Jorrie,

Over the past week I've done a lot of calculations to try to demonstrate that there is no need for a cosmological constant to explain the expansion rate and accelerated expansion of the universe. I hoped to find that increased "clumping" of matter over time could explain the acceleration. But for better or worse, no matter at what level I tested the amount of clumping (atoms, stars, galaxies, clusters, superclusters), none generates enough expansion to match the observed rate. The supercluster level comes closest, producing about 1/30th of the necessary expansion rate. Smaller levels of clumping are orders of magnitude more short of the mark.

So reluctantly I'll accept the need for the cosmological constant.

Accordingly, here is a revised "Flatness Theorem":

1. Theorem 1: The geometry of the universe is perpetually flat.
2. The universe has been characterized by an interaction horizon since early on, so unless the universe was always flat, it is almost infinitely improbable that any fortuitous combination of circumstances could account for the degree of isotropic flatness we observe today. Therefore, the universe must always have been flat, and by extension it always will remain incapable of diverging from flatness.
3. Theorem 2: Rest Mass preserves flatness by causing expansion.
4. The rest mass (or static energy) of matter and radiation expresses gravitation, which causes curvature of space. This curvature must be offset in order to maintain flatness. Vacuum expansion is the mechanism that maintains flatness.
5. Theorem 3: Space reacts to the presence of static energy by spontaneously producing new vacuum space.
6. Every Kg of mass causes local space to spontaneously "produce" (whatever that means) new vacuum space. In total across the observable universe, this new vacuum space is produced at a rate equal to the "escape velocity" of the universe. I calculate that new vacuum volume presently is being created at the rate of about 2x10⁶³ cubic meters per second.
7. Theorem 4: The cosmological constant = the rest mass of vacuum.
8. A cosmological constant is needed to explain the high observed production rate of new vacuum. For example, I calculate that the sum of the rest masses of the estimated 10 billion galactic superclusters accounts for the production of a mere 6.3x10⁶¹ cubic meters of new vacuum per second.
9. The vacuum of the present universe alone (without including any matter or radiation) in aggregate posseses the correct mass to account for the full vacuum production rate of 2x10⁶³ cubic meters per second.
10. Given that the vacuum mass alone accounts for the accelerating expansion rate, there is no need to attribute special characteristics to the vacuum, such as "dark energy" or "negative pressure."
11. I propose (but haven't tried to calculate) that vacuum mass is simply the "average" mass of the virtual particles which continuously pop into the universe via quantum pair production, multiplied each particle's (very short) average lifetime before annihilation.
12. Theorem 5: The Flatness Theorem provides a consistent model for inflation, expansion, and accelerated expansion.
13. Inflation is just a name given to an (arbitrarily) brief initial period of hyper-expansion prompted by the precipitation of mass into the universe via quantum fluctuations. The expansion rate tracked the astronomically high vacuum production rate needed to maintain flatness at a time when all of the universe's mass was compacted into a microscopically tiny volume.

Jorrie, I would appreciate if you could help me calculate one thing: What was the volume or radius of the universe at the inflection point when the aggregate vacuum mass exactly equaled the aggregate rest mass of matter?

I couldn't find "quantum pair production" in wikipedia. Could you please direct me to a definition.

Sure, try this on "Pair Production:

http://en.wikipedia.org/wiki/Pair_production

And:

http://en.wikipedia.org/wiki/Electron-positron_annihilation

Hi Jon.

Yep, this is much closer to accepted theory now. There are a few aspects that may be very debatable, but I'll leave that to other contributors for now.

"... help me calculate one thing: What was the volume or radius of the universe at the inflection point when the aggregate vacuum mass exactly equaled the aggregate rest mass of matter?"

It's easy from the Friedmann equation, because per your requirement, it must be when Ω_m/a³ = Ω_v.

For Ω_m= 0.27 and Ω_v=0.73, this gives a~0.718. Multiply by the comoving radius of the observable universe (about 46 Gly) and you get ~33 Gly radius. This corresponds to about 9.45 Gy age, which one can only get from an integration of the Friedmann energy equation (what my spreadsheet does).

Jorrie

Thanks Jorrie.

You said: Ω_m= 0.27 and Ω_v=0.73. So the equation uses today's ratio, not the Ω_m= 0.5 and Ω_v=0.5 that would have been the ratio .55B years ago?

Hi Jon.

"So the equation uses today's ratio, not the Ω_m= 0.5 and Ω_v=0.5 that would have been the ratio ?"

Yep, that's how those Ωs are defined: today's actual densities as a fraction of today's critical density. (But where did you get ".55B years ago" from?)

The denominators (aⁿ) in the Friedmann equation sort out the epoch dependencies - how else?

Note that I have included the curvature term (first one under the √), to sort out things when today's Ωs do not add up to unity (open or closed universe). In the flat case, that term becomes zero of course.

Jorrie

Hi Jorrie,

Sorry, I meant 0.425Gy ago...

I built a spreadsheet for the Flatness Theorem. I adjusted the volume ratio between superclusters and voids to 0.07, which made their new vacuum production rates add up properly to the total new vacuum production rate of the universe. With the adjusted numbers, superclusters presently produce 0.13133 of the total new vacuum production rate, and vacuum mass produces the rest.

The good news is that the spreadsheet also works well with the universe at the age of .945Gy, the inflection point you calculated Jorrie. I am fairly confident that the spreadsheet will work at any point in the history of the universe, including during inflation. Obviously the average volume of superclusters will need to be adjusted smaller starting at some point in the distant past, but I'm not aware of any formula for doing so. I guess I can calculate it backwards from the spreadsheet.

Hi Jon.

"Sorry, I meant 0.425Gy ago..." and "...the spreadsheet also works well with the universe at the age of .945Gy, the inflection point you calculated ... "

I guess these are just typos. My post gave an age of 9.45Gy for matter-vacuum energy density equality, which is about 4.25Gy ago.

Jorrie

Hi Jorrie

Yes, typos. Your decimal places are correct.

I did some more adjusting. At the present, the volume ratio between superclusters and voids needs to be .09, and superclusters produce .166 of the total vacuum production.

At 9.45GY, superclusters produce .348 of the total.

Hi Jon, you wrote: "At the present, the volume ratio between superclusters and voids needs to be .09, and superclusters produce .166 of the total vacuum production."

I'm not sure what these figure of yours mean. It is hard to find the ratio between supercluster volume to void volume. Using a rough guess that our Virgo supercluster is about average in size and then taking Astronomy Answers values:

In a radius of ~400Mpc, there are 130 superclusters, with Virgo's volume 1.2 x 10⁴ Mpc³. If I work out the volume of 130 such superclusters as a fraction of the 400Mpc radius volume (2.7 x 10⁸), I get ~0.006 to 1.

So the total supercluster volume may be around 0.6% of the total volume of the observable universe.

Jorrie

Hi Jorrie:

According to Wikipedia: "... the total number of super clusters in the universe is believed to be close to 10 million." http://en.wikipedia.org/wiki/Supercluster

In the same article:

"... superclusters are now understood to be subordinate to enormous walls or sheets, sometimes called "super cluster complexes", that can span a billion light-years in length, more than 5% of the observable universe. Super clusters themselves can span several hundred million light-years."

In my calculations, I use the term "supercluster" to mean all of the coherent mass structures that aren't voids. That includes sheetwalls and filaments. I run my calculations as if these "superclusters" are 10⁷ identical spheres, but of course that is only partially accurate. It's just the best I can do with the facts at hand.

Since Wikipedia indicates that voids contain around 10% of the matter of the universe, I assigned the other 90% to what I refer to as "superclusters". Wikipedia says that voids are thought to constitute 95-98% of the volume of the universe. However, it isn't clear whether that includes any of the sheet walls, filaments, isolated galaxies, and other assorted riff-raff. In any event, in my spreadsheet, the "best fit" I can achieve (which is very close), is putting "superclusters" at 91% of the matter and 9% of the volume. I am optimistic that my calculation helps to nail this ratio down.

You'll be happy to know that I got the Friedmann equation to work properly after you pointed out that the "scale factor" a = radius. For some reason I had thought it related to volume.

I'd like to now run my spreadsheet at the inflection point where Ω_m = Ω_r, which I understand is at about t=10⁵. Can you help me calculate the radius and age more accurately? My calculation yields a radius of 1.02x10³m, but I'm not confident I'm doing the math correctly.

Hi again Jon.

"In my calculations, I use the term "supercluster" to mean all of the coherent mass structures that aren't voids. That includes sheetwalls and filaments. I run my calculations as if these "superclusters" are 10⁷ identical spheres, ..."

I rather take a large sphere of known volume and try and 'count' the number of superclusters in order to calculate their total volume, as I referenced before.

"Since Wikipedia indicates that voids contain around 10% of the matter of the universe, I assigned the other 90% to what I refer to as "superclusters"."

I seem to recall that the 10% was the average matter density of the voids in relation to the overall matter density. If this is so, your assumption has no grounds - it also depends on the void:supercluster volume ratio. Also remember, that they talking matter density, including dark matter, but excluding vacuum energy.

"I'd like to now run my spreadsheet at the inflection point where Ω_m = Ω_r, which I understand is at about t=10⁵."

From a 'pedagogical pov', density parameter Ω_m cannot equal Ω_r, because they have fixed values. I suppose you are referring to real densities, i.e., the time when ρ_m = ρ_v. This is calculated just like the ρ_m = ρ_v case, only with Ω_m/a³ = Ω_r/a⁴ from the Friedmann equation.

With Ω_m = 0.27 and Ω_r = 8.35E-05, it gives a = 8.35E-05/0.27 ~ 3E-04, giving an epoch radius for the present observable universe of ~1.3E+23 m. My integration gives an age of the universe at that expansion factor of ~2.8E+04 year (T₀ + 28 thousand years).

Jorrie

Jorrie, thanks for the calculation. And for sending the spreadsheet. I'm happy to send you mine if you want it.

My spreadsheet assumes that vacuum mass (a term I prefer to vacuum energy) is spread evenly throughout the voids, at the normal density. I also assume that the matter found in voids is the same percentage of dark matter and baryonic matter as the universe as a whole. Not that it makes a difference for my purposes what kind of matter it is, since it all has the same mass. I'm calculating mass in Kg, not densities.

Here's an excerpt from an article about the Bootes Void. http://www.acceleratingfuture.com/michael/blog/?p=69

• It is known that about 98% of the volume of the universe is consumed by intergalactic voids. The universe is made up of superclusters forming thin "walls" around these huge voids, perhaps reminiscient of the way organisms consist of cells whose main density lies in walls enclosing cytoplasm. (But in contrast to the way that atoms' primary concentration of density is located in the nucleus.)
• Of course, certain things can be found within the void, mostly in the form of energy. The extragalactic background light (EBL) and cosmic microwave background radiation (CMB) fill up the void. Interestingly, there is no gap in the cosmic background radiation in the region of the void. The void almost certainly contains a lot of dark matter and energy, perhaps even at densities no different than those found within superclusters. This means that dark galaxies and dark energy stars can probably be found. And, of course, the void is filled with endless quantities of virtual particles, which are created and annihilated constantly on the smallest timescales.

I have another source that says voids comprise 95-98% of the universe, but I can't find it right now. Obviously there's got to be a wide margin of error. For example, are voids defined to include the vacuum of their boundary regions which are gravitationally bound to neighboring clusters? For my purposes, I think it makes sense to consider such bound vacuum regions to be part of the "superclusters" they are bound to. Thus increasing the supercluster-to-void ratio.

Hi Jon.

Pleasure and yes, I'll like to look at your spreadsheet. Since CR4 mail doesn't allow attachments, I think, I'll send you my personal email address in a CR4 mail.

I'll accept the 98% voids by volume for now. Sticking that into some calculations for the present observable universe of 46 Gly radius yielded this:

Vacuum mass-energy, spread evenly over whole observable universe: 2.5 x 10⁵⁴ kg

Matter mass-energy, 90% in superclusters and 10% in voids: 9.3 x 10⁵³ kg

Void mass energy = 98% x 2.5 x 10⁵⁴ kg + 10% x 9.3 x 10⁵³ kg = 2.54 x 10⁵⁴ kg.

Supercluster mass-energy = 2% x 2.5 x 10⁵⁴ kg + 90% x 9.3 x 10⁵³ kg = 8.87 x 10⁵³ kg.

This makes the voids weigh in at 65% and superclusters at 35% of total mass-energy. One can say roughly two thirds to voids and one third to superclusters.

Does this tally with your calcs in some way?

Jorrie

Jorrie, sorry for the delay in responding. As I tried to clean up my spreadsheet, I found that it no longer generates the results I had thought. In fact, I'm at the point of giving up on the idea that superclusters or any other discrete clumping of mass-energy can generate enough local escape velocity to make a significant contribution to the total expansion rate of the present universe.

There are multiple ways to calculate measurements for expansion driven by mass-energy. The method I selected is the simplest I could think of. At any instant in time, flatness requires that the universe is always expanding at the rate of its own "escape velocity", the Einstein-de Sitter curve. Of course, that becomes a self-reinforcing loop since the expansion creates more mass-energy in the form of vacuum mass-energy, which in turn drives more accelerated expansion. That's what I mean when I say that the Einstein-de Sitter curve keeps moving outwards (or upwards). And yes over time as you said it does come to approximate a pure de Sitter curve (insignificant matter and radiation content).

First I calculate the observable universe's escape velocity "from itself" using the formula V_esc = (2Gm/r)^1/2.

Then I calculate the incremental radius by which the universe expands in 1 second as being equal to its escape velocity (in m/s). I use the formula for approximating the volume of a "shell" around a sphere, which is 4πr² x (shell's radial thickness). I set the "shell's radial thickness" equal to 1 second's worth of expansion at the escape velocity. That yields the incremental volume of expansion in cubic meters per second.

By this means, I calculate that the universe presently is expanding at 2.49x10⁶³ m³/s. Like you, I calculated the combined mass of the voids at .1 of total matter + .98 of total vacuum mass-energy. I calculated the individual mass of each of 10⁷ superclusters at .9% of total mass + .02 of total vacuum mass-energy. I calculate the volume expansion caused by an individual supercluster, then multiply it by 10⁷ to total up all superclusters.

The expansion numbers I calculate are 2.12x10⁶³ m³/s for the voids and 1.78x10⁶² m³/s for the superclusters. Not enough to sum to the expansion rate of the universe as a whole. Morever, playing around with the spreadsheet tells me that adjusting the supercluster/void ratio won't solve the problem unless 90% of the matter is put into the voids -- which makes their density indistinguishable from the superclusters, obviously a useless scenario.

So now I'm trying a new tack. I think the Flatness Theorem still is useful even if expansion can be calculated only at the level of the total universe. So I'm creating a new spreadsheet for that, which I'll send to you when it's ready.

I've calculated that the expansion rate for the universe at 9.45Gy (the matter/vacuum inflection point) = 1.1x10⁶³ m³/s, and at 28,000 years (the radiation/matter inflection point) = 9.93x10⁵⁷ m³/s.

Hi Jon.

I think you do the volumetric expansion rate a bit wrong by means of your "shell method". The best is to simply take ΔVol= 4/3 Pi (R₂-R₁)³ and divide it by ΔTime. The present observable cosmos has a proper radius of ~4.35x10²⁶ and R is increasing at ~10⁹ m/s.

Remember that you can also not just stick 10⁹ m/s inside the brackets, because then you are dividing by time³. You have to calculate the real volume increase and then divide by time.

For the present observable universe I get a volumetric expansion rate of ~7x10⁷⁰ m³/s. Also check your 'inflection point' or rather 'energy equality' radii; I think they are similarly wrong.

Jorrie

Oops!

The formula ΔVol = 4/3 Pi (R₂-R₁)³ is wrong for similar reasons than what I mentioned above. Should read: ΔVol = 4/3 Pi (R₂³ - R₁³).

I think my results were right, because I did not use the offending formula.

Jorrie

Jorrie,

I can't use your ΔVol formula for calculations, because my spreadsheet doesn't support enough significant digits to yield a non-zero number in the parentheses.

So unless you have another suggestion, I'm going to use an approximation formula which is slightly more accurate than the one I used previously, ΔVol = Δr*4Pi(r+Δr/2)².

I don't understand your point about about s³. In my calculations, s=1 always, so s = s² = s³. So m³/s³ = m³/s² = m³/s.

Using 4.34x10²⁶ for the radius of the present observable universe, and escape velocity = 9.59x10⁸, I calculate ΔVol = 2.28x10⁶³.

Hi again Jon.

Another Oops! Yea I had a blunder in my spreadsheet and when I calculated it your way, I got your answer.

I then found and corrected the error in my spreadsheet and it now gives your answer as well, give and take a little bit. Sorry about that. (I get 2.25x10⁶³ m³/s, due to slightly different constants).

I get around the lack of significant digits by just working it out over a longer time (like 100 million years or so) and then scale it down again. Your approximation seems good to me as well.

Jorrie

Jorrie,

My spreadsheet has now put the final nail in the coffin of any idea that Gravitational Binding Energy (GBE) has any direct correlation with the expansion rate. GBE calculated for the universe as a whole produces too fast of expansion, and GBE calculated from the sum of superclusters is way too low. I even tried adding in the GBE of the supermassive black hole in each galactic center, but it only partially closed the gap.

But, good news, the universe's ΔVol driven by the "escape velocity" of total rest mass almost exactly equals the ΔVol calculated from the Hubble formula, Δr = H_o(bar)*r_univ.

In fact, by working backwards from the Hubble formula, I calculate that a more precise figure for the true mass of the universe is 3.16x10⁵⁴Kg. That makes the escape velocities calculated by both formulas equal.

Jon

Hi Jon.

Yep, I think it's not for nothing that the cosmologists struggled for almost a century now to get to a model that works out (fit all present observations).

"I calculate that a more precise figure for the true mass of the universe is 3.16x10⁵⁴Kg. That makes the escape velocities calculated by both formulas equal."

The two equations must give the same answer, that's true. The real value is probably uncertain by 10 to 20%. Remember, the present radius and H_o(bar) are interdependent and not very certain. They fit the ΛCDM model (I see they also call it the 'Double Dark' model), but the absolute values are model dependent...

I just use rounded numbers, i.e. Ho=70 km/s/Mpc and critical density 10^-26 kg/m3, giving a mass of ~3.54 x 10⁵⁴ kg. We are both close enough for all practical purposes...

Jorrie

Jorrie,

Yes, but it also confirms for me that matter, radiation, and "vacuum energy" are just 3 different forms of the same thing. Another "equivalence principle."

"Vacuum Junk" differs from "regular" dark matter in that it doesn't "clump" at all, which means that gravity has no effect on it. And it doesn't travel at relativistic speeds. So it isn't matter and it isn't radiation.

By process of elimination, it must be comprised of virtual particles.

"By process of elimination, it must be comprised of virtual particles."

You may well be right, but AFAIK, scientists could not (yet) find virtual particles with the right properties, not even theoretically.

It seems that they have a better chance of finding the dark matter particles in the LHC quite soon.

Jorrie

Jorrie,

Further to Vacuum Junk (vacuum energy):

As I understand it, a virtual proton/anti-proton pair has a combined mass of 1.7x10^-27Kg, and an average lifetime of 10^-25 seconds.

So if each cubic meter of vacuum has a mass of 10^-26 kg/m3, that means that each such cubic meter need produce a mere 10²⁶ virtual proton/anti-proton pairs per second to account for the total mass of Vacuum Junk. And that's not even counting the contribution of virtual electron/positron pairs.

Seems to me that the vacuum is hardly breaking a sweat!

Jorrie,

Further to my last post:

It's interesting to note that the rest mass/energy of the vacuum (7x10^-27 kg/m³) is about 10¹⁴ stronger than the radiation of the CMB, which I calculate at 4x10^-40Kg/m³. So why would cosmologists be confident that the CMB is anything other than a tiny "shadow" of the astronomically more intense vacuum energy?

Hi Jon.

"Seems to me that the vacuum is hardly breaking a sweat!"

AFAIK, this is one of the biggest headaches of the quantum physicists - the extreme weakness of the present vacuum energy. Quantum field theory predicts a 'zero point energy' (zpe) of the vacuum that is immensely larger than what is observed on cosmic scales. Something probably cancels out the zpe almost completely, but what?

Jorrie

Hi Jorrie,

I want to return to the cosmic energy chart you posted on 8-16:

I'd like you to think about potential energy in a different way. I think that potential energy should = -((Static Energy) + (GBE_initial - GBE_current))

Conceptually, total potential energy represents the kinetic energy that would be released if the universe were allowed to gravitationally collapse. By definition, until the point at 9.55Gy where vacuum mass/energy exceeds matter mass, the universe is increasing its potential energy as expansion causes matter to become ever more dispersed. If there weren't any vacuum mass/energy, expansion would cause potential energy to continue increasing until all of the initial GBE, 10¹⁵⁰ joules, is worked down to the point where it equals the static energy of matter, 10⁷¹ joules. At such point as the initial GBE were reduced nearly to zero, no more potential energy could be gained through expansion (without vacuum mass/energy).

Moreover, it seems to me that vacuum mass/energy is "non-compressable". For example, if the universe were enabled to collapse gravitationally, the density of the vacuum mass/energy would not increase. Instead, the corresponding portion of the vacuum energy would simply disappear along with the volume of vacuum space it formerly occupied.

In that sense then, expansion caused by vacuum energy/mass should not be thought of as adding any potential energy to the universe, at all. Because it could never be converted into kinetic energy via gravitational collapse. So vacuum energy has no intrinsic potential energy.

The picture is less clear to me with respect to the GBE of vacuum energy, but intuitively it ought not to have any intrinsic binding energy, for the same reason it doesn't have intrinsic potential energy.

So, my conjecture is that the GBE line should continue downwards after 9.55Gy at approximately the same slope it had before that (I think it approaches but never reaches zero). The potential energy line should start at 10-¹⁵⁰, and slope downwards parallel to the (extended) GBE line, until it approaches, but does not reach, the 10^-300 line.

It seems reasonable that the distant future universe, characterized by ultra-low matter density, will possess virtually no binding energy and will have gained a commensurate amount of potential energy.

Jorrie, oops, I screwed up.

I was confused by the fact that potential energy is always negative. So an increase in potential energy means it becomes less negative, not more negative.

But I think my conjectures about GBE and vacuum mass/energy are still valid. Vacuum mass/energy has no intrinsic GBE or potential energy.

Therefore, the GBE line would remain as I described. The potential energy line would be as you drew it up to 9.55Gy, and then would continue as a straight line until it approaches, but does not touch zero.

Also, although static energy (the rest mass of matter and radiation) is used to calculate potential energy, I don't see why it is additive to GBE. The effect of declining rest energy should be seen only as a change in the slope of the curve, not in its absolute value.

Finally, it would be interesting to find a way to calculate the time when GBE/c² will exactly equal the static mass. I think it is sometime in the near future, because my calculations show that the GBE/c² of the universe presently is at least 9.2x10⁵⁴kg, while static mass = 3.16x10⁵⁴. I don't know any easy way to calculate a true GBE number for the universe though, since in theory it should be added bottoms up from every level of matter clumping. The tops down calculation is meaningless, because the density of the universe at small scales is far from homogeneous.

Hi Jon.

Yep, you may be right. I'm starting to realize that potential energy and GBE are perhaps invalid concepts for the universe at large, as the Physics Forums guru slapped my hands for denying.

The collapse phase of a vacuum energy driven universe is a thorny one, since with a positive cosmological constant, it can never happen.

"Finally, it would be interesting to find a way to calculate the time when GBE/c² will exactly equal the static mass."

I guess you meant densities, because the mass-energies never decline, but I don't catch your drift here...

Jorrie

Jorrie,

Well, I just don't think GBE is very important to the expansion of the universe. My latest "bottoms up" calculation, which sums the GBE at levels of Stars, Super-massive Black Holes, Galaxies, Clusters, and Superclusters, and even adds in the nuclear binding energy of "metal" atoms for good measure, still generates a combined total GBE/c² of only 1.66x10⁵¹Kg. That number is 3 orders of magnitude smaller than the total rest mass of matter in the universe.

Given that GBE is increasing over time as clumping continues, I doubt that GBE could possibly have been significant to the expansion rate calculation at any recent time in the universe. And if you go far enough back, it probably is rendered insignificant by the total rest mass of radiation.

I think that at all times, total potential energy of the universe merely = -(GBE), so it isn't of significant magnitude either, in the context of the big picture.

The "expansion energy" line on your graph represents the energy needed to "disperse" the universe's rest mass at its "escape velocity" of 9.85x10⁸m/s. I think the resistance to that dispersion comes almost entirely from the inertia of the rest mass, not from its gravitational binding.

Intuitively, that reflects the low mass density of the vacuum, and the relative insignificance of total binding energy at the level of superclusters and below.

Jorrie,

It occurs to me that whether you consider the "midlife" expansion of the matter-dominated universe to reflect residual momentum from a single impulse (cannonball) or ongoing self-propulsion responding to inertial mass (rocket engine), you still need to hypothesize a missing "force" or "energy" to supply the expansion vector.

I can't say that I have a clear idea what manner of physical reality that expansion "force" or "energy" represents, but here is an analogy for my theory that incremental expansion is spontaneously produced as a reaction to the universe's inertial mass:

Picture a massive quantity of oil deposited carefully (no ripples) onto the surface of a perfectly still, infinitely broad body of water. Then watch (preferably in slow motion) as the oil's own weight causes the radius of the oil slick to expand, at first very quickly, then slowing over time.

The cosmological constant can also be factored in by pouring additional oil onto the expanding surface. The amount of additional oil added per second is equal to the Δarea of the oil slick per second. So obviously the amount of additional oil/second increases rapidly over time, and the expansion rate of the oil slick increases.

Of course this a limited analogy. It is only 2-dimensional, and may ignore some details such as surface tension (analogous to GBE?). And any coherent oil slick will have a minimum thickness of at least 1 molecule, so it cannot expand infinitely as the universe seemingly can.

That latter point raises an interesting question: As the average mass density of the vacuum has fallen towards the cosmological constant, is the observable universe still a coherent "thing", or has it already "fallen apart" into many separate "clumps" that mostly don't experience any current interaction with their neighboring clumps anymore? They may still be receiving "photon postcards" from each other's past, of course. I think coherence is a slightly different concept than the interaction horizon of a homogeneous universe. In the latter, the current interaction horizon can be shifted arbitrarily to any observation point, whereas in the former, current interaction horizons extend only to the gravitational-binding boundary of each clump.

Jorrie, further to the last point on my prior note (which was not the main point of the note!):

If the "interaction horizon" is defined as a distance at which we can receive a one-way signal from a source (without even being able to reply to the signal), apparently such horizon presently = redshift 0.68 = 1.93Gpc = 5.96x10²⁵ meters. That is 30x the radius of the Local Supercluster @ 1.9×10²⁴ m.

So our supercluster has not yet become entirely functionally isolated from a subset of the other observable superclusters.

Nevertheless, since superclusters apparently aren't gravitationally bound to each other, they are irrevocably on the road to mature as fully independent universes. So while they are unbound from the mothership but still able to communicate with it, it seems plausable to call them "juvenile" or proto-universes. At a time in the distant past when they apparently were still gravitationally bound to the mothership, we can refer to them as "embryonic" universes.

Hi Jon.

Thanks for the links and the spreadsheet. Will look at them in due course. I normally use Gott's paper and his very useful logarithmic maps of the universe.

Note that the z=0.68 indicates the present limit of 2 way communication, while the one-way causal contact is at some z=1.7 at present.

"So while they are unbound from the mothership but still able to communicate with it, it seems plausable to call them "juvenile" or proto-universes."

I would not call them that - by the time each supercluster is isolated from the rest, they are probably not too far from the 'degenerate phase', where all the mass-energy gets turned into radiation, if one believes Roger Penrose.

Jorrie

Hi again Jon.

"As the average mass density of the vacuum has fallen towards the cosmological constant, is the observable universe still a coherent "thing", or has it already "fallen apart" into many separate "clumps" that mostly don't experience any current interaction with their neighboring clumps anymore?"

Ever since inflation ended, there were a virtually infinite number of 'regions' that had no interaction possibilities with neighboring regions due to the distances between them being vastly larger than what light could have travelled since inflation. Isn't this the same thing?

Jorrie

Jorrie,

From my first post yesterday:

"I think coherence is a slightly different concept than the interaction horizon of a homogeneous universe. In the latter, the current interaction horizon can be shifted arbitrarily to any observation point, whereas in the former, current interaction horizons extend only to the gravitational-binding boundary of each clump."

One aspect of my distinction is that at some point in the future, the "generic" interaction horizon will be shorter than the radius of a supercluster, but despite that we'll continue to be able to interact within the entire area of our gravitationally bound supercluster. In that sense, each supercluster eventually becomes a permanent (or very, very long term) and relatively static observable universe of its own.

In contrast, any observation point located outside the gravitationally bound area of a supercluster will eventually have a very short event horizon and will not be able to interact with any supercluster.

Anyway, this subject is too philosophical to be important. I think it is relevant to my oil-on-water analogy, because the one-molecule minimum thickness of an oil slick may cause the slick to lose its unified coherence and drift into discrete, individually coherent patches. As the density of the universe drops over time, it similarly loses its unified coherence, and its superclusters will drift apart into discrete, individually coherent patches.

However, the oil-on-water analogy doesn't provide a strong analogy for the local coherence-maintaining force of supercluster gravitational binding. It would, if the oil had significant surface tension holding a slick together up to a certain maximum stable size (counterpart to an individual supercluster's stability size limit).

Jorrie, you'll recall that we had a discussion several months ago about the theoretical possibility that the universe is not expanding, but instead all of its contents are shrinking. I responded to support Guitarhunter's mention of the idea. Now I have uncovered a reference to this idea from the 1930's, by the famous British astronomer Arthur Eddington (who was one of the first to suggest that stars are powered by hydrogen fusion). Here is an excerpt from his book "The Expanding Universe: Astronomy's 'Great Debate', 1900-1931 (p.88-92), in which he muses about George Lemaitre's recently published work regarding the Big Bang:

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"All change is relative. The universe is expanding relatively to our common material standards; our material standards are shrinking relatively to the size of the universe. The theory of the "expanding universe" might also be called the theory of the "shrinking atom".

It is our instinctive outlook that we are always the same; it is our environment that changes. As with Anatole France's dog Ricquet—"Les homes, les animaux, les pierres grandissent en s'approchant et deviennent enormes quand ils sont sur moi. Moi non. Je demeure toujours aussi grand partout ou je suis."

Is not the expanding universe another example of distortion due to our egocentric outlook? Surely the universe should be the standard and we should measure our own vicissitudes by it. We se a relative change, and cry out that the universe is dissolving; as well might the growing child, who sees the familiar home becoming smaller, be dismayed at the vanishing property of houses and furniture.

The argument sounds plausible, but I do not deem it true. Even if our standards are held responsible for the expanding of the universe, they cannot be held responsible for its bursting. Moreover our constant standards are not necessarily puny. I have mentioned (p. 72) one cosmical dimension which remains constant, namely the radius of curvature R_s of empty regions of the universe. Since it stands in a constant ratio to the metre, it can be used equivalently. This is in fact the ideal cosmical standard and judged by it the universe changes whilst we remain true to size.

Although I do not think the suggestion goes very deep or that it has any philosophical moral, I will follow it for my last escapade in our new playground. Let us then take the whole universe as our standard of constancy, and adopt the view of a cosmic being whose body is composed of intergalactic spaces and swells as they swell. Or rather we must now say it keeps the same size, for he will not admit that it is he who has changed. Watching us for a few thousand million years, he sees us shrinking; atoms, animals, planets, even the galaxies, all shrink alike; only the intergalactic spaces remain the same. The earth spirals round the sun in an ever-decreasing orbit. It would be absurd to treat its changing revolution as a constant unit of time. The cosmic being will naturally relate his units of length and time so that the velocity of light remains constant. Our years will then decrease in geometrical progression in the cosmic scale of time. On that scale man's life is becoming briefer; his threescore years and ten are an ever-decreasing allowance. Owing to the property of geometrical progressions an infinite umber of our years will add up to a finite cosmic time; so that what we should call the end of eternity is an ordinary finite date in the cosmic calendar. But on that date the universe has expanded to infinity in our reckoning, and we have shrunk to nothing in the reckoning of the cosmic being.

We walk the stage of life, performers of a drama for the benefit of the cosmic spectator. As the scenes proceed he notices that the actors are growing smaller and the action quicker. When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing."

====================== end of excerpt ===================

Wow. Deep. Thank you Jon for turning that up. I am humbled to have my idea associated with one of the great thinkers. His analogy "cosmic spectator" and our role as a "microscopic blur" really cuts to my feelings of our position in the infinite cosmos and the role or existence of a god. The translation of the french:

The men, the animals, the stones grow while approaching and become enormous when they are upon me. Me, no. I always remain tall everywhere I am.

It's a reference to perspective, which seems to be the point of Mr. Eddington's (and my/our) idea.

Hi Guitarhunter,

Thanks for the translation. It's very powerful in its own right. One of the fun things about the astronomers and physicists before around 1950 is that they mixed equal parts of observation, math, broad speculation, and philosophy. Einstein did it as much as anyone. Nowadays it seems like cosmology theory is increasingly limited to computerized processing of ultra-complex observational data, and use of abstract math to invent new quantum particles to plug every gap. How can any of us hope to weigh in on the theoretical merits of yet another hypothetical particle?

Somebody famous (I forget who) said that a new perspective is worth 80 points of IQ. I for one am happy to take advantage of that formula, because if I stick to speculative theories, it puts a natural floor below my otherwise subterranean cosmology IQ. But the cosmology experts are on to that trick, too...

Hi Jon.

Yea, I recall that we eventually agreed that if one just takes today's observation at face value, one can 'reverse' it to a 'shrinking model' and everything will stay the same. Except that extrapolations become troublesome, e.g., sizes blow the Planck limit.

My guess is that Eddington wrote those words with his tongue in his cheek...

Jorrie

Hi Jorrie,

Maybe he was tongue in cheek, but Eddington was an avid theoretical speculator himself. I believe his personal theory was that the early universe was perfectly homogeneous, and that homogeneity is equivalant to nothingness, so it was natural that the early universe could spontaneously appear out of nothing. Hey, why not!

In a similar bout of speculation, Einstein seemed fascinated with what he referred to as the "eliptical" universe, which had the geometry of a mobious strip. So light would circle all the way round it and come back to the start, but upside down. Until the event horizon eventually cut off the circulation. My guess is that if he had lived long enough for observational evidence to show that the universe is flat, he would have been extremely disappointed.

Johannes Kepler of course lived in a much more religious era. His mathematical theory apparently was inspired directly from by his religious/philosophical instincts, applied to some basic observations about electromagnetism, as Wikipedia reports:

"Within Kepler's religious view of the cosmos, the Sun (a symbol of God the Father) was the source of motive force in the solar system. As a physical basis, Kepler drew by analogy on William Gilbert's theory of the magnetic soul of the Earth from De Magnete (1600) and on his own work on optics. Kepler supposed that the motive power (or motive species) radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it. Perhaps this assumption entailed a mathematical relationship that would restore astronomical order."

Our current appetite for speculative, mindbending theories doesn't seem so different from how most of the historical scientists thought. I hope that our current generation of mainstream cosmologists hasn't lost that. As I said, they seem fixated on the mathematics of inventing new hypothetical particles, and new scalar fields for existing particles. For example, from what little I understand about the theory of inflation, it involves a couple of twisting backflips by a hypothetical particle, followed by some front flips and a splashless entry into the pool. All other possible explanations are mathematically excluded (until they devise an even more complex set of particles and scalar fields). The complexity of this new regime more and more resembles pre-heliocentric orbital mechanics.

Hi Jon,

Thanks for the exerpt from Eddington (good refresher).

I especially liked your twisting forward/back flips, etc. in order to try to fill endless gaps (they are endless, you know). This scientific "marching in step" has taken on a life of its own, not that it shouldn't be pursued, but at what cost? All the mathematics and cosmology conceivable cannot take the place of what something like music can do for the soul in creating the inspiration, the exuberation, to pursue things like math, cosmology, physics and so on. Lets admit it, humanity has its own passion, rooted deep within itself, above and beyond the physical sciences. It is what drives us in our attempts to achieve greatness.

Sorry to get too philosophical, but your post sorta brought in on.

Anyway, back to the topic? Is there really any difference as to whether we (the universe) is expanding or contracting? Seems like the net effect would be the same. Besides, is there any way (at all) to prove one or the other?

From the excerpt you posted from Eddington: "I have mentioned (p. 72) one cosmical dimension which remains constant, namely the radius of curvature R_s of empty regions of the universe. Since it stands in a constant ratio to the metre, it can be used equivalently."

Looks to me like there's no proof here at all because R_s would always be the same since just as the metre changes, so does the empty regions of the universe change proportionately. I fail to get this one. Help me if I missed it.

Anyway, your point is well taken. Please continue.

-John

Hi John,

I don't think there is any difference between us shrinking or the universe expanding. If there was a difference, then one of the two theories must be wrong! Since it's all relative, in theory BOTH the universe could be expanding and we could be shrinking at the same time. Or any variation that keeps the relative scales consistent with observations.

We may never be able to know which is which. But, never say never in this business. Scientists have proven some things that a mere 20 years earlier were considered impossible to ever prove.

To me, the most interesting aspect of the alternative perspective would be to figure out which constants would change and which would remain the same. Like the speed of light, for example. I think there would be some very weird adjustments to physics. Someday I'd like to spend time working it through, even if the whole exercise is probably imaginary. Analyzing an alternative model generally provides some new insights even about the traditional model.

Jon, you said "To me, the most interesting aspect of the alternative perspective would be to figure out which constants would change and which would remain the same. Like the speed of light, for example."

I think the problem is that we can not figure out which constants remain "constant relative to everything else". Even c, although we consider it constant, is only so relative to us. If our environment (the universe) changes; distances change proportionately; then c is also relative, even though it remains, to us, a constant. There's no solution to this one, I'm afraid.

-John

Hi John,

You may be right. But I think that in the "shrinking" model, some constants may remain constant. It's worth thinking about, anyway.

Jon

Hi Jorrie,

Please see my post to Jon.

Regarding the Planck limit, seems like it would change proportionately to everything else. I don't see any way to prove expansion or contraction. Seems like it really comes comes down to Descartes; I think, therefore I am. Prove me wrong.

Hi John.

Can you really conceptualize that your body is shrinking and what's more, shrinking at an increasing rate, forever... (at least as far as the atoms in your body are concerned)?

I can't. It may be interesting to toy with, but why bother with such an extremely metaphysical idea? It gives no new insights as far as I can see.

Jorrie

Hi Jorrie,

You're right, of course, but it seems like the more knowledge I acquire, the smaller I feel. Does humility have anything to do with science?

-John

Hi John; "Does humility have anything to do with science?"

It was said by some big scientist (I forgot who), paraphrased as: "novices are mostly so sure of themselves and experts so full of doubt..."

Jorrie

Hi JJ,

"Regarding the Planck limit, seems like it would change proportionately to everything else."

We can't assume this, since it follows quantum laws which may not apply to larger things. If something could be compared to it, we could prove expansion or contraction.

For what it is worth, Isaiah 42:5 says that the Lord stretched out the heavens, which seems to fit with an expanding universe,

S

The following is a quick summary of a new model that I've advanced: The Dominium

The model begins with the same set of premises and conditions that were originally set forward and given the moniker, the "Swiss Cheese" model. In other words, at Big Bang creation, matter and antimatter were created equally, however, distribution was slightly random. Statistically, some areas would have greater concentration of one type over an other ("perturbations" or "imperfections" depending on which author you follow).

The Dominium model takes this core idea and adds one truly new hypothesis: matter/antimatter repulsion. As a result of like attracts like/opposites repel forces, the once heterogeneous mixture would be expected to undergo the process of "Self assembly"--as commonly noted in hydrophobic/hydrophilic extremely heterogeneous mixtures. As a result of self-assembly, the original matrix of the Universe became more organized rather than heading towards more chaotic (as is the case of self-assembly heterogeneous mixtures at the nano and atomic level)--in other words, this model assumes that classic understanding of entropy is flawed. Not all systems become more chaotic. This has been shown over and over again at the atomic, molecular, and nano levels, why couldn't this also apply at the galactic? With this solution, we achieve results consistence to observable phenomena: a uniform distribution of mass and flat event horizon.

Opposites-repel can also be used to predict and describe many other observed "anomalies." For example, the solar wind. With this new model, a clear and simple explanation for this phenomenon is forthcoming. Positrons produced through fusion are repelled by the extreme mass of the sun. As a result they are driven toward the surface. Along the way, some will annihilate. At some point densities and energies become low enough that they gravitationally self-sort (becoming miscelular positron packets MPP) and become immiscible with the surrounding matter. Although immiscibility prevents further annihilations, it does not prevent interaction. The MPP are continually pushed forward by the repulsion from the Sun's matter, while this occurs they would be expected to push matter in front of them forward. Hence the solar wind. Question: why haven't WIND or SWEPAM solar wind probes measured the presence of positrons in the titer? Answer, because these probes are matter-dense objects, and because gravitational effects are felt at very large distances, the positrons of the MPP would avoid the probes, therefore, you would expect to NEVER record their presence in the solar wind.

The actual model is quite long. Anomalies accounted for by this new model also include "dark matter," nebulae formation, the reason supermassive galactic central black holes stopped growing at one point in their development, explanation of the Tunguska event, and many more.

For a free download of the abridged version (91 pgs) go to http://www.hasanuddin.org/viewtopic.php?t=3&sid=6709b63831e91b0f6d8a4b99be6570c1

Or if you're really interested, the full book (194 pgs) is at online bookstores.

PS: Two words of caution. 1) It's written in lay language in the tradition of Sagan & 2) There is a truly ominous implication: mini black-holes are predicted to be stable... right now LHC at CERN is a hair's breath away from creating a mini black-hole

A New Model - Space-time Itself drives Cosmology

Mankind first discovered that space-time could be distorted through the effect of mass. The standard model of cosmology and most other models assume mass is the only thing that can distort space-time and they all meet the same difficulties when compared with observations of our universe. The assumption that only mass distorts space-time and the consequent clash with observation is the reason models need dark matter and dark energy. If we relax this assumption and allow a conjecture that space-time itself has a tendency to expand and can distort itself while expanding we generate a new class of models. (This seems a reasonable conjecture considering how space-time has behaved since).

Einstein and Eddington did not know about the expansion of the universe when a gravitational lens was first observed. But the actual segment of space-time Eddington observed was changing both to change the strength of the lens and to expand the universe (unknown to him). As the sun passed in front of the star field it first increased the local gravity field distorting space-time up gravity gradient and later as the sun moved away space-time moved back down gravity gradient to its relaxed position.

The movement of space-time as the universe expands is similar to the relaxing movement observed behind the sun. The expansion of space-time in the universe might represent the relaxation of distortion that was caused by an inherent "tendency to expand". Because space-time is moving/relaxing outward the gravitational gradient must have acted outward.

In this new model there is no need for a big-bang explosion or high initial matter velocities. All space-time starts in a small volume trying to expand. As the outer regions (or longest loops in a closed space-time) are only constrained on one side by neighbouring space they expand first and the next layers follow as congestion is eased. A pattern of space distortion emerges with more distortion at the centre and less at the edges. I call this a gravity "hump" after the shape of a space distortion graph drawn along any diameter. It is the opposite of the gravity well found around masses (and it prevented the early universe disappearing into one big black hole). The "hump" will "slump" as space-time expands down gradient. The model will evolve into the almost homogeneous, nearly flat, gently expanding and even more gently accelerating universe we observe today.

This "Hump-Slump" process is not balanced between outward momentum and mutual gravity. So it has no critical mass and there is no need for "missing" dark matter (but no objection to it either). The universe starts expanding more slowly so structure can start to form early at short ranges.

I am uncomfortable with dark energy which is created with new volume and must increase as the cube of linear expansion and even faster if expansion accelerates. There is no end to this escalating creation of energy. Dark energy is a property of space and needs to be transferred to matter to produce the effects we observe. The obvious candidate is expansive gravity, but that is denied in existing models. In the Hump Slump model the expansive gravitational potential replaces dark energy but is reassuringly finite.

The conjecture that space-time expands of itself seems plausible and consistent with observation to me.

Hi Cedar, further to our CR4 pm conversation, I will give a summary of my responses to some points in this post only, for the benefit of a general readership.

"The assumption that only mass distorts space-time and the consequent clash with observation is the reason models need dark matter and dark energy. If we relax this assumption and allow a conjecture that space-time itself has a tendency to expand and can distort itself while expanding we generate a new class of models."

Firstly, it was originally recognized by Einstein that all forms of energy distorts spacetime. Nothing has changed since. Secondly, Einstein also proved that space must either contract or expand (by 'itself', as you stated it), hence his 'cosmological constant' Λ, with which he attempted to make it 'static' (as he believed it should be^(a)). Hence, both your statements are incorrect.

"Einstein and Eddington did not know about the expansion of the universe when a gravitational lens was first observed. But the actual segment of space-time Eddington observed was changing both to change the strength of the lens and to expand the universe ..."

But, they surely knew that the Sun's mass/energy distorts spacetime (the whole idea of GR), hence the deflection of light that Einstein predicted. I still have no idea what you mean by the second sentence.

"I am uncomfortable with dark energy which is created with new volume and must increase as the cube of linear expansion and even faster if expansion accelerates."

Everybody is uncomfortable with it, but there is no better explanation at hand for the accelerating expansion. What is more, it comes straight out of the best two theories we have: general relativity and quantum physics. Despite the fact that they are not compatible at the deepest level, they both predict dark energy, or more precisely vacuum energy.^(b)

"Dark energy is a property of space and needs to be transferred to matter to produce the effects we observe. The obvious candidate is expansive gravity, but that is denied in existing models."

This describes (at least partially) the dark energy of standard ΛCDM cosmology! What you seem to replace it with is however very unlikely to have all the other properties that is required of dark energy. Unless you can come up with some mathematical description of your "Hump Slump model" and show how it predicts what we are observing, I can see no way to critique it in a meaningful way.

You can start by detailing how Hubble's law would hold in all directions. Then how it accounts for the observed fact of initial deceleration and only lately a small acceleration of expansion. I am afraid that the type of inhomogeneity that you describe to me in words (dense at the 'center' and rarefied at the 'edges') makes no sense in the cosmic scheme of things (at least to me).

-J

(a) The fact that Einstein later called the cosmological constant his "biggest blunder", did not make it go away from his theory. It was later (1990s) discovered to account for the cosmic expansion curve to an astonishing degree of accuracy. Here is a copy of the curve from my entry: http://cr4.globalspec.com/blogentry/13695/Measuring-Cosmic-Expansion

For more explanation, kindly read the Blog link given.

(b) BTW, vacuum energy density always changes with the cube of the linear expansion factor, irrespective of acceleration or deceleration of cosmic expansion (it even holds for cosmic contraction).

Hi Jorrie

You challenged me to "start by detailing how Hubble's law would hold in all directions" (in a non-homogeneous universe).

Above I have drawn two informal diagrams. On the left we have the past light cone. Time increases up the page and distance increases from the centre of the cone outward (I believe that is conventional). Simultaneous events are shown on the same horizontal line (with apologies to Minkowski) so that the diagram is easier to draw/interpret. We observe today from point B where the degree of expansion of the universe has reached the current value I will call expansion "XB". The CMB is observed coming from two places A1 and A2. In the homogeneous model A1 and A2 reach the critical degree of universal expansion that allows recombination to occur (expansion "XA") at the same time. They are equidistant from B so light sets out at the same time and takes the same time to travel through uniformly expanding space-time and it arrives red shifted by an amount related to the difference between the expansions XB minus XA1which is equal to XB minus XA2. (The translation from expansion to red shift is very clearly explained by you in the blog you refer to).

The diagram on the right is identical except that space-time is not homogeneous. Space-time has expanded twice as much on the right hand side as on the left. The critical degree of universal expansion that allows recombination to occur XA is reached earlier (lower on the page) on the right than on the left. The diagram is drawn with a simple linear gradient of space expansion and a contrast of twice the expansion across the page, but the result would be the same for any pattern of expansion and any degree of contrast (including no contrast i.e. homogeneous). A straight diagonal line represents the different times at which local conditions match XA and radiation is emitted at each point. Events A1 and A2 are no longer simultaneous but they do occur at the same degree of space expansion XA. In this case two light beams set out at different times and take different times to arrive but they travel through different gradients of space-time expansion (one up gradient and one down) but they arrive red shifted (exactly as before) by an amount related to the difference between the expansions XB minus XA1which is equal to XB minus XA2. Note only the degree of expansion at origin and observation are involved in determining red shift, not distance, not universal gradient nor any other factor.

If there were any identifiable beacons in the CMB their luminosity would be distorted just like their red shift (because expansion spreads photons sideways reducing the light collected in a fixed observation aperture). Closer beacons like Type 1A supernova (and parallax observations) in opposite directions would also show common "Hubble" characteristics. But in the non-homogeneous model comparable beacons are not at equal distance they are at points of equal space expansion (at different distances) and observed through paths in space that have compensating expansion. (Perhaps we could say they are "equally spaced" partly as a joke but also because the amount of space between them is the same it is just the degree of expansion that is different).

It should be no surprise that the diagonal line represents a path through space time faster than light. We could not see a CMB in all directions if recombination had not happened throughout our visible universe before the light got here. No matter, energy or information is moving we simply recognise the conditions XA appear at different places in that sequence. Of course in the homogeneous model the conditions appear simultaneously or "travel" at infinite speed.

I think this argument does demonstrate that Hubble's law would hold in all directions in a non-homogeneous universe because (when compared to a homogeneous universe) the non-homogeneous expansion places beacons in different locations that would look different except that they are exactly compensated by different conditions along the transmission path.

None of this directly supports the "Hump Slump" model but neither is the model disproved by an apparently uniform Hubble law or an apparently uniform (if slightly blotchy at one part in 10⁵) CMB.

Your Other Points:

I accept your last point "(b)" that I was not clear in my objection to Dark Energy. I am not experienced in constructing scientifically correct pedantic statements. By saying an accelerating universe creates energy "faster" I meant faster with respect to time not faster with respect to linear distance. So in the early small universe a little expansion occurs every day and a little Dark Energy is created. Later when the universe is bigger more energy is created every day even with the same amount of linear expansion. If the universe accelerates the creation of energy grows even quicker with respect to time (but not with respect to distance). As you say we are all uncomfortable with dark energy and the rapidly escalating creation of energy even if it is the best theory we have to date.

I also accept your earlier point "Hence, both your statements are incorrect" because I realise I have not described the current model accurately although I am aware of all the features you mention. What we can agree on (I hope) is that this new model is not like existing models in that it predicts a non-homogeneous expansion of the universe and it claims the non-uniformity is caused by a fundamental property of space-time that (I understand) may be absent from existing models or if present is claimed to produce a different result.

I will respond to your remaining points in another post.

Hi Cedar,

OK, I understand your 'hand-waving' argument now. BTW, I think you should rather call it "anisotropic" density rather than "non-homogeneous spacetime", because the latter may have a different meaning than what I think you intend. As I understand it, your argument is based on a postulate that the universe is denser in some direction than in the opposite direction from us (i.e., anisotropic), not so?

If we just look at the CMB redshift average, this should be consistent with what we observe, because the redshift at recombination (last scattering of light) would have happened at the same temperature everywhere (in all directions). Whether the small-scale variations in temperature would have been the same in all directions, I'm not sure, because the "opposite direction" would have started out denser and the expansion laws would have been different.

As far as Hubble's law is concerned, things will be very tricky, because the only physical law that makes sense is for the expansion rate in the denser (A1) direction to be smaller than in the less dense (A2) direction, i.e., anisotropic expansion. What will the math say about Hubble's law?

For one thing, the Hubble constant (Ho) will be different in different directions. We must remember that numerous independent distance measurements are used to determine Ho. It is clear from your example above that the proper distance to the CMB on the left side (A1) is less than the proper distance to the CMB on the right side (A2). Since they have the same redshift (and hence the same recession speed), Ho must be larger on the left than on the right. For the same reasons, a galaxy at a specific redshift in the two directions will be at different proper distances, and hence give different Ho. This anisotropic Ho does not fit observations.

Further, this causes an apparent contradiction. A larger Ho on the left signifies a faster expansion rate, but a higher density there should cause a slower expansion rate. Another way to look at it is that in order for the density to decrease the same amount in half the time, the average expansion rate must be double. So, you will have to show a credible mechanism for making denser regions expand faster than less denser regions, but without dark energy...

As it stands, I disagree with your statement: "I think this [your] argument does demonstrate that Hubble's law would hold in all directions in a non-homogeneous universe because (when compared to a homogeneous universe)..."

-J

Hi Jorrie,

The model was created to be the easiest structure possible to analyse red shift that could answer your challenge. It was not intended as a realistic model of the universe. Unfortunately much of your correct challenge that it is not realistic is wasted. However, you have made me realise that the model was too simple. A linear difference of space expansion along parallel lines is ok for red shifts but only a radial pattern of space expansion would allow luminosities to be modelled correctly. So you have found me wrong again.

What I think the argument with the light cones does confirm is that the CMB that is always emitted at the same space expansion (i.e. at the same temperature of recombination) and always observed from a single local expansion so it will always have the same red shift whether the universe is uniform or not.

Let's try another tack to look at the other observations. I will divide the journey of light from source to observer into 3 stages. In a static universe light simply travels from the origin to the observer. It displays parallax and luminosity features related to distance but no red shift. In a uniformly expanding universe light must make the same journey plus the distance by which the observer has expanded away from the source. (Note: the behaviour of the source after emission is irrelevant). In a uniformly expanding universe the distance expanded by the observer happens to be the same as that of the source. The light will be observed with slightly greater parallax and luminosity changes plus a red shift.

In a universe with uneven expansion the light could have been emitted in a region of space that was more or less dense than the observer at the time of transmission. So in addition (to making the journey and adding the distance the observer has expanded) the light must also adjust between the expansion at the source and the expansion the observer had at the time of transmission. If the origin space is less expanded the source will not have expanded as far away as in the uniform case but the expansion adjustment will be positive and will make the source appear further away (in red shift, luminosity and parallax) by an amount that exactly compensates the "lack of expansion". If the origin space is more expanded than the uniform case the origin will be further away than in the uniform case but the expansion adjustment will be negative making the source look closer by the compensating amount.

To summarise the light path has 3 stages. The path between positions at transmission and the expansion of the observer are present in both the uniform and the non-uniform cases. But in the non-uniform case the stars have already expanded by different amounts but the expanded space distorts the light to exactly compensate.

If we repeat the logic with a perfect cubic nebular of source stars rather than a single source you will see that the average red shift, the star counts and the average star density will all appear uniform even if the expansion is not. The Hubble constant measured between the nearer and further members of the nebula will also be the same in all directions.

I think I have now shown that all observations in radially symmetrical but non-homogeneous universe will look the same in all directions from any observation point.

I do hope someone can disprove this argument. I would hate to live in a universe where I can never know if it is uniform or not!

Kind regards

Cedar

Hi Cedar, you wrote: "Unfortunately much of your correct challenge that it is not realistic is wasted."

I don't think I tried to make it realistic. I think I challenged your model, which I still think is inconsistent in itself. It is time you come up with some mathematics (even if it is simple and approximate) to support your arguments.

As an example, statements like: "In a universe with uneven expansion the light could have been emitted in a region of space that was more or less dense than the observer at the time of transmission. So in addition (to making the journey and adding the distance the observer has expanded) the light must also adjust between the expansion at the source and the expansion the observer had at the time of transmission" means little, unless you can put it in a mathematical language of some sorts (i.e. a precise language that is not dependent on semantics...)

Bring on some more sketches and some quantitative discussion; otherwise nobody will probably take it seriously. It might be worth your while, because if what you say: "I think I have now shown that all observations in radially symmetrical but non-homogeneous universe will look the same in all directions from any observation point" is true, it will be truly revolutionary, IMO...

-J

BTW, the term "non-homogeneous" is still bothering me. The universe is in any case non-homogeneous on all but the largest of scales. This term normally means the irregularities in density in any given direction (like galaxies, clusters etc). The term "homogeneous" normally means that on the large scale, we can ignore these irregularities. What you are talking about is anisotropic density (on average, not the same in every direction) and the resultant anisotropic expansion.

Hi Jorrie

1) Name that Expansion

First let's nail the nature of the expansion and try to find it a name. Can you imagine a sphere of uniform gas (temperature, pressure & density) released instantly into a vacuum (without balloon debris in the way). A shock wave would pass inward through the gas at the speed of sound to reset pressures into a radial pattern of reducing pressure but the gas would move more slowly than sound, its motion dictated by local pressure differentials which are quite small in the centre. The outer gas would move first and fastest followed by inner layers and we will soon have a non homogeneous pattern of density, pressure, temperature, and motion. All measures will decline along any radius but every radius will be identical. This is a class of expansion types until we specify the exact variation of one measure with radius (all other measures can be derived from one - I think).

The Hump Slump is a specific example from this class where there is a causal evolution of the internal pressure and its consequences. I discovered it when searching for a mechanism that could drive expansion. I believe space-time is more closely analogous to an elastic solid such as an expanding bath sponge than to any fluid because no fluid can sustain a distortion but gravity (space distortion) is sustained over B-illennia. I have called this universe non-homogeneous to describe the density distribution of space-time but I accept that term is already associated with distributions of matter. I believe the distribution of space-time is much more uniform than matter on medium scales because space doesn't gravitate and clump together (into stars, galaxies etc).

So it is the expansion we are trying to name and this expansion varies along any radius but all radii are identical and expansion is uniform in each circumferential shell. The expansion is non-homogeneous. It is isotropic about the "centre" of expansion (and it creates the visual illusion of being isotropic along any radius and hence at every point as I will attempt to prove below). What about an-iso-radial expansion?

I have already chosen my favourite name but it describes the process - the Hump Slump. As our gas or bath sponge expands the graph of density or pressure along any diameter has a humped shape with a peak at the "centre" and that shape evolves to be flatter and wider with time.

2) Does the expansion appear isotropic?

I now have to demonstrate that this expansion does appear to be isotropic although it isn't really. I have had some trouble uploading diagrams drafted and inserted into Word-for Windows so I hope the diagrams are clear.

The first diagram "Static Universe" shows two perfect identical cubic star nebulas as described before the source and the observer. The diagram represents distance horizontally and time increasing vertically. Light is shown by tiny horizontal arrows at sequential moments in time. The distance between the nebulas is "d".

In a static universe light simply travels the distance between the source (S_S for Source-Static) and the observer (O_S). Parallax and luminosity measurements reveal the distance but there is no expansion or red shift.

Results: Light travels 1 x d, Parallax scales to d, Luminosity 1/d², wavelength of light unchanged.

The second diagram "Uniform Expanding Universe" shows the nebulas expanding by equal amounts in size and distance identically. The time interval is chosen so that the universe doubles in linear scale.

In these later diagrams the centre of expansion will be off to the right with expansion increasing along a horizontal radius to the left. A vertical dotted line represents the "Mid Space Line" which is a co-moving frame of reference and the point where equal amounts of space separate the nebulas (but uneven expansion will spread the space over different distances in the non-uniform case.)

The light travels the original distance between the nebulas plus the expansion of the observer only. (Observer labelled O_U for observer-Uniform) The distance increases by the expansion of both the observer and the source. Both nebulas double in linear size so 4 times the area is drawn and 8 times the volume is there and we could check average star densities etc. still match.

Results: Light travels 1.5d, Distance separation is the original d plus both expansions of 0.5d each total 2d. Parallax 2d (twice as far away), Luminosity 1/(2d)²=1/4d², wavelength of light doubles (between initial expansion of source and final expansion of observer).

The third diagram "Non-Uniform Expanding Universe" shows the nebulas expanding at different rates. I have chosen to show a case where the expansion of the source is double the expansion of the observer. They start at different sizes and have already expanded to different positions before the light sets out.

I have also chosen to show the case where the expansion of the observer is the same as the "uniform" case to allow easy comparisons. The source nebula will have expanded faster and the initial distance is no longer "d" but 1.5d. We could construct an example where the initial distance was again "d" and the observer had expanded by 1/3d and the source by 2/3d and the nebulas were appropriate initial sizes. I have not drawn this alternative diagram.

The nebulas start out at different sizes due to prior expansion. The observer (O_N for observer-Non-uniform) has expanded to unit size and will expand to double on linear scale. The source is already expanded to double on linear scale and will double again. The light travels the original distance 1.5d plus the expansion of the observer 0.5d so total 2d. The distance is the initial distance 1.5d plus the expansion of the observer 0.5d and the expansion of the source (twice as fast on twice the size) 2d total 4d.

A new mechanism now comes into play. The observer sees the source through space that is not uniform. The image of the source contracts as it passes into less expanded (more dense) space. So each of our observations now contain a correction of 4 times on linear scale for this "optical illusion" (should it be called a spatial illusion?).

Results: Light has travelled the 2d (The initial separation was greater). The separation is 4d (see above). Parallax 4d corrected by 0.5 difference of linear scale = 2d (same as the uniform case), Luminosity is 1/(4d)² corrected by the area factor 0.25 = 1/16d² x 0.25 = 1/4d² (same as the uniform case), wavelength of light doubles (between initial expansion of source and final expansion of observer - Also the same as the uniform case).

If the non-uniformly expanding universe appears to be uniform in the radial direction and is uniform in the circumferential direction it should be indistinguishable from a uniform isotropic universe in all directions.

I accept that this is not a full mathematical proof for all observations in both radial directions, nor for all values of universal expansion and all unequal expansion functions, nor is the generalisation to all diagonal directions proved. But this one case is demonstrated and the others seem plausible. I don't have the mathematical skill to generate a formal proof so I can only hope someone who likes the idea will collaborate. (All offers would be welcome folks!)

Kind regards

Cedar

Woops,

Typo in 4th last paragraph " A new mechanism now comes into play".......

The text says the correction is "4 on linear scale" This should read "2 on linear scale". The correct number has been used in the calculations further down in the original document.

The explanation is that space at the source is expanded to 4 on linear scale but the space at the observer is expanded to 2. Therefore the ratio is 2:1 not 4:1.

sorry! Cedar

Hi Cedar,

I did try to follow your arguments, but to me they are very confusing, to say the least. I may be partly because of your non-standard usage of terminology, but the concepts are also weird. I can understand your 'mass-less gas bubble' that is released into a vacuum, but to relate that to spacetime expansion? Nope, I don't follow.

Minkowski's flat spacetime 'expands' at the speed of light, simply because the time axis grows at the speed of light. Cosmic scale space expands over time. This is a totally different concept than what 'spacetime expansion' would be. Since you are only talking about empty space in your "Hump Slump" model, it resembles something between the empty Milne and the cosmological-constant-only de Sitter models. The Mine model is unrealistic, but the de Sitter model is physically possible, because matter could become so rarefied that it is undetectable on the really large scale.

The big difference with your model is apparently that it ignores gravity (I believe it is not a solution to Einstein's field equations) and it starts to expand from an 'edge' and not everywhere simultaneously, like in all standard cosmic models. But, let's suppose the cosmos somehow works according to your model. Yes, from the 'center', expansion will be isotropic, just like in any standard model. The expansion will be non-uniform, unlike any standard model that I know of. From any other point than the 'center' I find your apparent isotropy hard to accept.

"In a static universe light simply travels the distance between the source (S_S for Source-Static) and the observer (O_S). Parallax and luminosity measurements reveal the distance but there is no expansion or red shift."

At cosmic distances, where cosmic redshift would be meaningful, parallax cannot be observed. They use SN1a, by measuring flare-up/decay time (to determine the exact type of SN) and then apparent luminosity to determine distance. As a consequence, I do not follow the rest of your argument.

"Results: Light travels 1 x d, Parallax scales to d, Luminosity 1/d², wavelength of light unchanged."

Do you perhaps mean distance when you you wrote 'parallax'? If so, what sort of coordinates system is distance measured in? Light-travel-time, comoving coordinates, proper distance, or other? This is not straightforward in any expanding space.

"The third diagram "Non-Uniform Expanding Universe" shows the nebulas expanding at different rates."

In standard terminology, 'nebulas' do not expand - they are gravitationally bound structures and stay effectively unchanged in size as the cosmos expands - only the distance between bound structures, like between us (in Virgo cluster) and the Coma cluster, increases over time. The 'd' in your diagram reminds me of the proper distance at at the time of emission and your '2d' looks like light travel time (distance). However, being non-standard cosmology, I have no idea how to verify that, apart from not quite understanding your terminology. For the same reason I cannot follow your 'proof' of general general isotropy...

-J

Hi Jorrie,

I am sorry we are having this difficulty of understanding. Thanks for persevering. I am desperately searching for a way to be clearer so we can concentrate on the Physics.

You have said "I can understand your 'mass-less gas bubble' that is released into a vacuum, but to relate that to spacetime expansion? Nope, I don't follow." The description of a gas was there to explain the shape of the expansion I have in mind which you do seem to have understood by paragraph 3. It was not intended to explain the mechanism that causes the expansion.

You have said "The big difference with your model is apparently that it ignores gravity". Space distortion in my model arises from two causes and they are overlaid. One cause of space distortion is all the forms of mass-energy and all the effects we call gravity exactly as they exist in Einstein's field equations and the standard model. In addition my model allows space to distort itself as it expands independent of the effects of mass. So when I describe this second contribution from space alone I AM ignoring mass and its gravity until it is time to overlay the two effects together to see the overall picture. When I am describing the unique features of my model the unique space distortion contribution is inevitably more prominent than the common mass-energy contribution.

In part 2 of my post I tried to show that a universe that expands unevenly will look like a universe that expands evenly - for every observation. The uneven expansion of the model universe has two effects, it distributes matter unevenly in unevenly expanded space but it also distorts all optical observations. I presented the results of observations for 3 cases, a static universe, the standard evenly expanding universe and the unevenly expanding universe of my model.

I do realise that stellar parallax is very limited in range but I did need to show all optical observations are deceived by uneven space distortion so I presented the parallax result for each case together with the far more useful apparent luminosity and red shift. The standard model expanding universe and the unevenly expanding universe produced exactly the same observations after the "optical illusion" is taken into account.

You ask "what sort of coordinates system is distance measured in? Light-travel-time, comoving coordinates, proper distance, or other?" For the static universe and the uniformly expanding universe I am using exactly the same measures as you would. The initial distance between the objects is exactly what god would measure with a big tape measure made of matter - the proper distance. In the static and standard models the initial separation is simply "d". But in the case of uneven expansion if I want the observer's expansion to match the standard case the source expansion has to be different for the expansion to be uneven. I chose 1.5d as the initial distance to analyse. In the standard case equally expanded objects expand by equal amounts to a separation of "2d". In the uneven case unevenly expanded initial positions get more uneven as they continue and reach a separation of "4d". But the whole point is that this difference is disguised by the "optical illusion". The space at the observer is only half as expanded as that at the source so the distance that really is double looks the same (whether measured by parallax (impractical) or by luminosity or by red shift.)

In the standard model the dotted line is a co-moving coordinate that stays equidistant between the objects as I wrote. In the uneven model there cannot be a single moving co-ordinate that could match two different motions. However there is a moving co-ordinate for every spherical shell in the expansion. If we choose a spherical shell between the objects that divides the quantity of space between them equally (a small volume of dense space on one side and a larger volume of less dense space on the other) it will stay in the same relative position as the uneven expansion continues. This moving co-ordinate is "equi-spatial" rather than equidistant.

You also said "In standard terminology, 'nebulas' do not expand - they are gravitationally bound structures and stay effectively unchanged in size as the cosmos expands" Woops I named this wrongly! You had asked in the previous post whether the density of matter or average star counts would reveal the true asymmetry despite the optical effect. I decided to show a cubic region of expanding space to demonstrate it is subject to the same two compensating effects as individual point objects. I had the idea that if a non-gravity bound set of stars could be placed at each corner it would be easier to analyse the expansion and illusion. Inspired by your question about averages I thought why not have identical star populations in the cubes and I made the mistake of calling them nebulas. If we had a population of non-gravitational marker buoys in space this idea may have helped. As it was it just added to the confusion. Sorry.

Kind regards

Cedar

Hi Cedar,

The meaning of your idea is becoming clearer now, to me at least and it has some merit.

I am about to recommend that you take it to the next step of "going public"^(a), but there are still some terminology that should be improved. Otherwise, other readers may still be confused. I will try to make a list with comments, as they appeared in your posts.

1. Your term "non-homogeneous" density (or expansion) is still a bit confusing. It is also not anisotropic, as I originally thought. It is almost like a planet with highest density at the center and less density as you go radially outwards. What about simply "radially decreasing density" as a description of the "hump-slump" model? "Radially increasing expansion rate" would also be confusing, because in a way, this is exactly what we are observing in the standard model.

2. "Parallax and luminosity measurements reveal the distance..."

I think you should replace all the 'parallax measurements" references with "proper distance (measurements)". Parallax is just the first rung of the so-called "distance ladder". Whenever required, use light-travel-distance as well, because it is sometimes significant, as you know.

3. "The distance increases by the expansion of both the observer and the source..." Very confusing - I figured out what you mean, but rather use "spatial expansion at the observer and the source". Many readers will know that the source and the observer cannot expand themselves, but not everybody will.

4. "The image of the source contracts as it passes into less expanded (more dense) space." You give this statement without explanation or rationale. Personally, I think it is untrue in a cosmological context, so to make it more acceptable, you will have explain a bit.

5. "Space distortion in my model arises from two causes and they are overlaid. One cause of space distortion is all the forms of mass-energy and all the effects we call gravity exactly as they exist in Einstein's field equations and the standard model. In addition my model allows space to distort itself as it expands independent of the effects of mass."

You should take notice of the fact that this also fits the standard ΛCDM model precisely. Lambda does exactly cause space to expand independent of the effects of mass. The only difference is that that Λ does it at the same rate throughout space, not from the 'edges inwards', like in your model. Be a bit more descriptive.

6. Your modeling is not very clear, neither in drawings, nor in calculations. I recommend that you use a graphics package to prepare sketches and then to save them as .jpg on your computer. Then it is a simple matter to upload them by using that 'camera' icon on the top frame of the CR4 editor.

7. I have tried to include your model's characteristics into a more standard cosmology, but there are various pitfalls that I'm still working on. Here is an example of how it could perhaps be represented.^(b)

The black bullets are matter concentrations sitting on the 1-D space 'today' and the blue bullets are the same matter when the expansion factor was half of what it is now (in every direction). The leftmost side has clearly expanded half as mush as the rightmost side and the matter density there is twice that of the right side. The normalized scales can be Hubble time, Hubble radius, expansion factor, or whatever. It is only the ratios that count, as I think you would agree.

The green spiral represents photons now reaching the 'green observer' in the densest (leftmost) region, with the photons emitted in the past from hot matter in the least dense (rightmost) region. The red spiral represents photons now reaching the red observer, with the photons emitted in the past from identical hot matter, located in the densest (leftmost) region. The spirals are accurate representations of the photon paths on the linearly expanding, but asymmetric hypersphere (I actually ran the simulation backwards, contracting from present densities to the original emission densities).

Analysis of the situation is quite tricky, because due to gravitational redshift, cosmological time proceeds differently for the two regions. I will nevertheless try to interpret it in a future post.

Regards,

Jorrie

(a) Old threads like this one eventually disappears 'off the radar horizon', because most readers will eventually 'unsubscribe' from them to reduce clutter in their mail boxes.

Once you have the terminology reasonably well sorted (and since you now feel more comfortable with Blogging), I recommend that you start a new topic of your own (just click "Start a Discussion" near the top of the right panel) and specify all that they ask for. I normally just use the "General" category, but you may consider others on the list as well.

Write a good introductory summary, not too long, because there will be time to elaborate in replies to comments from others. This will put your post well inside the radar horizon for a while and you are almost guaranteed to get some other people to respond.

Once you are confident with this process, you may even ask CR4 Admin to help you establish your own CR4 Blog...

(b) Note that my simulation has no edge, because it represents a closed oblate hyper-spheroid in 4-D hyperspace, of which only the top-half is shown here in 2-D.

Hi Jorrie,

I owe you sincere thanks for the effort you have put into clarifying and improving an idea you are not even convinced about.

Your terminology and presentation ideas 1-3 & 5-6 seem excellent. I am already working this advice into a representation of the model. Perhaps in place of "Radially increasing expansion rate" that "would also be confusing, because in a way, this is exactly what we are observing in the standard model." we could try "radially escalating expansion rate" having explained that in the standard model expansion increases as an arithmetic progression always proportional to distance but in the new model expansion increases faster than simple proportion.

You have challenged my quote: 4. "The image of the source contracts as it passes into less expanded (more dense) space." You give this statement without explanation or rationale. Personally, I think it is untrue in a cosmological context, so to make it more acceptable, you will have explain a bit.

As I see now see this (with your help) it is NOT new. In the standard model differences of space expansion only occur with time. But observations from more expanded (future) space are distorted to create exactly the identical "optical illusions" (e.g. that things are further away than they "were") that I copy into my model - except that I use it across space (as well as time). The effects I claim for observing from more dense space are what past observers would see if time ran backward.

The premise of the standard model is that expanded space makes sources look further away than the light has actually travelled. I had thought I invented the optical illusion bit - but I now realise I didn't.

In item 5 you say: "The only difference is that that Λ does it at the same rate throughout space, not from the 'edges inwards', like in your model".

I think this means the standard model is NOT distorted by "Λ" because it expands uniformly. In my model space IS distorted and that gives rise to expansive gravity (that removes the cosmological need for dark matter and replaces dark energy). So I think there is a valid distinction here and it is the distortion (but not the expansion).

Item 7: It is now my turn to try to grasp your modelling (of my model) I need a little more thinking time.

Kind regards

Cedar

Hi Cedar,

I'm intrigued by the possibility that such a scheme may produce the same general observations, which I am busy still busy modeling. I do not quite believe that such a cosmos is technically possible, but that's an issue for later.

You wrote: "... we could try "radially escalating expansion rate" having explained that in the standard model expansion increases as an arithmetic progression always proportional to distance but in the new model expansion increases faster than simple proportion."

Take note that the "simple proportion" is only for observations 'now'; it decreases over time, but it is not an expansion rate, but a recession rate. Expansion rate currently increases over time. For these reasons, your proposed "radially escalating expansion rate" is not very good either. Maybe you should just call it the 'hump-slump' and leave it that...

"The premise of the standard model is that expanded space makes sources look further away than the light has actually travelled. I had thought I invented the optical illusion bit - but I now realise I didn't."

Hmm... Nope. The light from the CMB has traveled 13.7 billion light years of actual (its own local) space in 13.7 billion years. The fact that the source (region) was only 14.2 million light years from us when that light left it and that the source (region) is now some 46 billion light years from us, has nothing to do with light travel time and/or distance.

"I think this means the standard model is NOT distorted by "Λ" because it expands uniformly."

As long as the cosmos is spatially flat (as we think it is), no distortion happens on the large scale. If it is not flat, both matter and Λ causes 'optical distortions' over distance and time - the standard model handles that quite well.

I do not follow your arguments about "expansive gravity (that removes the cosmological need for dark matter and replaces dark energy)", probably because you have never explained how your model is supposed to achieve that.

I will post a first order analysis of my simulation of your model within a day or so.

Regards, Jorrie

Hi Cedar, just a typo correction, which may otherwise cause confusion.

I wrote: "The fact that the source (region) was only 14.2 million light years from us when that light left it and that the source (region) is now some 46 billion light years from us, ..."

The lower value should have been 42 million light years, because the expansion of the CMB from then till now is about 1100 times.

I am still battling a bit to get the gravitational time dilation for the left side of the distorted hypersphere in my simulation right, but I think I have found a way around the issue...

Regards,

Jorrie

Hi Jorrie,

1) In Post 62 I said: "In the standard model differences of space expansion only occur with time. But observations from more expanded (future) space are distorted to create exactly the identical "optical illusions" (e.g. that things are further away than they "were") that I copy into my model - except that I use it across space (as well as time)."

It would now seem that if there are no observations of secondary effects that challenge the standard model (observed through space that expanded with time) we shouldn't expect any that challenge my model (observed through space that is more expanded in a different place).

2) You have quoted me and commented as follows:

"The premise of the standard model is that expanded space makes sources look further away than the light has actually travelled. I had thought I invented the optical illusion bit - but I now realise I didn't."

Hmm... Nope. The light from the CMB has travelled 13.7 billion light years of actual (its own local) space in 13.7 billion years. The fact that the source (region) was only 42 million light years (typo corrected) from us when that light left it and that the source (region) is now some 46 billion light years from us, has nothing to do with light travel time and/or distance.

Well actually I think my comment is correct. Expanded space does make every source look further away (i.e. it alters red shift and luminosity) than light has travelled. The CMB does not have the red shift of an object at "13.7 billion light years" distance it has a lot more. This is because expanding space has stretched the wavelength while the light was travelling (in one interpretation) or expanded the area a given photon density is stretched across by more than the inverse square for the distance travelled (reducing apparent luminosity).

But my point was that optical distortion from different expansion of space is already recognised in the standard model - but only for expansion from past to present - it does not allow different space density to exist across space at the same time as my model would. The effects of looking from expanded space to less expanded space should be the same however the expansion arose.

3) You have challenged me that expansion could not begin from the "edge" or outside limit of the universe. We can define an arrow of time from the times which existed before to the time now. Surely we can also define an arrow of spatial expansion from the volume which existed before to the new volume that only exists now? Space has proved it can find somewhere to expand into over billions of years. The new model is only suggesting that space expands along the arrow of space just as it is already known to expand along the arrow of time. Is this yet another example of the interaction and essential symmetry of space and time in space-time? The new model is in this sense more symmetrical between space and time that the standard model.

4) You objected to: "I think this means the standard model is NOT distorted by "Λ" because it expands uniformly."

Perhaps we could agree on the phrase: "the standard model is NOT distorted by THE NON-UNIFORMITY OF "Λ" because "Λ" is uniform, unlike my model. This is what I meant in the context.

5) The difference between the Hump-Slump model and the Standard Model may be very small. In the light cone diagram we noted that the apparent speed of the recombination "front" was significantly greater than the speed of light at a time when the visible universe was relatively small. So the time window for recombination to complete across the universe will be small. Equally we know the Hubble flow and its acceleration are modest so the space density gradient must also be small.

6) The linear progressive radial space expansion you are modelling is a member of the same class of models as the Hump-Slump and it is a valid test the optical illusion hypothesis. But I am sure you realise the H-S has a causal relationship between the compression of space, its freedom to expand and its density gradient that leads to a continuous curve of space density.

Kind regards

Cedar

Hi Cedar, you wrote: "Expanded space does make every source look further away (i.e. it alters red shift and luminosity) than light has travelled. The CMB does not have the red shift of an object at "13.7 billion light years" distance it has a lot more."

Nope again. A source "looks" as far away as the light has traveled, irrespective of expansion. That is the definition of "light travel distance". If you could have traveled with the photons and you had an odometer to measure displacement through the space around you, that's the reading it would show.

Redshift only tells us by how much space has expanded during the time that the light was in transit. By using some model, we then convert that to a measure of 'distance then' and 'distance now'. This is the 43 Mly and 46 Gly of the LCDM model respectively. Light has not traveled any of those distances, it has done 13.7 Gly in that model.

"But my point was that optical distortion from different expansion of space is already recognised in the standard model..."

You seem to equate 'spatial expansion' to 'optical distortion', which is a bit of a problem. Flat spatial expansion does not distort images; their images represent the perspective of the true light-travel distances, as defined. The reduction in apparent size exactly fits this distance.

I'll defer comments on your other points, until we have some agreement on the above basic issues, one way or the other; otherwise we will be arguing in circles. As it stands, I do not quite follow what your saying. My motivation for continuing to work on the simulation is to try and determine whether it is true that your model will predict the things we observe. I'm not yet convinced of that...

Regards, Jorrie

PS: I'm writing in "Americanese", because the bulk of technical books and documents seem to be in that 'tongue'. I'm not a native English speaker myself, so I try to stick to one variant.

Hi Cedar, I have now progressed far enough with the hyper-space simulation of your model to understand it reasonably well, at least in general features. I think I can now refute it, at least in terms of disagreement with observation. I will start with a summary of my general findings and then give a few technical details.

The figure that I gave in post #61 is essentially correct in representing your model's radially changing density postulate. See that post's point 7 for some explanation, if required. The distorted hypersphere has variable spatial curvature over observation distances.^(a) So, it has to give some 'distortion' (as you called it) in the angular size measurements of distance objects/structures. This is not observed.

If curvature is zero (flat), parallel lines remain parallel and there is no possibility of large scale magnification or reduction of images of distant cosmic objects. If the curvature is positive, parallel line in all directions converge and eventually cross, like in a convex lens and distant images will be magnified. Negative curvature makes parallel lines converge like in a concave lens and distant images will be reduced in angular size.

The observed cosmic curvature from WMAP is that the cosmos is flat to within 1% in all directions.^(b) What's more, it has always been even flatter in the past, so when we look back in time (over distance) we see a very, very flat cosmos. The fact that density may change over time (with the uniform expansion) does not alter flatness. It is only changes in density over distance that is ruled out.

Now, your model gradually changes density over distance and hence cannot be flat. So, unless the cosmos is so large that we cannot observe this radially changing curvature, it is in conflict with observation. If 'your' cosmos^(c) is too large to observe the radial density change, I think the idea is irrelevant anyway - Occam's Razor should be applied and the standard LCDM model preferred.

Regards,

-J

(a) The hypersphere is just an easy polar coordinate way of presentation. The curvature of the circle does not quite represent spatial curvature, which is determined solely by density and expansion rate. However, higher density and less expansion rate does make the curvature more positive in general.

(b) The 95% confidence WMAP value is Ω = 1 ± 0.01, with Ω = 1 meaning 'flat', or expansion rate exactly balanced by the total energy density of the cosmos. This includes ordinary mass ~ 3%, dark matter ~24%, cosmological constant (vacuum energy) ~73%. The latter is sometimes called 'dark energy', but it is only one class of possible dark energies.

(c) That is if your model is physically feasible at all, of which I am very unconvinced. But say you can show that it is feasible, why would anyone take notice if it has no observable consequences? It would then be like 'Lorentz Ether Theory' (LET) in the place of relativity. Identical observations, just a different philosophical base, with little use in science. Detail calculations are much simpler in Einstein's relativity than in LET. I suspect the same issue with your theory.

Erratum: wrong word usage in my prior post here: "If the curvature is positive, parallel line in all directions converge and eventually cross, like in a convex lens and distant images will be magnified. Negative curvature makes parallel lines converge like in a concave lens and distant images will be reduced in angular size."

Should have read: If the curvature is positive, [locally] parallel lines in all directions converge and eventually cross, like in a convex lens and distant images will be magnified. Negative curvature makes [locally] parallel lines diverge like in a concave lens and distant images will be reduced in angular size.

-J

Hi Jorrie,

Sorry about the spelling correction which I hadn't noticed it was automatic by my spell checker as I work in "Word". I endorse the blog concept of no language criticism, but in fact I think your English is clearer than mine. I am dyslexic and a very poor speller without automatic help. BTW English was last determined by the inhabitants of England in the 1800s, America "owned" it in the 1900s and I suspect India will determine its future. We have long been minority users and American is today's democratic choice.

I had not fully appreciated the subtle effects of the standard model on distance measure and I have not worked through examples like this before. My model does not have some of these effects and I was assuming all subtle effects could be ignored to focus on the fundamental differences of the models. Worse still I was thinking about the light travel distance that would have been if there was no expansion but calling it just light travel distance which is wrong and misleading to the reader.

Can you confirm if you think I have now got it right please?

1) If space is flat and there is no expansion the "gods tape-measure" distance is constant and equal to the light travel distance. All optical measures are consistent with that distance. There is no red shift (except that due to peculiar motions such as Andromeda approaching us).

2) If space is flat and expands uniformly for all time (a naïve version of the standard model) the distance between source and observer depends on the time you measure it (the co-moving distance is constant and when multiplied by the expansion factor for the chosen time gives the god's tape-measure distance for that time). Your statement "images represent the perspective of the true light-travel distances" is true because all optical measures will reflect the new "increased" true light travel distance. But my intended statement would have been equally true that compared to the no expansion case the light travel distance is increased because perspective lines are expanded and the "spread of photons" is increased (I was saying they are distorted by expansion - not in the sense a wavy mirror distorts but in the sense a telescope gives a false impression of distance). If the expansion is uniform for all time the red shifts will always correlate with the other optical measures.

But all of this only applies if space is flat and expansion is consistent for all time. Wikipedia on page http://en.wikipedia.org/wiki/Distance_measures_(cosmology) qualifies its distance measure table as follows:

A comparison of cosmological distance measures, from redshift zero to redshift of 0.5. The background cosmology is Hubble parameter 72 km/s/Mpc, Omega_lambda = 0.732, Omega_matter = 0.266, Omega_radiation = 0.266/3454, and Omega_k chosen so that the sum of Omega parameters is 1.

In my model there is no Lambda so there is no expansion effect due to it and there is no critical mass so no logical reason to adjust parameters to critical density value where the sum of Omegas = 1. Of course I do have Hump Slump expansion that tends to mimic critical behaviour over a wide range of matter densities. Until I have a mathematical definition of the Hump-Slump expansion pattern I have no way to determine deviations from the naïve model. In practice I assume space is flat and expands consistently for all time in a yet undefined radially increasing pattern.

3) Before we look at the near Hump-Slump case lets consider a new simpler uneven universe the static "see-saw" model. There is no overall expansion and no change of expansion during our observations but space was distorted in a one-off prior event. To one side of the observer space is progressively more dense or shrunk while the opposite side is progressively less dense or expanded. There are convenient mirrored sources either side that were at equal distances before the event but are now at different distances but still separated by the same amount of differently deployed space. The source on the shrunken side is less far away in distance but has the same amount of space progressively less compressed as we move between it and the observer. Local parallel lines move apart as we travel into space with ever lower density. As the light travels through this space the sideways spread of photons and the apparent light travel distance determined by perspective are both increased. The source on the expanded side conversely is further away but its light travel distance is reduced by the increased compression of space it experiences while travelling. The result is that the source objects are both seen as identical "images".

4) The naïve version of the Hump-Slump model is closely comparable with the naïve standard model "2" above. There is no co-moving coordinate but we can define a "Consistently moving" coordinate equi-spatial between the objects as in my diagram. We then see the effects of expanding space as in the standard model overlaid by changing effects similar to the static ones in the "see-saw" model. Light travel distances never shrink in this model (thank heavens!) but they do increase at different rates.

You have said: You seem to equate 'spatial expansion' to 'optical distortion', which is a bit of a problem.

I hope you can now see the sense in which I do see spatial expansion and optical distortion as equivalent effects when compared to the light travel distance in a static universe. If the model allows space to be contracted and thus light travel distance to be reduced at least in relative terms it is an important concept.

I do now see that your statements about the red shift of the CMB are correct for the full standard model.

Kind regards

Cedar

Hi Cedar, in brief, my answers to your numbered points, and a surprise...

1) Correct

2) "I was saying they are distorted by expansion - not in the sense a wavy mirror distorts but in the sense a telescope gives a false impression of distance".

OK, but I do not view increased light travel distance as a 'distortion', I meant it as like a proper convex or concave lens that magnifies or reduces an image respectively. Flat space does neither, despite expanding.

"... Omega_k [curvature density parameter] is chosen so that the sum of Omega parameters is 1"...

In the standard model Omega_k is zero for all practical purposes. Your model cannot have Omega_k = 0, because this requires the same critical density everywhere simultaneously.

3. "The source on the expanded side conversely is further away but its light travel distance is reduced by the increased compression of space it experiences while travelling.The result is that the source objects are both seen as identical "images"."

This does not work for an average near flat cosmos (Omega ~ 1), with one side expanding faster then the other. This is what I calculated for post #67 and there is a clear difference in the observations in the two directions. I used the equations of the reputable David W. Hogg in his paper: Distance measures in cosmology, eq. (16), for the Comoving transverse distance. The magnification and reduction are not canceled out by the expansion differences. At z=1 it is only about 10% difference, but it grows rapidly to ~ 50% difference at z=8, the farthest galaxies that we can observe today.

4. That said, there is however cases where the lack of canceling is so small that it is probably not observable with the accuracies we have today. Let's say there is no dark energy, with dark matter present only in our region of space, with progressively less DM as we look farther out. Let's say it gives us a total local density parameter Ω ~ 27% of critical density (of which ~ 24% is dark matter, as observations suggest); but at z = 1, some 9 to 10 billion light years away, say Ω ~ 3% (all ordinary matter). Note that this not a 'flat' cosmos, but a very 'open' one.

However, it would be consistent with an inflationary big bang, with us residing in a unique 'hot spot'^(a) that was about 8 times denser (and hotter) then the regions today sitting at z = 1. It would be much like your hump-slump model, but with "roughly standard physics" driving it, I think. I do not quite know how to correctly simulate such a non-homogeneous case dynamically, but I have approximated it with my homogeneous cosmo-calculator and Hogg's equation 16 for the two different density parameters (27% and 3%, without cosmological constant).

I 'observed' in both directions - first 'from here,' to a structure in the far (3%) region at z = 1 and then from 'there', but this time a similar sized structure in our 27% density neighborhood^(b). I find a 1 % difference in apparent size (Comoving transverse distance), which is far outside the capability of today's "precision cosmology" (when all observational uncertainties are factored in). Hence, despite the different spatial density gradients, the structure nearly 'looks the same' in both directions - as you postulated, but with a different physical model.^(c)

I'll still need to verify this better - it may contain errors and other observations that refute it - but at least it seems intuitively reasonable. Shows you, one must never give up too soon.

Regards, Jorrie

(a) This level of hot spot is not observed anywhere, but we will never know if there may be some like it outside of our observable universe. They may perhaps be common on the ultra-large scale - as 'island universes'...

(b) I made the 'physically sound' assumption that structures do not expand, just the distances between them do.

(c) Note that the only 'physically sound' way in which this expansion can get started is via an inflationary BB, otherwise the whole thing should collapse into a black hole before anything can happen. I think your model will suffer this fate...

-J

Hi Jorrie

We have to nail whether expansion/contraction magnifies/diminishes an image. You have said "Flat space does neither, despite expanding" I think differently.

To be absolutely clear we are discussing a naïve model with flat space and completely consistent expansion for all time. There are no other adjustments to be made and specifically no cosmological distance algorithms are relevant to this simple model. We can widen our discussion when the mechanism is clear.

1) First let me try an analogy. A circular balloon like a tyre tube has a rubber sheet stretched across. A man draws two converging lines (and the joining line at the wider right hand end) as part of a triangle of perspective pointing to a light bulb 10 feet to the left. I did not tell you he is in an air lock and he pumps it down to half pressure so the balloon and diagram double in size. Both the wide separation of the lines on the right of the diagram and the narrow separation of the lines on the left double in size as does the width so the angle is unchanged. The perspective triangles projecting from these lines before and after expansion are congruent but one is double the size. So the point where they converge is now twice as far away at 20 feet.

Would you believe he then adjusts the air lock pressure to twice the balloon pressure? This time the congruent perspective triangle is half the original size and points to a place only 5 feet away. These are "Flat pressure regions" that have simply expanded and they do change the size and distance of images. If we had a "space lock" and a pen that could draw fixed perspective lines on space we could repeat the experiment with flat space time as it expands to show the same result. Do you agree?

2) Now consider a photon on a 1000 light year journey. In my first case it travels through expanding space that will double its size over the journey. After 1 year it has covered 1ly of the journey but the space ahead has expanded by about 0.999lys. Next year it has covered about 2lys and space ahead expands by about 0.998lys etc. The photon eventually gets there because the remaining space gets smaller so the expansion ahead decreases. The perspective image of its origin is constantly updated to reflect the new space density the photon currently sits in right up to the destination. In my second case the space ahead is contracting from 1000lys to 500lys. After one year it has covered one light year but the space ahead has contracted by about 0.499ly etc. The same logic would apply if the photon was travelling through space that was unchanging but frozen with a density gradient from one end to the other (The static see-saw model I introduced last time). Do you agree?

3) In my model it is the space that had already expanded to double the observer's expansion (i.e. is 2 units of distance away) that sends light into (relatively) contracted space that gets its light travel distance shortened to half (1 unit) and its image perspective adjusted from double distance to the light travel distance (1 unit). It is space that has only expanded by half (0.5 units) that sends light into expanded space that gets its light travel distance extended to double (1 unit) and its image perspective adjusted from half distance to the light travel distance (1 unit). Do you agree?

Sorry if all that is a bit heavy but we do need to agree whether the mechanism works or not in simple examples before we can apply it to realistic models.

4) You have then presented your modelling using distance calculation methods derived from the current model. I am pleased you got some results and I will investigate them and Hogg's work. I am not yet sure if it is valid to apply these standard model measure algorithms to my non-standard model. I had not expected to see us "residing in a unique hot spot" in my model. We should be the same as everywhere else in a shell of equal radius with hotter inside and colder outside along any universe radius.

As you know I think the recombination event crossed the then small universe faster than light speed so there never was a strong contrast with the instant recombination of the current model. With a low Hubble constant and very little acceleration observed in the real universe the Hump Slump effects are not dramatic today. I would like to think more about this before drawing a conclusion.

5) You have said: (c) Note that the only 'physically sound' way in which this expansion can get started is via an inflationary BB, otherwise the whole thing should collapse into a black hole before anything can happen. I think your model will suffer this fate...

My expectation of my model is quite different. I think the intense density gradient in the first moments (ranging from the highest density ever possible to zero density in a tiny radius) produces an expansive gravity like force that will overwhelm any attempts to curve space by mass-energy. I believe this mechanism to prevent the immediate collapse is one of the great strengths of the Hump Slump model.

The mutual gravity was demonstrably overcome then (the universe did expand) and it still is today - though more gently. It is during this period when the radial components only of mutual gravity were resisted that the circumferential components were unhampered that mutual gravity would have been very strong at short range and structure would have started to form early.

I notice that you have never challenged me when I describe The "Narrow" Theory of Space Density. I do not believe in Inflation, but that is the subject of the "Wider" Theory of Space Density.

I will be away for a couple of days and may not be able to respond quickly.

Kind regards

Cedar

Hi Cedar, I think the root of our problem may be an interpretation of what 'flat space' means. You wrote: "To be absolutely clear we are discussing a naïve model with flat space and completely consistent expansion for all time."

Not sure what you mean by "consistent", but if it refers to a constant expansion rate, then it can only be 'flat space' if it is completely empty (no normal/dark matter and no dark energy, i.e. Minkowski spacetime). The cosmological equivalent of 'flat space' (zero spatial curvature) is one with energy content, but where space expands exactly at the critical rate for the energy density of the time, which may be decreasing as space expands, depending on what that energy is. Or, we can state it the other way: if space is observed to expand at a specific rate, then it to be 'flat', it must have a specific (critical) energy density at that time.^(a)

If the above is what you meant by "consistent", it is correct, but then you will have to explain how your model will ensure 'flat space', despite an apparent lack of enough energy (e.g., no dark energy and too little matter for the expansion rate observed).

A constant expansion rate can only result in 'flat space' forever if some form of energy is continuously created at the correct rate (normal/dark matter or dark energy of a special kind, not exactly lambda^(b)). If we only take the observed normal matter into account, our universe (and your model) must be 'wide open', surely not flat. You may claim that your model does not comply with the standard physical cosmology equations, but then what physics does apply?

The important thing is that if you cannot explain the above in a physically sound way,^(c) you are faced with the dilemma that your model sports hyperbolic curvature. This reduces the image (angular size) of a distant object, when compared to the linear distance perspective of 'flat space'. This is what Hogg's equation 16 says (in fact for Omega_lambda=0, one can use his eq. 17).

I have repeated my prior calculations using eq. 17 and a 3% normal-matter-only cosmos. I still get a 10% angular change at z=1 and some 50% change at z=8 (compared to a flat cosmos).

Regards, Jorrie

(a) An interesting way to look at it: energy (of any sort) curves space positively and expansion rate curves space negatively. We have flat space only when the two effects cancel exactly. As an aside, vacuum energy (lambda) has the peculiar property (negative equation of state) that does both simultaneously.

(b) Standard lambda will eventually accelerate the expansion, while keeping the curvature zero (if it is zero now, as observations suggest). Inflation is theorized to have 'delivered' a precisely flat, rapidly expanding space, possibly by means of an extremely large lambda. There are theories of how this large lambda got reduced to the tiny one that is compatible with today's observations, but not all problems with that have been solved.

(c) I am puzzled as to why you want some "new physics" that will probably be even more difficult to comprehend and explain than lambda. I'm sure that in the end you will need something similar to lambda…

-J

In my post #, I wrote: "Let's say there is no dark energy, with dark matter present only in our region of space, with progressively less DM as we look farther out."

and

"I do not quite know how to correctly simulate such a non-homogeneous case dynamically, but I have approximated it with my homogeneous cosmo-calculator and Hogg's equation 16 for the two different density parameters (27% and 3%, without cosmological constant)."

I thought this could work, with the caveat: "I'll still need to verify this better - it may contain errors and other observations that refute it - but at least it seems intuitively reasonable."

Well, intuition failed here, because I did a better set of calculations and found that it does not work at all. The overall geometry becomes very 'open' and predictions do not tie up with observations. What did come out is that one needs the opposite: a low density in our vicinity and a normal density (Ω=1) average on the large scale - most interestingly, without dark energy, but with dark matter.

I did not simulate this, but remembered such a postulate being advocated some time ago, around 2008. I now found that David Alonso et. al did an accurate analysis and simulation of said postulate. They reported in Large scale structure simulations of inhomogeneous LTB void models (2010) and other previous papers that they referenced. If they are proved correct in their simulations, they show very good agreement with the latest WMAP data (within observational limits).

I am busy preparing a new Blog post in this for some time next week.

Regards, Jorrie

PS: Sadly, this put paid to any further work from my side on your hump-slump model, because apart from being 'open' and not in agreement with observation (as I wrote in prior post), I think it also suffers from fatal inconsistencies.

Sorry about that...

-J