expansion.

In a practical cosmological model, the spacetime around the galaxy has curvature ('indentations') that causes a gravitational field relative to its center of mass, influencing every entity in its vicinity. On the large scale, the sum of all these 'indentations' on the balloon does affect the overall expansion rate, but not due to a 'local resistance' to local expansion.

Consider this: if all the matter in the cosmos could instantly be converted into gas that is homogeneously spread throughout the universe, the expansion rate would not change. The models that describe observations so very accurately depend only on the overall energy density - provided that it is reasonably homogeneous at large scales, which is what we observe.

Jorrie

Thanks for your two replies Jorrie. After reading them and pondering some more I think I can offer a simple, "brute force" analogy/explanation why the expansion of space is smooth at small scales.

Going back to the "D'oh" analogy, here is how the pennies retard the expansion of the D'oh: The pennies simply take up space. Since D'oh expands and pennies don't, the more pennies there are in a given loaf, the less D'oh can fit in the pan, and the less the loaf will expand, relatively speaking. At the extreme, if the ratio of pennies to D'oh is nearly 100%, the rising of the loaf would be negligible. The analogy assumes that any quantity of D'oh will expand infinitely, at a fixed rate of expansion over time.

So, if the penny / D'oh ratio is high enough at a given point in time, the pennies can be seen to significantly retard the expansion of the loaf simply through displacement. Yet the pennies remain untethered, and can be pushed along smoothly as the D'oh expands. Since the expanding D'oh and the rigid pennies get "pushed along" at the same rate, there is no local distortion of the D'oh.

The current estimate is that 73% of the observable universe's energy density is comprised of dark energy, and the remaining 26% is all matter. (About 23% out of the 26% being dark matter). At 26% matter, that's a lot of pennies in the D'oh! And at some not-too-distant time in the past when the observable universe was half of it's current volume, the "matter" pennies would have displaced 52% of the space otherwise available for D'oh. I assume that cosmologists have mathematically calculated the maximum historical ratio of matter to dark energy shortly after the Big Bang that would yield the current rate of expansion and acceleration of expansion, given the age of the universe. Do you know what that ratio is, Jorrie?

Also, if it's not too much trouble to ask, at the current rate of expansion (ignoring the accelerating rate of expansion), approximately how many years does it take for (a) the volume of an arbitrary subset (say, 1^-10) of the presently observable universe to double, and (b) the radius of that subset to double? I know that V = 4/3(pi)r³, so the answer to (a) is a lot less than the answer to (b).

Hi Jon.

You wrote: "... here is how the pennies retard the expansion of the D'oh: The pennies simply take up space."

I don't think so! The present energy density of the universe is about 10^-26 kg/m³, including dark matter and dark energy - no way enough to make your scheme work, I think.

Shortly after the inflation epoch of the BB, there were virtually no dark energy and little in the form of matter density. Radiation dominated the energy density. Look at my CR4 Blog entries on Cosmological Equations for an explanation. I have posted an Exel spreadsheet that you can download and play around with. I used it to plot some graphs for the Blog entries.

The curve tells us that the expansion factor will double in roughly 11 Gy. If the expansion rate remains the same as today it will take about 14 Gy for a doubling to occur. So what will happen to a subset of the observable universe at those times? All galaxies that are not gravitationally bound to a cluster/super-cluster will drift apart and double their light-travel-time distance. Hence all free space volumes will be 8 times today's volume in 11 Gy.

In co-moving coordinates there is no change in distance, of course. (If this is not a familiar term/statement to you, please read the free download from the Cosmology Introduction page of Relativity 4 Engineers.)

Interestingly, the radius of observable universe would not double in light-travel-time radius - in 11 Gy it at can obviously only increase by 11 Gly in radius. Hence it will shrink by 5 Gly in in co-moving radius, meaning some of the most distant galaxies and quasars that we observe today will be far over the horizon by then. In real terms, our observable universe actually shrinks.

In conventional terms, the actual matter (visible and dark) density will in 11 GY from now be about 1/8th of today's density. Dark energy density will be the same as today, making up around 92% of the critical energy density. As said before, if current trends continue, dark energy will eventually be utterly dominating.

Hope this helps!

Jorrie

Hi Jon, I wrote: "- in 11 Gy it [the observable universe] at can obviously only increase by 11 Gly in radius. Hence it will shrink by 5 Gly in in co-moving radius, meaning some of the most distant galaxies and quasars that we observe today will be far over the horizon by then. In real terms, our observable universe actually shrinks."

The 11 GLy increase in observable radius is correct in light-travel-time, but the 'shrink by 5 Gly in comoving radius' is wrong. For a long time to come, we and our descendants will still in principle be able to see new galaxies that formed shortly after the BB, but then farther than the present 13 Gly light-travel-time that we can observe.

Those farthest galaxies that we can observe today, is 45 Gly from us in comoving coordinates.^[1] Our descendants will eventually be able to observe out to about 63 Gly comoving radius, but then the observable universe will start to shrink due to the accelerating expansion. Scary (and confusing) stuff!

Jorrie

[1] http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v624n2/59364/59364.html?erFrom=911584242234823148Guest

Thanks for sharing those calculations about the expansion rate, Jorrie.

However, your brief dismissal of the "D'oh and pennies" analogy baffles me. You said "the present energy density of the universe is... no way enough to make your scheme work, I think."

My understanding is the ENTIRE current (positive sign) pro-expansionary vector of the cosmos is contributed by the "negative pressure" of the dark energy density of the vacuum, which acts like anti-gravity. This pro-expansionary vector is significantly offset, but not completely offset, by the (negative sign) anti-expansionary vector supplied by the energy density of matter and free radiation.

Notwithstanding that the absolute energy density of the universe is small (about 10^-26 kg/m³), there is nothing else driving the expansion of space. However small it is, by definition it has to be enough!

The D'oh analogy doesn't depend on the absolute density of the D'oh. It depends merely on the relative "quantities" of gravitation (mass and radiation) and anti-gravitation (dark energy).

The one different idea underlying the D'oh analogy is that gravitation does not actually supply a (negative) anti-expansion vector. Instead, gravitation simply dilutes the amount of the energy density equation (which must always total to 1) that can be supplied by dark energy, which is the sole pro-expansion vector. Gravitation itself is a zero vector.

I re-read your post of 4/14/07 1:37AM on "Cosmology Equations Part 3". I don't understand some aspects of your explanation.

You say that upon the end of the Inflation phase, the expansion rate "started to slow down" as energy-borrowing from the vacuum came to a near stop, and the total energy of matter and radiation came to dominate. Then you go on to say that every cubic meter of space continued to possess a small dark energy, such that as the expansion of space continued, more energy was "borrowed" from the vacuum and the total amount of dark energy increased, and after 5Gy came to exceed the total energy of mass and radiation.

Here's why I'm confused:

1. You make it sound as if the end of the Inflation Epoch was a prolonged event, where the rate of expansion had a sort of "momentum" flywheel effect left over from Inflation. But my understanding is that the Inflation Epoch ended rather instantaneously, at the instant that all particles (quarks, anti-quarks and gluons) "precipitated out" of the supercooled false vacuum. Supposedly, the Inflation Epoch began at 10^-35 seconds after the Big Bang and ended before 10^-32 seconds. After that, all of the elementary particles (including photons, protons, neutrons and electrons) had formed by 3 seconds after the Big Bang. As of that time (at the latest), the Inflation Epoch could not have left behind any residual "momentum of expansion". Any expansion of space that occurred after that point would depend solely on the amount of matter, radiation and dark energy which already existed at that instant.

2. If I'm correct about #1, then in the first instant after Inflation ended, the pro-expansionary vector of the then existing dark energy must have already exceeded the anti-expansionary vector of all the matter and radiation. Otherwise the universe would have immediately ceased expanding and begun contracting. (According to your figures, that contraction would have continued for 5 Gy until the total density of dark energy exceeded the density of matter and radiation, then it would have reversed course again and resumed expanding.)

3. Since the total density of dark energy increases linearly with the expansion of space, there should have been a constant rate of acceleration of expansion from the end of Inflation until the present. Yet the standard model suggests that the rate of acceleration was approximately zero until 5Gy, and only thereafter has become larger than zero. If the (negative) anti-expansionary contribution of matter and radiation has been fixed (flat) from the beginning, that implies that NO new dark energy was created until after the 5Gy point. Which completely contradicts the model.

So maybe the simplest way to phrase my question is, what net pro-expansionary vector caused space to expand (in fact at a constant rate) during the first 5 Gy after the Inflation Epoch? Why wasn't that vector more than offset by the larger anti-expansionary vector contributed by matter and energy?

Do you see what I'm getting at? It's as if the standard model assumes a constant "baseline" rate of spatial expansion even in the absence of any dark energy, matter and radiation.

Hi Jon, one final comment on the D'oh analogy: "The D'oh analogy doesn't depend on the absolute density of the D'oh. It depends merely on the relative "quantities" of gravitation (mass and radiation) and anti-gravitation (dark energy)."

The absolute density of the cosmos must be about 10^-26 kg/m³ for it to work as it does, i.e., being nearly flat. The ratios just changes the form of the expansion curve, not the present expansion rate (Ho), for we measure that one after all! The ratios change the expansion rate of the past and future only.

"1. You make it sound as if the end of the Inflation Epoch was a prolonged event, where the rate of expansion had a sort of "momentum" flywheel effect left over from Inflation."

This is what theory and observation tell us. The end of the accelerating expansion rate was abrupt. It was like when you stop the rocket engine - the velocity reaches a peak and then decreases. The rate of expansion changed smoothly from very, very large to the rate observed today.

The notion of an abrupt change is a very common misunderstanding and may come from misinterpreting a log-log expansion curve, which I discussed in a previous post.^[1] Here is the graph again:

The slope of the log-log expansion curve

Log(r/r_p)/Log (t/t_p)

represents accelerating expansion when it is above unity (45°) and decelerating expansion when it is below unity. The expansion rate (dr/dt) changes smoothly at all times, even where the curve is straight, unless at 45°. This is just the way log-log curves work.

I have scaled r so that r_now is the radius of the present observable universe. See [1] for more discussion on it.

"2. If I'm correct about #1, then in the first instant after Inflation ended, the pro-expansionary vector of the then existing dark energy must have already exceeded the anti-expansionary vector of all the matter and radiation."

The dark energy density was negligible after the inflation epoch, because the radiation and matter density were enormous. The same radiation, matter and dark matter in today's observable universe occupied a volume that was mere meters in diameter.^[2] Dark energy (cosmological constant) density was the same per square meter as what it is today (<10^-26 kg/m³) and hence utterly negligible.

The expansion rate was enormous at 10^-32 seconds after the BB (11 time units in the plot) and it also decreased rather rapidly at first. At around 5 Gy, the density of matter and dark energy equalled out and the deceleration stopped at some point, while there was still a significant expansion rate. Dark energy started to win the battle and since then there was a mild accelerating expansion, not visible on the log-log plot due to its scale.

"3. Since the total density of dark energy increases linearly with the expansion of space, there should have been a constant rate of acceleration of expansion from the end of Inflation until the present. "

OK, I think you know now why this is wrong. The dark energy density is constant; it is the total amount of dark energy that is on the increase with the expanding space. This is the essence of modern cosmology.

Finally, consider this: say there was no dark energy, but just enough ordinary and dark matter to make the universe as flat as what we observe. The enormous expansion rate just after the inflation period would smoothly change as in a parabola to eventually (at infinite time) slow down to as close to no expansion, without collapsing back, as is possible.

Hope things are clearer now.^[3]

Jorrie

[1] CR4 Blog entry on Inflation.

[2] George Smoot: Wrinkles in Time

[3] I am definitely not an expert on this and am just reporting what standard theory says. My main sources for the eBook were the standard post-grad handbooks of Peebles (Principles of Physical Cosmology) and Peacock (Cosmological Physics).

As bizarre as it seems, I have done some looking and found NO detailed explanation for what caused the expansion of space after the Inflation Epoch. Most treatises simple take it as a given.

I do have not seen any reference indicating that the post-Inflation Epoch expansion is a relic of some "momentum of expansion" left over from the Inflation Epoch.

I have seen the word "kinematics" used a few times. I think the implication is that the kinetic energy and pressure of very hot matter and radiation is the basic driver of expansion. One book compared it to "children running back and forth, bumping into the walls, pushing the walls outwards." As the universe expands, this kinetic energy is converted into gravitational potential energy, and the matter and energy accordingly lose energy and cool.

I can picture that "pressure" could push the universe "outwards", but given that there is nothing "outside" the universe, and therefore no pressure differential, this doesn't make much sense. Thus, I don't think that kinetic energy caused matter and energy to move through space.

The implication seems to be that kinetic energy/pressure simply has the opposite effect on space curvature that gravitation has. That is, while gravitation causes space to "curve", kinetic energy/pressure causes space to "flatten out". Whether the effect of kinetic energy/pressure is to curve space in the opposite direction as gravitation, or simply to flatten it in an absolute sense, isn't explained. I think it must be the former rather than the latter, because of the readily acknowledged possibility that an open universe has "negative curvature". Whereas gravitation causes "positive curvature."

It is bizarre in the extreme, that while the curvature of space by gravitation has received so much detailed attention, the "anti-curvature of space" by kinetic energy/pressure seemingly has received no attention. For example, why isn't anybody conducting experimental observations to observe whether photons bend outwards when they pass near a very energetic body, (or alternatively whether the inwards bend of gravitation is partially cancelled by the flattening effect of kinetic energy/pressure)?

Also, why does the Friedmann-Lemaître-Robertson-Walker (FLRW) metric make intuitive sense in this light? Increasing the amount of matter/radiation density in the universe increases the effect of gravitation, but it simultaneously and proportionately increases the (opposite sign) density of kinematic energy/pressure. I don't see how the formula takes account of that.

In the "cannonball" analogy, the effect of gravitation (curvature of space) tapers off with distance, and there is no "force" (merely momentum) continuing to push the cannonball forward after it's launch. Conversely, in the FLRW model, apparently the effect of gravitation remains constant after launch, whereas the cannonball relies on continuing kinetic energy/pressure to propel it forward after a non-powered launch, and that kinetic energy/pressure diminishes as the universe expands. I have seen NO scientific text explaining that distinction.

There is an unfortunate tendency for cosmological science literature to overly focus on the latest exciting "headline news" of new observations and theories, at the expense of giving a step-by-step explanation of how the whole universe "machine" actually works.

Hi Jon. On the explanation for expansion rate after inflation:

As a matter of fact, there is no accepted explanation for how inflation happened either. It is still just a postulate. What we have is models that fit the observations of the day and they cannot always answer the 'how' question, as you pointed out. I think all the models and analogies fall far short of the realities of a real universe, but they are the best we have at the moment.

The real "anti-curvature of space" agent is dark energy (the cosmological constant) of course. About it we know even less than about inflation, despite the fact that it is operating right now, as we speak.

You also wrote: "Increasing the amount of matter/radiation density in the universe increases the effect of gravitation, but it simultaneously and proportionately increases the (opposite sign) density of kinematic energy/pressure."

I do not agree with this statement. If we could take today's universe, with its present expansion rate and dump a sudden large amount of evenly spread matter/energy into it, the expansion rate will drop, or at least the increase of the rate will drop. This is what the λCDM FLRW model tells us.

If we keep all other parameters the same, just add extra matter energy, the spatial curvature would go positive. If we now force the curvature (in the model) back to zero again, then yes, something else must change - either less cosmological constant or a larger expansion rate. But this does not quite mean that more matter causes a larger expansion rate.

I do not understand what you mean by "Conversely, in the FLRW model, apparently the effect of gravitation remains constant after launch, whereas the cannonball relies on continuing kinetic energy/pressure to propel it forward after a non-powered launch, and that kinetic energy/pressure diminishes as the universe expands."

Jorrie

Hi again Jon.

Your mention of the 'cannonball analogy' made me think of a variant which can create a distance vs. time curve to almost match the cosmic expansion vs. time curve.

Imagine a small ion engine attached to the cannon ball. It continually produces a very small thrust vector in line with the cannon ball's travel away from Earth, let's say initially exactly at escape velocity. Initially, the thrust will make a negligible contribution against gravity and the cannon ball's speed will remain closely at escape velocity (√[2GM/r]) for its distance.

As the gravitational acceleration (GM/r²) diminishes, the small constant thrust will eventually become significant and propel the cannon ball slightly faster than escape velocity for the distance. At some point the small constant thrust will exceed the gravitational force and start to accelerate the cannon ball gently at first, but with growing speed and acceleration as time goes on. This will produce a distance-time curve similar in shape to the blue expansion curve of the ΛCDM model on the right.

This analogy does not explain anything, but it makes it easier to understand the model, I like to think...

Thanks Jorrie. My sense is that you will agree with my interpretations if I can explain myself more clearly on a few points.

1. Cannonball analogy. I agree with your explanation and chart. However, the scenario I propose is different for the ΛCDM case. According to the ΛCDM formula, the deceleration force of gravity remains constant regardless of how much the universe expands (the cannonball travels). Meanwhile, the kinetic energy/pressure of matter/radiation can be thought of as a motor attached to the cannonball, which continuously contributes a propulsive force, but is also continually being "throttled back" smoothly, by a little bit each second, (matching the ΛCDM curve, and never being throttled back all the way to zero.) The constantly decreasing propulsive force of the cannonball is the analogy for the constantly decreasing outward expansion vector contributed by kinetic energy/pressure, as the universe expands and cools.

This demonstrates that the ΛCDM case is a sort of mathematical "inverse" to the normal cannonball scenario from which the ΛCDM formula was derived. I just think that should be emphasized when the cannonball is used as an analogy. The significance is that the universe was not "flung" outwards by a single launch event at the end of the Inflation Epoch. Instead, the universe continues to "power" itself outward, using its own (ever-declining) self-powered propulsive engine. That engine is, and will remain, powerful enough to overcome the constant rate of deceleration caused by its own gravitation.

2. Would adding matter to the universe (at the end of the Inflation Epoch) have contributed increases in both acceleration and deceleration forces? Clearly it would have. More matter means more gravitation, which supplies the increased deceleration force. More matter also means more kinetic energy/pressure within the same initial volume of space, which supplies increased acceleration force.

When the ΛCDM model talks about increased gravitation causing more negative (closed) curvature, it is simply using General Relativity terminology to describe the deceleration force of gravity. Negative curvature = more gravitational force.

When the ΛCDM model talks about increased density causing more positive (open) curvature, it is describing the acceleration force contributed by kinetic energy/pressure. The more density, the more kinetic energy/pressure. Positive curvature = higher density = more kinetic energy/pressure.

The more matter there is at the end of the Inflation Epoch, the faster the universe's initial expansion velocity out of the gate, and the sooner that gravitation will cause it to decelerate (but never drop to zero velocity). Conversely, the less matter at the start, the slower the universe's initial expansion velocity, and the more gradually it will begin to decelerate.

3. I don't agree that dark energy is the real "anti-curvature of space". Dark energy, and the resulting acceleration, is very interesting now in the future. But as you pointed out, in the first 5 Gy, dark energy made no significant contribution to either curvature or rate of acceleration. The great majority of the 1100X expansion of the universe since the CMB has been driven by kinetic energy/pressure, not by dark matter. I think that objectively makes kinetic energy/pressure a lot more important, and a lot more worthy of attention and study. The fact that it receives almost no attention in the literature is truly puzzling.

Hi Jon, no, I'm afraid I disagree with all three main points that you are making. It looks like we are not far from the point where we will have to 'agree to disagree'!

1. You said: "According to the formula, the deceleration force of gravity remains constant regardless of how much the universe expands (the cannonball travels)"

How do you read that into the ΛCDM model? It is based on the original Einstein-de-Sitter model, to which Λ was later added. With Ω_m=1, Ω_v= Ω_r= 0, the expansion curve looks like on the right. This is also the parabolic distance curve of a cannonball shot away from Earth at escape velocity, without propulsion or drag, just plain old Newtonian, inverse square law gravity.

"... significance is that the universe was not "flung" outwards by a single launch event at the end of the Inflation Epoch. Instead, the universe continues to "power" itself outward, using its own (ever-declining) self-powered propulsive engine."

The self-powering is provided first by the inflation epoch and much later only by the cosmological constant Λ. In the first 5 Gy or so after inflation, the 'engine' was non-existent or insignificant at least. The engine's power relative to gravity is however continuously increasing, not decreasing. Λ is constant (like my ion propulsion), so the contribution increases due to more and more space being created. The gravitational effect of matter decreases with expansion.

2. "Would adding matter to the universe (at the end of the Inflation Epoch) have contributed increases in both acceleration and deceleration forces? Clearly it would have."

If the additional matter was added by the phase transitions that ended inflation, the matter density would have been higher and the radiation density lower. There was only a very insignificant contribution of dark energy then, so one can leave that out of the equation. The initial expansion rate would have been higher (for Ω=1) and so would have been the deceleration, but there is no accelerating force directly after inflation.

If the additional matter was somehow added after the phase transitions that ended inflation, the matter density would still have been higher, the radiation density would not change and initial expansion rate the same. The universe would have become closed (Ω>1) and expansion would have decelerated faster. Still, no accelerating force until much, much later.

This is what the ΛCDM model says and it is in accordance with all the standard text books.

"When the ΛCDM model talks about increased gravitation causing more negative (closed) curvature, it is simply using General Relativity terminology to describe the deceleration force of gravity. Negative curvature = more gravitational force."

I guess you have meant positive curvature on both counts? Curvature is proportional to Ω - 1, so negative curvature = less gravitational force (Ω < 1). This also applies to your next paragraph. The last paragraph of you point 2 is perfectly correct, but I think your prior conclusions about what it means are not quite correct.

"3. I don't agree that dark energy is the real "anti-curvature of space".

I used the term "anti-curvature of space", in the sense that you first used (I think): matter curves the universe positively and the dark energy curves it negatively. More matter and it becomes 'closed', positively curved; more dark energy and it becomes 'open', negatively curved. When the two Ωs adds to 1, the curvature is zero, of course.

"The great majority of the 1100X expansion of the universe since the CMB has been driven by kinetic energy/pressure, not by dark matter. "

Are you not mixing 'dark energy' and 'dark matter' up here? Whichever one you meant, it is not true - from observations, dark energy dominated the (increasing) expansion rate for the last 8 Gy or so the. Dark matter on the other hand contributed to the deceleration of expansion and it dominated during the first 5 Gy.

You concluded: "I think that objectively makes kinetic energy/pressure a lot more important, and a lot more worthy of attention and study."

From the 1930s to the 1980s, this was essentially all that was studied - the FLRW model without the ΛCDM. Dark matter was thought of in the 1930s, but not brought into the expansion models until in the 1980s, as far as I remember. I recall that the issue was that the theoretical maximum amount of dark matter possible was not enough to make the universe 'flat'.

The full ΛCDM model only became the favorite in the 1990s, when the accelerating expansion was observed and everything seemed to fall into place. It seems only natural that the pre-1990 models will get less attention nowadays.

Jorrie

My goodness, I hope we don't have to agree to disagree.

1. Curvature terminology. If I introduced confusing terminology in a prior note, I apologize. As of my last note I began using what I believe is the standard terminology:

• Gravitation contributes to a "negative" or "closed" curvature, and on the largest scale that gives the universe the shape of a sphere (with an extra dimension).
• Energy density contributes to a "positive" or "open" curvature, and an open universe is hyperbolic (like a saddle).
• If gravitation and energy density are in balance (e.g., at "critical density"), the universe is flat and infinite.

2. Einstein-de-Sitter Parabola. I agree that the expansion curve you show is the correct curve for this model. However, that parabola is a function of the interaction of two force vectors over time - deccelerative (gravitation) and accelerative (Inflation Epoch remnant momentum as you say, or alternatively kinetic energy density/pressure as I say). Exactly the same parabola can be generated in two different ways:

• Your way: Hold the effect of the accelerative contribution as a constant, while decreasing the (deccelerative) contribution of gravitation over time. This scenario assumes (as I understand you to say) that the universe was "flung" outward at the end of the Inflation Epoch, and thereafter, having only its initial momentum and no ongoing "propulsive force" of its own, it slowed like a cannonball flung into space, where the cannonball feels less and less effect of gravitation as gets further from "earth", due to the inverse-square law. Thus the parabola.
• My way: Hold the contribution of gravitation as a constant, while decreasing the accelerative force smoothly over time. This scenario assumes that the early universe was very "hot" and dense with kinetic energy/pressure, thereby propelling itself in an ongoing manner. The initial rate of expansion was very rapid due to the high density, and the rate slowed over time as the energy density fell (dilution as a factor of volume) and the matter "cooled". In this scenario the contribution of gravitation stays constant over time, because in aggregate the effect of gravitation on the expansion of space does not decline pursuant to the inverse-square law. Thus the parabola.

In both of the above scenarios, I am ignoring the contribution of dark energy, because the parabola you show does not factor in the contribution of dark energy.

3. "Residual Momentum of Expansion" theory. Jorrie, I see nothing in the literature describing the Inflation Epoch as having imparted a "residual momentum of expansion" to the universe which "flung" it outwards with a single "push". All I see is the simplistic analogy to a cannonball, which describes the formula for the parabolic curve but does not describe the dynamics of the underlying causation. On the contrary, I see multiple references to the kinematics of "hot" energy density propelling the expansion of space. Can you point me to a source which describes the causation dynamics of this "Residual Momentum of Expansion" theory?

Given that energy density and gravitation are generally accepted as flip sides of the same coin in the context of the curvature of the universe, isn't it most logical and straightforward that they also be flip sides of the same coin in the context of acceleration and decceleration of expansion? After all, as I said, the whole concept of "negative curvature" of space is nothing more than General Relativity terminology for the deccelerative contribution of gravitation, so it seems implicit that "positive curvature" must relate to the accelerative contribution of energy density. The "positive curvature" contribution of energy density acts to flatten space, which means it is acting directly to negate the "negative curvature" contribution of gravitation. By definition I believe that requires energy density's "anti-negative" contribution to be described as an accelerative force.

Hi again Jon.

With this reply I just want to first try and establish a common terminology, because I think part of our differences of opinion are simply terminology.

I take a 'closed' geometry as having positive curvature. AFAIK, in a positive curvature system, two light rays starting out locally parallel will converge and later cross. The Earth's surface is a two-dimensional closed system with positive curvature.

The opposite happens in an 'open' geometry system, that is labeled negative curvature. (Wikipedia on curvature: "A positive curvature corresponds to the inverse square radius of curvature; an example is a sphere or hypersphere. An example of negatively curved space is hyperbolic geometry.")

I see gravitation and energy density as somewhat interchangeable (F/m = GM/r²), much like mass and energy are interchangeable (E = mc²). Hence, I take both gravity and energy density as working in the same direction, as (negative) potential energy, closing the system (tending towards positive curvature).

What is making space open, in my books, is (positive) kinetic energy of expansion, driving it towards negative curvature. When kinetic and potential energy are balanced (add up to zero), the space is flat, of course.

My view is that the cosmic inflation epoch produced a flat space with a precise balance between the positive kinetic energy of expansion and the negative potential energy of radiation, matter and vacuum energy. How it did that is somewhat clouded in quantum physical mystery, to me at least.

I will look out for accessible technical literature that makes this clearer and let you know. The various forms of the Friedmann equations essentially say that, but it is not instantly recognizable as such.

Jorrie

OK, thank you for pointing out my stupid mistake, which led me to an incorrect analysis.

I agree now that the standard terminology says that the higher gravitation driven by higher density = POSITIVE, CLOSED curvature, like a sphere. Lower gravitation driven by lower density = NEGATIVE, OPEN curvature, hyperbolic.

Therefore, I was incorrect in saying that density and gravitation pull in opposite directions, and are flip sides of the same coin. Oops.

I also agree that the Friedmann equations treat the initial expansion (before dark energy's influence) as being like a cannonball rather than a rocket. A cannonball in the sense that it is "fired" with a single impulse of momentum from the source, and no ongoing self-propulsion unit. The source of that impulse cries out for explanation. And as you noted, the metaphor becomes mixed with the addition of dark energy, whereby the Friedmann equations require what formerly was a simpleminded little cannonball to strap on a supplementary ion engine.

Having said that, I still wonder if the "rocket" analogy couldn't be applied somehow to provide a simpler mathematical model for the evolving rate of expansion. That is, if kinetic energy/pressure could be posited as providing an ongoing contribution to expansion, while gravitation provides an opposing contribution. One could postulate that both of these "forces" decline over time at nearly equivalent rates of a³, after a brief initial burst of rapid expansion driven by radiation at a⁴. Because the rate of expansion would remain constant over time in this model, the factor that must be added to the equation to account for the re-acceleration of expansion recently could be much smaller than what is currently assumed for dark energy. (The "base" rate of expansion would not decline parabolicaly as described in the Einstein-de-Sitter graph).

Hi Jon - it's a pleasure.

I have also struggled with those same issues for years and also came up with some simpler models, most of them eventually rejected for lack of agreement with observation. The cannon ball with the tiny engine is still not too bad, though.

On your 'simpler model', you said: "Because the rate of expansion would remain constant over time in this model, the factor that must be added to the equation to account for the re-acceleration of expansion recently could be much smaller than what is currently assumed for dark energy"

The problem is that the decreasing expansion rate for of the first ~5 Gy is actually observed nowadays. It is only 'visible' in regions more than 9 Gy from us, so it requires Hubble and other super-telescopes to observe.

I arrived at one simplified model that actually gives a 'close enough for all practical purposes' shape of the expansion, as plotted on the right. Taking Ho as 71 km/s/Mpc, curve (i) is the Einstein-de Sitter universe (only ~10 Gy old), (ii) is the ΛCDM curve (13.7 Gy old) and the solid line (iii) is my simplified model (~14.5 Gy old).

I describe it in my eBook (chapter 16, down-loadable from here). Briefly, it is taking the Hubble constant literally as constant over 'look-back' time and also a straight relativistic Doppler interpretation of the cosmological redshift.

I think my curve fits inside the error band around the cosmologists curve. But, alas, it offers even less of an explanation than many others...

Sorry for hammering this one a bit, but it is not quite right to say that there was "... a brief initial burst of rapid expansion driven by radiation at a⁴...". Standard inflation theory did not operate by radiation energy, but by quantum vacuum effects, I think.

Standard ΛCDM cosmology says that the dominant radiation energy density (at a⁴) operated only as a 'brake' directly after inflation, not as a 'thrust'. The radiation density was much smaller in the ΛCDM case than in the Einstein-de-Sitter case, hence the slower start and the lesser 'braking' observed.

Something that I did not think of before: did the fact that a cosmological constant, dark energy, or whatever, was 'reserved' during inflation (for future use), cause inflation to produce less radiation and matter and at a lesser expansion rate, i.e., a lot less momentum of expansion? Food for thought...

Jorrie

Jorrie,

Thanks for the correction about radiation -- I agree that in the Friedmann equations it acts only as a brake.

It's not obvious to me why your "simplified model" for the expansion curve doesn't have a physical explanation. You say in your ebook that "there is no physical justification for a precisely linear Hubble law right to the end of the observable universe." Why not?

One other point. I understand how, mathematically, dark energy neatly keeps the universe exactly (or almost exactly) at critical density at all times from the beginning to the end. Which says that since the end of the Inflation Epoch, space has always been "flat", and should remain flat into the distant future. But I don't understand what mechanism enables the "density" of dark energy to contribute flatness to space, when that density is divorced from gravitation (and in fact contributes anti-gravitation through negative pressure). I understand how it nicely fulfills the Friedmann equations, but some empirical explanation of the underlying causation is required. It is readily apparent why gravitation manifests itself as positive curvature of space, at least in General Relativity terminology. But I am not aware that General Relativity also specifies that energy density independently (without any contribution from gravitation) manifests itself as positive curvature of space. If GR doesn't explain why, then has some other theory been accepted as the likely underlying cause?

Another related point. The fact that the newly created space (vacuum) has exactly the correct energy density to preserve the overall flatness of the universe seems far too important to be merely a lucky or anthropic coincidence. Apparently the universe insists upon remaining flat at all times. Which is remarkable given that space is not flat at small scales. I will postulate that as a basic law of nature, at all times and under any conditions, the quantum sea is incapable of producing (or perhaps sustaining more than briefly) any form or quantity of matter or energy that will change the equilibrium of flatness. I don't think that in the present, each quantum unit of space can possibly "sense" the sum total flatness of all the other quantum units in the universe. Which implies me that the universe always has been flat at the largest scale, and has no mechansim (including Inflation, Big Bang, etc.) which would ever cause a change in overall flatness.

I think this is another form of your question about Inflation having "reserved" a placeholder for dark energy.

Jorrie, further to your question about Inflation having "reserved" a placeholder for dark energy:

I submit that the everything that happens in the universe must continuously conserve the universe's overall flatness. Therefore matter and dark energy need to be directly substitutable for each other on a one-for-one basis in terms of energy density. Otherwise, the universe couldn't have remained flat continuously since Inflation ended, as the proportions of matter and dark energy changed.

Doesn't it follow then, that the universe doesn't care about the proportionate mix of matter and dark energy, or how rapidly that mix is changing (rate of expansion)? I see nothing that required Inflation to initially "deposit" any particular mix. But I hazard to guess there can be only a single solution for the absolute total amount of matter plus dark energy combined that would yield a continuously flat universe.

Hey, if that were actually true, then we would know that the full universe has a specific amount of stuff in it -- meaning that it can't be infinite! Moreover, if we have enough information to calculate the absolute total quantity of stuff in the full universe, and we assume that the present relative mix of matter and dark energy in our observable universe is roughly representative of the mix of the full universe, then we could estimate the actual size of the full universe. That would be fun!

However, I struggle with the math...

Hi Jon.

On your previous remark on my simplified model: it fails on precisely what you mentioned later - the flatness of the universe. My model does not preserve that, or otherwise it has to continually convert one form of energy into the other at a changing, but precise rate. there is no justification for that. The other two curves do conserve the flatness.

One must note that the absolute value of mass-energy and radiation energy remains roughly constant in the ΛCDM model, while the absolute value of dark energy grows with expansion. This causes the dark energy density to remain constant while the other two densities decrease with expansion, with radiation density decreasing faster (the 1/a⁴ factor).

You wrote: "I submit that the everything that happens in the universe must continuously conserve the universe's overall flatness. Therefore matter and dark energy need to be directly substitutable for each other on a one-for-one basis in terms of energy density."

The fist part is correct, but consider what I said in the previous paragraph. Further, it is only at the end of inflation that the ratios could have been adjusted and then we would have seen a different expansion curve. Remember that the expansion rate today has to be what we measure. Read that with the measured shape of expansion curve and it allows only one particular initial mix of energies.

Inflation theory apparently predicts a 'flat' mixture (Ω = Ω_m + Ω_r + Ω_v = 1, today's values), but it does not predict the size of the components correctly. AFAIK, it predicts too large a value for ρ_v by a huge amount. I calculated the ΛCDM model's required densities (given today's Ω components) at the end of inflation as orders of magnitude:

ρ_v ~ 10^-26 kg/m³; ρ_r ~ 10⁷⁶ kg/m³; ρ_m ~ 10⁵³ kg/m³; ρ_tot ~ 10⁷⁶ kg/m³.

Today's orders of magnitude are:

ρ_v ~ 10^-26 kg/m³; ρ_r ~ 10^-31 kg/m³; ρ_m ~ 10^-27 kg/m³; ρ_tot ~ 10^-26 kg/m³.

Based on the values of the expansion factor, the universe has expanded by a factor ~10⁸⁰ in volume since inflation ended. Unfortunately, we have no idea of the total size of the cosmos after inflation (or now), so we cannot calculate the absolute energy values then or today...

Jorrie

Thanks Jorie.

1. Mix of mass/radiation and dark energy. When I said that the universe didn't "care" about the mix of mass/radiation and dark energy at the end of Inflation, I meant that from the perspective of looking forward from then, unconstrained by what actually happened later. Not from our present perspective looking backwards. I agree that a specific mix was needed to create the actual expansion curve that happened. My point was different -- that the mix could just as well have been different, which yes, would have yielded a different expansion curve, but my postulated law of nature still would have been satisfied, because overall flatness would have been preserved. My only point being, that when the universe was "balancing" itself at the end of Inflation, it didn't need to explicitly reserve for a specific mix of dark energy -- it just happened to play out with the mix (and resulting expansion curve) it did because of whatever the other initial conditions were.

2. Substitutability. Are you saying that it is mathematically impossible for dark energy to "be directly substitutable for each other on a one-for-one basis in terms of energy density? Doesn't the density of matter/radiation in space drop off exponentially with radius, but linearly with volume? Analogy: Dissolve "X" quantity of salt in 5cc's of water. In a 2nd step, add 10 more cc's of water. The density of dissolved salt falls by a factor of 3, not a factor of 8. And if the water added in the 2nd step already had its own salt density equal to (X per 5cc's), then the added water doesn't change the density at all. The latter is what I had in mind, that vacuum inherently has energy density "dissolved inside it" that is equal to the energy density of matter/radiation.

As you mention, one fly in the ointment is that radiation is diluted by expanding space at a faster rate than matter, because of the redshift effect. Even a temporary density imbalance causes a a problem for my "Conservation of Flatness Law". I'm grasping at straws here, but could there be a solution in the fact that radiation does not actually "displace" any volume of vacuum, while matter does (due to the Pauli Exclusion Principle of quantum mechanics)? So, (in a certain sense) radiation can dissolve within any given volume of vacuum and thereby increase the energy density without increasing the total volume. An equivalent energy density of matter on the other hand would displace vacuum and therefore occupy a larger volume. Hmmm, I'm not sure that this adjustment would be enough mathematically to compensate for the dilutive effect of redshift.

Since we have no redshift data reaching back to the radiation-dominated era, other than the CMB at one isolated point in time, do we really have suffient observational data to nail down the early part of the expansion curve? You never know what surprises might be lurking out there!

3. Conservation of mass/energy? Your math about the total rest mass-energy at the end of Inflation being 10²² times today's value is really interesting. Does redshift really have enough magnitude to mathematically account such an enormous loss of energy?

I can readily picture how the expansion of space stretches the wavelengths of photons and thereby causes redshift. But in my mind that ought to cause dilution of the photon energy, not absolute loss of the energy. How can cosmologists just shrug off the anihilation of 99.99999999999999999999% of the total mass/energy content of the universe?

4. Residual Momentum of Inflation. Is it your understanding/assumption that at the first instant after the end of the Inflation Epoch, the universe was "fired outwards" (cannonball analogy) at exactly the same residual rate of expansion as the immediately preceding rate of Inflation? Or did Inflation give up some of its expansionary momentum at the instant when it "precipitated out" all of the matter/radiation into the universe?

5. General Relativity. Since cosmologists seem satisfied that energy density alone is a perfect substitute for gravitation in causing positive curvature of space, then for the sake of simplicity we should remove gravitation entirely from General Relativity. We should just say, for example, that "An orbiting satellite follows a 'straight' path in the positive curved spacetime caused by Earth's energy density".

Then we can knock the audience out of their chairs by going on to explain that "A satellite also can orbit around an empty vacuum, due to the positive curvature of spacetime caused by the vacuum's energy density!!!" Even though vacuum energy has negative pressure which causes anti-gravity, the satellite still will orbit the vacuum because the latter's energy density causes positive, not negative, curvature of the local spacetime. Cool, dude!

Hi Jon. Some comments on your rather tough questions.

"1. Mix of mass/radiation and dark energy." I agree with your view.

"2. Substitutability." At any given instant, I suppose rest energies can be substituted, but that will immediately change the deceleration or acceleration of expansion at that time, e.g., radiation density produces twice the deceleration of mass for the same energy density and vacuum energy produces acceleration.

Yes, there must be some uncertainty on the radiation-dominated era, which we cannot yet observe. One thing in the cosmologist's favor is that they could predict the CMB's temperature and 'wrinkles' very accurately in advance.

"3. Conservation of mass/energy?" This 'loss' is what the Friedmann equation tells us. One must remember that the calculation I did was without the kinetic- and potential energy, just plain rest energy (density times volume). I'm not sure if inclusion of the other energies may change the picture completely. Still working on that - it's easy for matter alone, but with radiation and vacuum energy...

"4. Residual Momentum of Inflation." Basically, what cosmologists do is work the Friedmann equation backwards and see what expansion rate was required at around T₀+10^-32 seconds. Then they assume that the inflation epoch delivered exactly that expansion rate, I think.

The following is from an interesting paper^[1] on mapping the cosmos and tracking back by means of the Friedmann equation: "So we simply start the clock at the end of the inflationary period where the energy of the false vacuum [large cosmological constant] is dumped in the form of matter and radiation. Thus when we trace back to the big bang, we really trace back to the end of the inflationary period."

"5. General Relativity."

Remember that cosmologists are talking average densities over the global cosmos that is assumed to be isotropic and homogeneous on the large scale. Standard General Relativity works with inhomogeneous energies. The satellite will not care too much if Earth is suddenly compressed into a neutron star or black hole. However, one can probably say that this is so because the average energy density 'below' the satellite remains unchanged?

But... orbiting a piece of empty space on vacuum energy? No-way!

Jorrie

[1] J R Gott III, et.al. Download from: http://www.astro.princeton.edu/~mjuric/universe/

Thanks Jorrie for taking on tough questions!

I just realized something that seems very important to the calculations. According to the accepted theory, apparently there are two quite different kinds of vacuum cohabiting the universe today:

• "Normal Vacuum" has zero energy density. This is the vacuum created by the "residual momentum of inflation" (the cannonball). Once created, it possesses no cosmological constant and adds nothing further to the expansion rate of the universe. I believe that through rapid initial accretion it has come to comprise the overwhelming majority of the vacuum in the present universe. However, the creation rate for "new" Normal Vacuum is declining at a parabolic rate and eventually will approach zero.
• "Dark Energy Vacuum" is the type that has energy density and negative pressure (the ion engine strapped to the cannonball). This type of vacuum contributes 100% of all of the cosmological constant. It started out as a negligible quantity (or none at all) and has added acceleration to the expansion increasingly over time. The creation rate for "new" Dark Energy Vacuum is increasing at a parabolic rate.

This means that the average energy density of the total vacuum in the universe is increasing over time, because the proportion of Dark Energy Vacuum increases at an accelerating rate compared to Normal Vacuum. That seems intuitive -- over time the universe its transferring its energy density away from mass/radiation and into the vacuum.

Of course only the Dark Energy Vacuum is interchangeable with the energy density of mass/radiation on a one-for-one basis, and the Normal Vacuum is ignored for the calculations. It should be straightforward to calculate roughly what percentage of the total vacuum of space is comprised of each type, at any point in time, including the present.

Further to the Conservation of Flatness Law, one could say that Dark Energy Vacuum is constantly being "sucked into existence" from the quantum sea as the universe expands, in order to supply replacement energy density to preserve a flat universe.

Maybe this is analogous to Inflation also having sucked matter and radiation into existence from the quantum sea, which also was necessary in order to restore flatness. Or even better, hopefully matter and radiation were sucked into existence evenly throughout the brief period of Inflation, such that even on an instantaneous timescale Inflation did not cause the universe to depart from flatness.

I wonder if the two types of vacuum currently are homogeneously intermixed, or whether there might be bubbles of one or the other. As mentioned in the Gott article you cited, if a bubble of pure Dark Energy Vacuum of any significant size forms, it may set off another exponential "explosion" of Inflation, which could quickly consume our observable universe. So homogeneous mixing must be the prevalent condition.

I wonder if the two types of vacuum interact with each other, or are inert? Maybe there aren't really two kinds of vacuum because the Dark Energy immediately "radiates" into the Normal Energy and creates one homogeneous mix. Of course, by definition Dark Energy is called "dark" because we haven't detected it. If it had a propensity to "radiate itself" away from its source, we might have detected the resulting radiation by now. So it is reasonably plausible that individual quanta of Dark Energy Vacuum retain a distinct ongoing identity as compared to individual quanta of Normal Vacuum. That would be consistent with the apparent assumption that the two kinds of vacuum are just different quantum states of a single kind of "space".

If they do remain distinct (even in infinitesimal quantities), then normal radiation must interact differently when it travels through Dark Energy Vacuum because the latter's energy density causes a local curvature of space, which Normal Vacuum does not. Unless radiation interacts with Dark Energy Vacuum in the same manner it interacts with matter (e.g., absorption and re-emission), something is changing over time in the way that radiation travels through space. This is because, as stated above, the average energy density of the total vacuum is increasing over time.

Hi Jon, at least we give it a try!

You wrote: "According to the accepted theory, apparently there are two quite different kinds of vacuum cohabiting the universe today:"

I don't know about that. The only 2 kinds of vacuum energy that cosmologists are talking about is the normal vacuum and the false vacuum, and the one makes a 'phase transition' into the other. It's somewhat like steam having a phase transition into water and releasing energy in the process. Whether 'steam and water' can both exist, I do not know. AFAIK, dark energy is not viewed as a 'false vacuum' in the mainstream, but I may be wrong.

You said: "This means that the average energy density of the total vacuum in the universe is increasing over time, because the proportion of Dark Energy Vacuum increases at an accelerating rate compared to Normal Vacuum."

This is contra the present leading theories. The energy density of the matter and radiation decreases, while the vacuum energy remains constant, so the total density is still on the decline. Eventually the vacuum energy density will dominate and the total energy density will effectively remain constant 'for ever after'. It can only possibly increase again if there is a contracting phase coming, which looks unlikely with present knowledge.

So, you'll have to invent a 'new cosmology', or rework your ideas to fit the accepted one.

"It should be straightforward to calculate roughly what percentage of the total vacuum of space is comprised of each type, at any point in time, including the present."

For a flat universe, it is indeed easy to calculate the portions of the different energies for any epoch since inflation ended, even with dark energy. This is essentially what the Friedmann equation does. BTW, I figured how to calculate the total energy of a flat universe for any epoch - it is precisely zero!

The positive kinetic energy of expansion always equals the negative potential energy content. This is essentially the two sides of the Friedmann equation. So, even during the radiation dominated epoch, there is no total energy lost due to the redshift - it remains zero. The expansion rate just slows down faster due to the 'losses' on the other side.

Some tiny progress at last (which should have been obvious from the start...)

The only problem is that we cannot calculate the absolute energy value of either side of the Friedmann equation, simply because we don't know the size of the universe. We need an equivalent mass to multiply (half the square of) both sides with. We can however do so for the observable universe, because given a size and a density, we know the equivalent mass-energy of both sides.

Jorrie

"...value of either side of the Friedmann equation, simply because we don't know the size of the universe..."

An attempt to find whether Hubble's (omnidirectional) red-shift is increasing or decreasing along the time-axis, resulted with "Increasing" recently, wasn't it?

Hi Yuval, I'm not sure what you are asking (what is increasing or decreasing?).

The redshift is dependant on distance and time and is always decreasing with them.

The size of the universe is apparently forever increasing, the expansion rate is presently increasing and with it the total kinetic energy content, balanced by an equal negative potential energy content for a zero total energy.

Hope this answers your question; otherwise please rephrase...

Jorrie

If the indication is that the expansion rate is increasing, doesn't it say that the universe is destined to evaporate rather than collapse?

Or, is this indication only a temporary phase in the evolution of the universe?

Hi again Yuval.

The standard ΛCDM model says that the expansion rate will continue to increase until the cosmos contains only vacuum energy and nothing else (even protons and black holes may have decayed trillions of years from now).

Quantum gravity (toy) models have different outcomes, like a 'big crunch' and also small (then empty) regions collapsing to create many new big-bangs. This one is attractive because it apparently avoids violating the 2nd law of Thermo.

Obviously, no one knows much about the far future...

Jorrie

The baring of the laws of thermodynamics on the destiny of the universe, has always intrigued me the most.

Intuitively, one can picture the opposite of the big-bang, being a cold, dispersed, thinned universe,with single atoms or even sub atomic particles flying apart, loosing their initial energy...

Obviously, this is not the case, or is it?

Jorrie:

It's good to know that all that energy didn't just disappear. It makes a lot of sense that it just converts one-for-one into potential energy. Potential energy is a funny concept though. As mass density continues declining with the expansion of the universe, it seems that the opportunity to actually convert that potential energy back into kinetic energy (through gravitational pull) is being lost forever. That makes this particular flavor of potential energy pretty sad...

I agree with your reaction to my suggestion there are 2 kinds of vacuum energy. I shouldn't have said it was an "accepted" proposition, because I am usually very confused about what the accepted propositions are anyway. I agree that the distinction between false vacuum and normal vacuum is a different concept from what I described.

I'm not trying to invent a 'new cosmology' here. I'm just trying to apply the Conservation of Flatness law to the observed universe and see what it tells us. In that respect, I continue to see a theoretical problem with the concept that the average energy of the vacuum is a constant.

Clearly there is a direct correlation, in the basic Einstein-de-Sitter expansion graph, between the rate of expansion and the average energy density of the universe. It looks to me like E_V = D_A, (in normalized units), where E_V is any change in the volumetric expansion rate, and D_A is the corresponding change in the average density of the universe. Thus, when the average density drops by 1/2, the volumetric rate of expansion also drops by 1/2. (By volumetric rate I mean the rate of increase of volume, not radius). For lack of the real name I will refer to this the "Density-Expansion Equivalence" principle.

This principle is necessary to satisfy the Conservation of Flatness Law. For example, shortly after the end of Inflation, the universe was astronomically dense. But it preserved its flatness by imparting a correspondingly astronomical rate of expansion to the universe. The rate of expansion over time must always decrease at the same rate as the decrease in density, along the curve plotted by the Einstein-de-Sitter graph.

However, at the present time, we observe the rate of expansion to be increasing, not decreasing. This "excess expansion rate" is the amount by which the observed (positive) expansion rate exceeds the (negative) acceleration of the expansion rate generated by the Einstein-de-Sitter curve. Therefore, the Density-Expansion Equivalence principle requires that the average density of the universe must be increasing at a rate equal to the excess expansion rate.

Since, as you point out, the energy density of matter and radiation is continuing to decrease, the density of the vacuum must be increasing even faster, at a rate equal to the sum of (a) the excess expansion rate and (b) the rate of decrease of matter/radiation density.

The only explanation I can see for this rapid increase in vacuum density is that each recently created quantum of vacuum must have a higher energy density than each quantum of vacuum created in the more distant past. Thus, two kinds of vacuum, "old vacuum" and "new vacuum". For simplicity, my guess is that the energy density of old vacuum = zero.

Hi again Jon.

My major comment to your last reply is that you seem to be 'stuck' on an increasing vacuum energy density. Standard theory has the vacuum energy density as constant;^[1] it's the total vacuum energy that is on the increase with the spatial expansion, not the density.

The 'critical density' is always on the decrease, because it is defined as the density that makes an Einstein-de Sitter model balance (containing only matter that remains constant in mass, whatever that total mass may be). In the ΛCDM model, the total density is still decreasing today, but it is close to it's minimum value, after which it will remain constant. This is when matter density has been diluted to be negligible.

"Conservation of Flatness" simply means that the kinetic and potential energies must add to zero. Your "Density-Expansion Equivalence principle" applies only to the Einstein-de Sitter model. In the ΛCDM model the energy density tends towards constancy while the expansion rate tends towards growing more and more positive.

Sorry Jon, but you'll have to think again if you want to stay inside the 'standard box'. Nothing wrong with thinking outside of it, but then the arguments must still agree with observation.

Jorrie

[1] This applies only after the inflation epoch. Before the end of inflation epoch, Λ could have had a very large and possibly changing value. AFAIK, the simplest plausible inflation models still have it as a large constant until the phase transitions started near the end of inflation.

Hi Jon, further to my comment #77.

Maybe some of the problems that you seem to have with the standard model originate in the 'negative pressure' of the vacuum, e.g. Wikipedia's definition: "A positive vacuum energy density resulting from a cosmological constant implies a negative pressure, and vice versa. If the energy density is positive, the associated negative pressure will drive an accelerated expansion of empty space; see dark energy and cosmic inflation for details."

The positive vacuum energy density acts just like normal matter and 'brakes' the cosmic expansion. The negative pressure of the vacuum 'pushes' the expansion just enough to keep the zero energy balance, or if you like, to maintain Ω=1. This is why some books say that vacuum energy works both ways - contractive and repulsive.

One must remember that it is not the same as positive or negative pressure inside a balloon, where positive pressure would expand the balloon and add to the gravitational mass of the balloon. (The dangers of simple analogies.) Vacuum energy is a strange beast. It does not push against the 'outsides' of space, but works 'inside' it, quite possibly through some extra dimension...

Anyway, it seems that we owe our existence to vacuum energy - they say we are made of 'star dust' - I would rather say 'vacuum dust' left by inflation, so watch out next time you empty the dust bag of the vacuum cleaner...

Jorrie

Jorrie, I understand the theory that dark energy has positive density but acts like anti-gravity due to its negative pressure, with the anti-gravity effect exceeding the gravitational contribution of its positive density. Thus acting as a cosmological constant of the vacuum to drive the observed acceleration of expansion.

What I utterly fail to comprehend (and which I think you are alluding to by referring to the balloon model as "simplistic") is why the dark energy theory isn't considered to be obviously self-contradictory on its face, and therefore unsustainable. The concept of the universe having curvature has no meaning except to describe in GR terminology whether expansion is below, at, or above "escape velocity" from its own gravitation (Einstein-deSitter graph). Therefore, if expansion is accelerating and is above escape velocity, that fact per se defines the universe as being "open", having negative curvature. Yet all observations and current theories demonstrate the universe to be flat, flat, flat.

AFAIK, all vector contributions to GR curvature are additive, whether their sign is positive or negative (disregarding that the addition might not always be 100% linear). Thus, if for example, dark energy has n positive gravitation (due to its energy density) and -2n gravitation (negative due to its negative pressure), then dark energy must have a net gravitation of -n. Thus contributing net negative curvature to the universe. After all, how could that large -2n gravitation factor logically not contribute anything at all to the curvature?

Simply declaring that dark energy doesn't follow this obvious logic because it is "different" and "exotic" doesn't wash as science. Yet every source I have seen in the literature makes no effort to explain this obvious contradiction. Are you aware of anyone who has given an empirical explanation of why this isn't self-contradictory? I'd love to hear it, and please, without resort to extra dimensions, strings, and other stuff that mainstream cosmology doesn't depend on.

I don't see why you are so ready to drink the Kool-Aid!

Hi Jon. You wrote: "... if expansion is accelerating and is above escape velocity, that fact per se defines the universe as being "open", having negative curvature."

This contradicts what you defined as curvature in the preceding sentence, well, sort of. A better definition than 'escape velocity' is that the curvature depends on the sum of the kinetic end potential energies: positive total energy is open, negative total energy is closed. In the cannon ball analogy, it boils down to the same thing.

I fail to comprehend your: "dark energy has n positive gravitation (due to its energy density) and -2n gravitation (negative due to its negative pressure), then dark energy must have a net gravitation of -n. Thus contributing net negative curvature to the universe."

In the ΛCDM model the density of vacuum energy adds negative potential energy and an equal amount of positive kinetic energy to the mix, with a net contribution of zero to the total. I think science does not explain the 'contradiction', because they reckon there is none!

I have eventually succeeded in calculating the kinetic energy of expansion of the observable universe using the WMAP values. The graph looks like on the right. I may be out by a factor 10 or more in absolute value, but I'm confident that the curve shape is right.

We are presently at log(t)~10. The kink at log(t)~2 is where the matter density took over from radiation density and the 'runaway' at log(t)~11 is when vacuum energy will totally dominate.

The potential energy is just a mirror image below the log(E)=0 line (negative energy), so that the total energy remains zero. The "ultimate free lunch"!

Jorrie

Jorrie, first, your kinetic energy graph is awesome. I think that the astronomical scale of kinetic energy loss (conversion to potential energy) is a really fundamental aspect of expansion that hasn't been highlighted much AFAIK in the literature.

I don't know if you noticed, but when you include graphs in your posts, sometimes they cover up some of the text. The only way I found to uncover the missing text is to hit the reply button and read it that way.

You said the following about my incomprehension of dark energy:

• "In the ΛCDM model the density of vacuum energy adds negative potential energy and an equal amount of positive kinetic energy to the mix, with a net contribution of zero to the total. I think science does not explain the 'contradiction', because they reckon there is none!"

I don't understand what you're saying. I have not read anything about a concept that dark energy adds "negative potential energy". What I have read is that dark energy adds "negative pressure" which acts as anti-gravity. If negative potential energy were added, doesn't that imply that the universe must contract, so that the total potential energy of gravitation in the universe shrinks? But since dark energy is supposed to drive accelerated expansion, instead it must it contribute enormously to positive potential energy over time.

From Wikipedia's entry on dark energy (italics added):

• "The gravitational repulsive effect of dark energy's negative pressure is greater than the gravitational attraction caused by the energy itself. At the cosmological scale, it also overwhelms all other forms of gravitational attraction, resulting in the accelerating expansion of the universe."

The repulsive effect is large than the gravitational attraction. That's exactly what I mean when I said, for simplicity, that the gravitation contribution of dark energy = n, and the anti-gravitation contribution = -2n.

If positive curvature is caused by gravitation in GR, then why isn't gravitational repulsion its mirror-image in GR -- meaning that it causes negative curvature?

Here is an excerpt from an article that is the closest thing I can find to an explanation for why dark energy doesn't cause negative energy. But at the end of the day, this is just an assertion, and doesn't not explain any empirical cause:

• Still, anti-gravity is'nt the right way to describe dark energy, says Virginia Trimble of the University of Southern California at Irvine.
• "It doesn't act opposite to gravity," Trimble says. "It does exactly what general relativity says it should do, if it has negative pressure."
• Trimble has a fairly simple way of imagining the phenomenon.
• "If you think in terms of the universe as a very large balloon," she says, "when the balloon expands, that makes the local density of the [dark energy] smaller, and so the balloon expands some more, because it exerts negative pressure. While its inside the balloon its trying to pull the balloon back together again, and the lower the density of it there is, the less it can pull back, and the more it expands. This is what happens in the expanding universe."

http://www.space.com/scienceastronomy/astronomy/cosmic_darknrg_020115-1.html

Despite this explanation, I don't understand why positive pressure in a gas (which represents kinetic energy) causes "true" gravitation, but negative pressure in a gases does not cause "true" anti-gravitation. That's the crux of the issue.

By the way, while I was hunting around for explanations for dark energy, I found the following article. It presents an interesting theory that the expansion of space is NOT smooth at small scales (remember my D'oh theory?), and that if there is enough differential in expansion rates at small scales, the acceleration of expansion can be explained entirely without need to resort to dark energy! Of course, the article also points out that there are good reasons to be skeptical of this theory.

http://space.newscientist.com/article/dn11498-is-dark-energy-an-illusion.html

Hi Jon, thanks, I hope I'm right on the energy scales. A little more on it down below.

Sorry about the problem with the graphs covering the text sometimes. It does not show up on my laptop, but I use a fairly wide screen and only a narrow 'favorites' column on the left. Try making your viewing area larger. I've started to write the text next to the pictures to save scrolling up and down when reading the text with the graph. Perhaps not such a good idea...

You asked: "What I have read is that dark energy adds "negative pressure" which acts as anti-gravity. If negative potential energy were added, doesn't that imply that the universe must contract, so that the total potential energy of gravitation in the universe shrinks?"

Yep, if you were to add only (negative) potential energy, the expansion rate would slow down. Not so if you add an equal amount of positive kinetic energy to balance out the negative potential energy, which is what the Λ in the flat ΛCDM model requires. The potential energy of the observable ΛCDM universe can be written (from the Friedmann equation) as:

Ep → -M(Ω_m/a + Ω_r/a²+a²Ω_v), with the '→' here meaning 'proportional', M is the observable rest-mass-energy (density x volume) and a the time-varying expansion factor. The equivalent kinetic energy can be written as:

Ek → M(dR/dt)², where R is the time varying radius of the observable universe. If used with a flat ΛCDM expansion curve and the right constants of proportionality, then E= Ep + Ek = 0, or simply Ek = -Ep at all times. If you add any form of positive energy density inside the bracket of Ep, then Ek must go up by an equal amount that Ep goes negative. IMO, this is the easiest way to comprehend the complexity.

The fundamental mechanism of the accelerated expansion is through negative pressure, which is not quite the same as energy, but can be converted into it in a non-linear fashion. This is probably the reasoning behind Wikipedia's statement: "The gravitational repulsive effect of dark energy's negative pressure is greater than the gravitational attraction caused by the energy itself. At the cosmological scale, it also overwhelms all other forms of gravitational attraction, resulting in the accelerating expansion of the universe."

I think that Virginia Trimble's balloon analogy is quite misleading in this respect. She said: "... when the balloon expands, that makes the local density of the [dark energy] smaller, and so the balloon expands some more, because it exerts negative pressure. While its inside the balloon its trying to pull the balloon back together again, and the lower the density of it there is, the less it can pull back, and the more it expands." [Bolding for emphasis is mine, not hers]. It is for reasons like this 'confusion' that I dislike the balloon analogy in the dark energy context.

The believe (since Einstein's time) is that the vacuum (dark) energy density is constant, so there is more negative pressure as the universe expands, but also more gravitational pull created by it. However, the negative pressure wins out and the acceleration tends towards the positive side as time goes on.

You wrote: "Despite this explanation, I don't understand why positive pressure in a gas (which represents kinetic energy) causes "true" gravitation, but negative pressure in a gases does not cause "true" anti-gravitation. That's the crux of the issue."

I've long stopped thinking in terms of pressure (which is just a component of energy) that tends to confuse the cosmological issues. I take the Friedmann equation literally, because it is after all an exact solution to Einstein's field equations for the case of a homogeneous universe at the large scale. Talking of that - I've noticed Rasesan's claims, but find his view a bit hard to swallow:

"Rasanen counters that 3D maps of galaxies, such as the 2-degree Field Galaxy Redshift Survey, show differences much closer to the minimum 20% level needed to account for the cosmic acceleration."

I'm not confident that he calculated the density distributions correctly - it's not simple from the redshift surveys. I believe it is much closer to the 0.001% level that Niayesh Afshordi mentioned and it is unlikely (but not impossible) that the bulk of the scientists could be out by so many orders of magnitude.

Jorrie

Hi again John.

Oops, the system inadvertently posted a reply just as I was starting to type it.

Since it only allows 15 minutes to edit a reply, and you can't delete a blunder like that, I've decided to do a quick edit and then post a proper reply below.

Jorrie

Hi Jon. Here's what I wanted to say as clarification.

In #84 and #85 you asked: "What I have read is that dark energy adds "negative pressure" which acts as anti-gravity. If negative potential energy were added, doesn't that imply that the universe must contract, so that the total potential energy of gravitation in the universe shrinks?" and I replied:

"Yep, if you were to add only (negative) potential energy, the expansion rate would slow down...." Although this is essentially true, one must tread carefully with such a statement.

It only applies if you get some ordinary energy density (not dark energy) from somewhere and dump it evenly throughout the cosmos today, without changing the expansion rate to suit a flat cosmos (i.e. it becomes closed). The rate of acceleration will decrease immediately and hence one can say that the expansion rate will become less than what it would have been without that extra energy-density.

Jorrie

Hi Jorrie.

As a thought experiment, let me suggest that, on the contrary, as the ongoing creation of new vacuum inherently creates new kinetic energy, it simultaneously also creates new positive potential energy, not negative. That way, it can serve an interesting function:

One could paint this order of events:

1. The first precipitation of quantum matter/radiation out of the vacuum drove the universe out of equilibrium. It was out of equilibrium either in the sense that there was a positive kinetic energy and no offsetting negative potential energy, or because there was offsetting negative potential energy, and the universe isn't stable having a net-negative potential energy.
2. The universe tried to restore equilibrium by commencing inflation to create some positive potential energy. Since the universe was very dense with astronomically hot matter/radiation at the time, the rate of inflation was explosively fast -- nearly an infinite rate. (Despite being very fast, the rate of inflation followed Einstein-de Sitter curve, but it was an increasing rate of inflation because new matter/radiation continued to precipitate out of the vacuum).
3. As the universe rapidly inflated, the rate of precipitation of additional new matter/radiation soon fell behind the rate of inflation, causing the temperature to drop below a threshold such that it was no longer possible for net new matter/radiation to form. At that point, as overall density had fallen by a lot, the rate of inflation lost momentum, and we entered the post-inflation epoch with a rate of expansion that would naturally decline over time at the Einstein-de Sitter rate.
4. Because of the Conservation of Flatness Law, the universe was incapable of directly imparting an expansion rate that was faster than the Einstein-de Sitter rate. Even if the universe expanded infinitely at this rate, it could never make any headway towards correcting the accumulated potential energy deficit. Therefore, it was inevitable that all of the vacuum created by inflation and subsequent expansion would have an added cosmological constant, which eventually would enable the potential energy equilibrium to be restored through an excess expansion rate above the Einstein-de Sitter rate. (Another way of saying this is that the cosmological constant represents what happens to quantum vacuum when its potential energy account is overdrawn).
5. At such time as the potential energy equilibrium eventually becomes restored (or perhaps becomes mathematically capable of being restored in the infinite future as the universe expands infinitely), the cosmological constant will drop to zero, and the rate of expansion will begin to fade towards the normal Einstein-de Sitter curve.
6. The combination of the momentum of expansion and the accumulated volume of vacuum carrying positive cosmological constant might temporarily drive the universe slightly past the equilibrium point. This could lead to a series of oscillations where the cosmological constant swings between positive and negative, trying to reach exact equilibrium. But the cosmological constant approaches zero over time.

Can't we easily calculate how much time the universe would require to reach equilibrium at the current rate, such that the total amount of positive potential energy accumulated since the big bang exactly equals the total kinetic energy (or is it rest mass?) of the universe? (Ignoring the possibility of oscillations).

A couple of additional points on this thought experiment:

Although kinetic energy has a significant effect on the early shape of the expansion curve, I think that rest mass is a better metric for measuring the universe's accumulated deficit of potential energy. This is because, as your chart shows, even without a cosmological constant total kinetic energy approaches total rest mass over time. In other words, because of redshift, radiation energy is able on its own to partially "repay" its potential energy deficit, but only down to the level of its own rest mass.

Your chart shows that total rest mass started out at about 10⁹⁵ joules, but radiation subsequently "repaid" a lot of that, such that at present the accumulated potential energy deficit is only about 10⁷⁰ joules. So that is the amount that the cosmological constant still needs to repay.

The irony of the cosmological constant is that over time, as shown by your chart, the newly created vacuum adds an enormous amount of new rest mass to the universe, which might be expected to increase the potential energy deficit. But the opposite is what actually results, and the deficit will eventually decrease to zero. This is because we postulate that the cosmological constant also contributes (at least for now) positive potential energy to the universe, at a far higher rate than the new rest mass it contributes.

Hi Jon.

I'm still struggling to verify the validity of my graphs by using the physics forums that I know. As you probably know, physicists are generally not very keen to get involved in anything that looks slightly 'out of line' and it is hard for engineers to communicate with them.

What I've learned so far is that they do not like the term 'rest mass' for the universe and call it 'meaningless'. They also do not talk of potential energy of the cosmos, but rather the 'gravitational binding energy', which is not quite the same as potential energy.

Lastly, they say that one cannot use Newtonian binding energy to calculate the cosmos, you need general relativity (gr), but then, gr does not apply to the cosmos as a whole! And I seem unable to get them to think of just a piece of cosmos, the piece we call the observable universe.

All very confusing! Until I've cleared up this mess conceptually, I'll probably not have the energy to reply to your 'thought experiment' properly. But I promise I will!

Jorrie

Hmmm, how distressing to hear that physicists are even crankier than engineers!

I don't see what all the fuss is about. According to Wikipedia, "The gravitational binding energy of a system is equal to the negative of the gravitational potential energy."

The formula for calculating both of them is the same, except that in the case of potential energy, the equation has a negative sign. For gravitational potential energy:

• For a spherical mass of uniform density, the gravitational binding energy U is given by the formula^[1][2]
• 
• where G is the gravitational constant, M is the mass of the sphere, and r is its radius.

And for gravitational potential energy: "[-U] as calculated above measures the potential energy of the whole system. This can be visualised as if two bodies in space were released from rest and allowed to come together under the force of gravity. The sum of the kinetic energy gained by the two objects is exactly equal to the decrease in the potential energy of the system."

So I suppose that the absolute value of both the gravitational binding force and the potential energy of the universe at any given time would be equal to the amount of kinetic energy that would be released if expansion of the universe were magically brought to a halt, and the universe were allowed to collapse entirely.

However, this seems meaningless, because a considerable additional "force" would be required to counteract the rate of expansion and thereby enable gravitational collapse of all that matter. It could be thought of either as collapsing by gravitational attraction "through space", or (symmetrical to the expansion), contracting by "annihilating" all of the intervening vacuum.

On the surface, it might seem that gravitational binding energy inherently is reduced, and the total potential energy is increased, by the expansion of space itself. That is, as r increases indefinitely, the masses continue to become more distant from each other, and gravitational binding energy decreases. But I would argue that this isn't so, and that the expansion itself (at the Einstein-de Sitter rate) contributes zero gravitational binding energy and zero potential energy.

This can be demonstrated in conventional Newtonian terms. I.e., what is the gravitational [self-]binding energy of a system comprised of two masses, where they have a pre-existing momentum away from each other at exactly their escape velocities? I would submit that the answer is zero. I would further submit that such a system experiences no gain in potential energy as the distance between the masses increases.

In that spirit, the hypothetical "force of expansion" should be ignored entirely, since it's not physically "pushing" on anything, and (ignoring the cosmological constant for the moment) it's not changing either the absolute amount or the relative proportions of gravitational binding force and gravitational potential energy in the universe.

Hi Jon.

You wrote: "I don't see what all the fuss is about. According to Wikipedia, "The gravitational binding energy of a system is equal to the negative of the gravitational potential energy." "

I know about this one, but that's a pure Newtonian definition, which probably does not apply to the whole of the history of the cosmos. Energies and velocities and pressures were probably outside of the Newtonian regime.

I've tried a more relativistic 'Friedmann' route and also got unstuck, because Einstein's general relativity also refuses to get drawn into cosmic scale energies...

Your "I.e., what is the gravitational [self-]binding energy of a system comprised of two masses, where they have a pre-existing momentum away from each other at exactly their escape velocities? I would submit that the answer is zero." seems very strange to me.

In a Newtonian sense, it is the potential- plus kinetic-energy that is zero, not the gravitational binding energy, which only becomes zero at an infinite separation between the two bodies.

I'm posting the Blog entry on the energies tomorrow (15th) and will hopefully have more time to respond to discussions after that!

Jorrie

Jorrie,

On further thought, I agree with you that the gravitational self-binding energy of two masses moving apart at escape velocity is not zero. Momentum and velocity are separate from binding energy. Self-binding energy remains the same regardless of the momentum and velocity of the two masses.

So OK, gravitational self-binding energy does decrease, and potential energy does increase, as the universe expands. But it seems to me that it becomes a simple exchange, where the former decreases and the latter increases in equal amounts. As the radius of the universe increases towards infinity, the velocity of expansion drops towards zero. The gravitational self-binding energy also drops towards zero. The potential energy growth flattens out and almost stops, and remains finite, equal to what the original self-binding energy was before expansion began (but with opposite sign).

The bottom line is that gravitational self-binding energy and potential energy always add up to zero, so in that respect the expansion of the universe neither adds nor subtracts energy from the system.

Jorrie,

Further to my earlier post today:

"The bottom line is that gravitational self-binding energy and potential energy always add up to zero, so in that respect the expansion of the universe neither adds nor subtracts energy from the system."

The only net energy that I can see which is either gained or lost by the system is the loss of kinetic energy due to the redshift of radiation. In my opinion, this redshift loss does not contribute any potential energy to the total system. For example, it does not speed up the rate of expansion. It just disappears.

So where is this lost kinetic energy going? It makes sense to me that it is going back into the "quantum sea", to partially pay back the deficit of potential energy borrowed when matter and radiation originally precipitated out of the quantum sea during inflation. But the energy represented by the rest mass of all the matter/radiation in the universe could not be repaid this way, and the deficit is still outstanding.

I need to slightly modify the description of my thought experiment. Inflation and "normal" expansion (Einstein de Sitter rate) was not caused in any sense by the universe's need to restore a zero total energy balance, because it could not help achieve that goal. As I pointed out above, the only consequence of the normal expansion of space is to convert the gravitational self-binding energy of the universe into an equal amount of potential energy. That doesn't change the total amount of energy in the universe. So, the only reason for both inflation and the normal expansion of space was to maintain the geometric flatness of the universe.

As I posited in my thought experiment, the cosmological constant must be the alternative mechanism that the universe is using to restore the universe's energy balance. Thus, over time, total (rest mass energy + kinetic energy + gravitational self-binding energy) must = total (potential energy created by normal expansion) + (potential energy created by the cosmological constant). Since gravitational self-binding energy and kinetic energy are already dropping out of the equation due to the "normal" expansion rate, over time the equation will approach (rest mass energy) = (potential energy created by the cosmological constant).

Hi again Jon.

Our lengthy dialogue has prompted me to keep on pondering how much of the energy the false vacuum has been 'dumped' into matter and radiation energy at the end of inflation.

My preliminary results come from the spreadsheet that I used to calculate the rest energy and the kinetic energy of expansion (according to the ΛCDM model) since inflation. The graphs shown here portray a sobering picture.

At log(t) ~ -40, directly after inflation, the kinetic energy outstripped the rest energy by a factor ~10³². This means that an extremely tiny portion of the energy of the false vacuum has been converted into radiation and matter. The rest remained as an enormous kinetic expansion energy.

If there were no radiation and matter converted, it would have made very little difference to the cosmos at large, but then there would have been nothing but energy, and no 'us'. So is the material cosmos only an aberration? Taken to the limit, are 'we' just an aberration?

Jorrie

Jorrie, I don't want to make demands on your time, but...

It would help if you put labels on this chart showing various time events, such as you have on Fig. 15.4 in your ebook, and maybe use a positive-only time axis running from 0 to 70.

Somehow it seems odd to me that there were points in time when the universe's kinetic energy were below its rest mass. I can grasp the opposite case, where the excess kinetic energy has a physical manifestation as heat. What is the physical manifestation of a relative deficit of heat?

At what temperature does rest mass exactly equal kinetic energy? Since the kinetic energy never dropped to zero, the temperature apparently always remained well above absolute zero.

Regarding your question about matter being an aberration -- I don't think so, because as I understand it, stable matter was required to "freeze" out of the vacuum as the temperature dropped through a certain absolute threshold during inflation, leaving a hot dense "quark-gluon plasma" of particles and anti-particles behind.

Even though Conservation of Flatness didn't specifically require matter in the mix, it was inevitable that matter would form anyway, given the ambient conditions.

Also, matter isn't unique in the sense that if any of the various forms of energy didn't exist as they did, the universe as we know it would not exist.

Hi Jon, thanks for your suggestions and pointing out a flaw! I include some crude markers in the updated graphs.

You said: "Somehow it seems odd to me that there were points in time when the universe's kinetic energy were below its rest mass."

Kinetic energy can be less than rest energy for slow moving masses, but when I looked again at the spreadsheet, I noticed that the recession rate of the radius of the observable universe always exceeded c. This rang an alarm bell.

Looking at the spreadsheet, I realized there was a factor c² missing in the constants of proportionality for the potential energy, making the units not Joules. Fixing that, the rest and kinetic energy curves look like below.

Figure 1:

The kinetic energy curve comes from varying a form 0 to any positive value and calculating both t and Ek for every a, where:

Ek = -Ep = Erest Ho² Ro² (Ω_m/a + Ω_r/a²+a²Ω_v) Joule,

where Erest is the time varying critical rest energy of the observable universe in Joule (i.e., energy to have the critical energy density required for Ω=1), Ho is the present normalized Hubble constant, Ro the present co-moving radius of the observable universe. The product Ho Ro is dimensionless and so are all the remaining parameters.

If I'm now correct, the fractional false vacuum energy that went into radiation and particles drops to the the incredibly low value of 1 part in 10⁴⁹. Speaking of negligible...

With all the lessons learned out of our discussion, which is 'hidden' so way beyond the forum 'horizon', I suspect very few noticed. I'll summarize the salient point in a new Blog entry so that we can get more inputs from 'outside'.

With this in mind, I will not immediately respond to your reply #89, which is a little bit of 'alternative theory', by the looks if it. Will look at it in detail later...

Jorrie

Jorrie,

How can Erest be "time variable"? I thought that the rest mass and rest energy are always constant in Einstein's theory.

SL

Hi SL, not logged in?

Only if the universe had only non-relativistic matter inside it could the rest energy have remained roughly constant over time. If you look at the blue Erest curve, you will see that during the matter dominated epoch, ~5 < log(t) < ~10, or roughly from 1 million years to 5 billion years, the blue curve runs horizontal, meaning constant energy.

Before the matter-epoch, radiation dominated and it loses energy due to the redshift. After the matter-epoch, vacuum energy dominated and it grows with the expansion of the vacuum.

So in general, Erest of the cosmos is time varying. One must also realize that 'constant rest energy' is just an idealization for theoretical purposes. If a mass absorbs radiation and gets warmer, or radiates and gets colder, its rest energy also changes.

Recall the teaser: "Why is a wound clock heavier than an unwound one?" Because winding it has added energy to the clock and through E=mc², it has more rest mass and is hence heavier.

Jorrie

Loved the teaser. Never heard of it.

Hi again, Jon.

Further to my post #67, I am still working on the possibility of some 'reserved' energy during the end of inflation, but I find it very difficult.

Towards that end, one cannot know the total energy of the universe, but one can at least make an estimate of the total energy in our observable universe. In proper distance it has a radius of some 46 Gly or a volume of ~400,000 Gly³. This translates to the order of 10⁸⁰ cubic meters. With the total density of ~10^-26 kg/m³, the total rest mass-energy of the observable universe is then ~10⁵⁴ kg, or ~10⁷¹ Joule today.

I found a good fit for the volume of the observable universe just after inflation of about 45 cubic meters, giving a volume expansion of ~10⁷⁸ times since inflation (not quite the 10⁸⁰ that I posted last time). Interestingly (almost absurdly), the total rest mass-energy was ~10⁷⁶ kg, or ~10⁹³ just after inflation, 10²² times the total rest energy today!

What happened to the 'missing' rest energy? The secret lies in the radiation energy being redshifted away. Radiation made up almost all of the total energy after inflation. At the time of 'last scattering', the CMB time, that radiation energy was redshifted to less than a third of the matter energy, which was then already the dominant form.

The kinetic energy of expansion is not so easy to calculate, because the horizon of our observable universe has moved away from us at an average of ~3 times the speed of light. Just after inflation, that rate was at least 10²⁵c. How do we calculate a kinetic energy with those rates? I haven't got a clue at present, but still working...

Jorrie

My, my. I'm gone for a few days and I come back to find an open can of worms. Thank you Jon for your insightful and intricate attempt to defend my radical, albeit drug-induced, theory. I'm nowhere near either of you guys as far as justifying these concepts using current theory, I just read and wonder. (Jorrie, you may remember my push-a-stick faster than light theory from a few months ago)

Well, as far as crackpot theories go, this makes as much sense to me as what's currently out there. Since some past crackpot theories have become vogue as new information becomes available, I propose to immediately take credit and lay claim to "The Guitarhunter/Jonmtkisco Incredible Shrinking Matter Theory."

Thanks guys for all your insight and interest in this new and brilliant theory.

Oh, and I once saw Bigfoot. Tom C.

Thanks for the support guitarhunter. There is lots of history for the idea that drugs can spur creativity. Some good, some not so good!

I want to reiterate that upon further reflection I don't consider the Shrinking Matter model as a theory of the cosmos at all. I am proposing no changes in the underlying physics of the cosmos. Instead, I'm defining one among many possible coordinate systems that could be used to measure cosmic events. In this system the "fixed" coordinates are defined to exactly co-move with the expansion of space.

In that spirit, I propose naming this the "Expansion Co-moving Coordinates" system, or E.C.C.

Hi Jon, you wrote: "In this system the "fixed" coordinates are defined to exactly co-move with the expansion of space."

This is exactly what cosmologists use - they call it co-moving coordinates and measure distance in Mpc. The difference to your view is that nothing shrinks. At short distance co-moving coordinates are equivalent to light-travel distance (in light-years). Only at long ranges, where expansion becomes noticeable, does it differ from light-travel distance.

This is exactly the flaw in your reasoning. I suggest you read The Infinite Lattice in a previous post and perhaps this pdf download from my website. It should clear your mind from the problem.

Jorrie

Jorrie, thanks for the explanation. I think your Escher-lattice model is very helpful in visualizing the kind of co-moving coordinates that cosmologists use. I feel that what I'm saying is logically consistent with it. It's just a change in perspective. I still don't see why a change in perspective must be characterized as a "flaw".

In terms of the lattice model, I'm suggesting that, in ECC metrics, as the blue bars lengthen (spatial expansion), we will contract the relative size of the red boxes accordingly, such that the total size of the lattice remains fixed. In ECC metrics, I don't think the red boxes will all contract at equal rates. The rate of contraction of each red box will be a function of how much mass it contains -- the more mass, the more rapid the contraction. Red boxes containing no mass (and minimal radiation beyond the CMB, etc.) will experience near-zero contraction.

Rolling time backwards towards a time shortly after the big bang, the red boxes (especially the mass-bearing ones) will displace virtually the entire lattice, as the lengths of the blue rods approach zero. Again, the total "exterior" size of the lattice remains fixed.

If all of the blue bars have equal length at any point in time, this exercise obviously results in substantial local distortion of the lattice as we roll the time "movie" forwards and backwards. The purpose of looking at it this way is to see whether it can illuminate any relationships that are less apparent in traditional "symmetrical latice" metrics. For example, it seems like the local distortion must inevitably twist the angles formed by the most or all of the blue bars in various directions over time.

Hi Jon. You wrote: "I think your Escher-lattice model is very helpful in visualizing the kind of co-moving coordinates that cosmologists use. I feel that what I'm saying is logically consistent with it."

No it is not.

In the linearly expanding 'Escher lattice' below, our measured redshift of every red cube (galaxy) increases linearly with the number of blue bars between us and the galaxy (i.e., redshift increases linearly with the comoving distance of the galaxy). This is because every bar expands (in length only) with the same percentage in the same time interval.

Escher Lattice

In the real universe, the expansion rate of every bar varies over time, but the expansion rates of all the bars are the same at any given cosmological time.

Now hold the length of the blue bars constant and let all the red cubes shrink at the same rate (more or less your ECC model). I challenge you to show how this scenario can produce the linear redshift-comoving distance relationship.

Jorrie

OK, I can see we are starting to bore your target audience with this "inane" discussion of the ECC model.

Jorrie, you said: "I challenge you to show how this scenario can produce the linear redshift-comoving distance relationship."

As I tried to explain previously, observers on any red box will be shrinking relatively (not necessarily absolutely) compared to the length of the blue bars. The observers' "measuring sticks" will shrink proportionally. The longer the distance that light from an observed distant red box has been travelling, the more the measuring sticks on the observers' red box will have shrunk by the time the light arrives. This will be observed as redshift increasing as a function of distance.

Jorrie, I'm not trying to debate whether matter is actually shrinking as opposed to space expanding. All I'm saying is that it is obviously very straightforward to perform a mathematical transformation whereby a variable (spatial expansion) is fixed as a constant, and a constant (size of matter) is allowed to change as a variable. It's not "rocket science". All of the normal equations of cosmological science should work the same way they did before, once they are converted to ECC metrics.

It's just a matter of perspective, and I hope it might be a useful perspective.

Jon

I know that I've made too many entries already, but I had a new thought that I felt was interesting enough to pass on.

I defined the ECC metrics to keep the total size (volume) of the universe fixed as a constant over time. This results in the size of matter being a declining variable over time. However, it occurs to me that even when using ECC this way, the blue bars will still increase in length over time, reflecting that fact that more empty space must be created to "backfill" for the (relatively) shrinking matter.

At a time shortly after the Big Bang, a very high percentage of the universe must have been filled with massive particles, leaving corresponding little room for empty vacuum. At some future time, matter will have become an infintesimally small percentage of the volume of the universe.

Looking at this with ECC metrics, the total amount of matter, v(m), at t(initial) = the amount of vacuum (dark energy), v(de), at some t(future).

This then allows for the possibility of a one-for-one conversion over time of each physical quantum of matter into the same sized quantum of vacuum filled with dark energy. One could speculate that instead of dark energy appearing spontaneously from the void through vacuum quantum fluctuations, maybe it is a direct quantum remnant of the matter that preceeded it in the same physical volume.

Hi Jon.

OK, I'll accept that one can convert from the standard metric to yours without changing anything, but I'll be hesitant to then draw conclusions from the latter that makes no sense in the former - after all, they should be exactly equivalent.

An example is your: "This then allows for the possibility of a one-for-one conversion over time of each physical quantum of matter into the same sized quantum of vacuum filled with dark energy".

This does not match the standard model, where vacuum energy quanta is constantly increasing while matter energy quanta remains constant. Your 'inversion' should then be stated: vacuum energy quanta remains constant while matter energy quanta are on the decline.

Starting to sound very meta-physical.

Jorrie

I agree with your qualification on accepting the new metric.

I'm not entirely sure about your second point. With respect to vacuum energy, I agree that the negative pressure quanta should remain constant, or not exist at all, because there is no need for increasing total negative pressure as the mechansim to drive spatial expansion. The attribution of negative pressure to dark energy in the standard model seems like an ad hoc explanation for expansion rather rather than something required by first principles. So I'd suggest that in ECC metrics, the postulated negative pressure of dark energy be dropped entirely for the sake of simplicity.

On the other hand, don't we need the "new" vacuum that "backfills" the disappearing matter in ECC metrics to have a positive energy density? I thought that was necessary in order for the geometry of space to remain flat. The critical density needs to add up to 1.

I'm not sure if your suggested formulation means that the total quanta of vacuum energy in the universe remains constant, or alternatively, that the vacuum energy of each individual quantum of space remains constant. I think that the latter formulation keeps total energy density of the universe appropriately constant (exactly offsetting the declining matter energy), while the former formulation does not.

It also seems satisfying that in the ECC metric, it could be postulated that each quantum of matter converts directly into one quantum of dark energy at some point in time, while the energy density of each such quantum is conserved.

On another tangent... I wonder if, in the ECC metric, gravitation could play the role of an artifact of, a mediator of, or even a catalyst for, the conversion of mass into dark energy.

Gentlemen

While reading the mind-stretching banter is interesting on a certain level, it seems to be lacking merit considering this:

What if some of this mental energy were applied to everyday problems for everyday people who need a little direction?

I am certainly NOT saying fore go all "brain pursuits" and feed the homeless, but a little goes a long way in helping a neighbor build a better life for themselves. Another benefit, at least for me, I get more satisfaction helping my neighbor!

Guest is right. All this reading and thinking I'm doing here is keeping me from doing drugs, thereby increasing the supply of drugs available to school children. Just think of the lives Elvis saved by personally keeping available supplies low.

Matter shrinks. That's my story and I'm sticking with it.

Hey Jon, why not post our theory as a CR4 question and open this up? It'll be big.

How do you post a CR4 question?

Hi Jon. "How do you post a CR4 question?"

Look just below your member name, near top right in this window.

Jorrie

The best models say those sources were only meters apart then, but today they are around 90 billion light years (ly) apart, 45 billion ly each way, with us in the center.

I continue to see that it is accepted that we are at the center of the Universe. That concept brings so many profound questions to mind my feeble mind does not know where to begin. I will ask 2 questions

1. What is the determining factor to regard us being at the center.

2. Is this not a mathematical improbability, or at least a very egocentric (no pun) idea; that we are at the center of this vast expanse of Universe? (this is not a loaded question, that is to say it is free of philosophical underpinnings. For now.)

with regards,

cr3