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# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. You are welcome to comment upon or question anything said on my website (http://www.relativity-4-engineers.com), in the eBook or in the snippets I post here.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

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### Our Observable Universe a Transient?

Posted July 23, 2012 9:00 AM by Jorrie

Our presently observable universe may be no more than a brief transient between two more dominant static states, a recent (quite credible) paper suggests.[1] Granted, the term 'static state' has been redefined a little, but the author uses very convincing arguments for his ideas.

The first static phase is what we normally call 'inflation'. But how can inflationary expansion be static? The trick is to define 'static space' as a constant Hubble sphere radius (the cosmological event horizon), rather than as a constant proper radius.[2] Parts of the universe that fall (or are shifted) outside this radius cannot have any effect on us whatsoever, not even gravitationally.

The standard inflation period had a very high, but constant expansion rate (H) and hence a small constant Hubble radius R_H = c/H, somewhere near the Planck scale (t~10-43 seconds, r~10-43 light-seconds). This (presumed) part of our cosmic history is not all that well understood in present gravitational theory[3] - hence the quest to find a consistent theory of quantum gravity.

At around 1011 Planck time units (10-32 seconds), some form of symmetry breaking occurred, causing a gradual lowering in the expansion rate (H) and thus an increase in the Hubble sphere radius. More space became observable and could influence larger volumes - it is described as the emergence of space. Present observations suggest that we are in this 'emergent phase', but that the Hubble radius is now asymptotically approaching a constant value again.

The Log-Log plot (above)[4] shows the proper radius curve of our observable universe in grey and the Hubble radius in red, both against time. Note the dramatic increase in proper radius during the inflationary epoch up to 10-32 seconds, yet the Hubble radius stayed near the Planck scale. After the symmetry breaking, radiation energy decelerated the very rapid expansion rate until around 300,000 years, when radiation energy ran out of steam, being red-shifted out of contention. Matter energy took over as decelerating agent until around 10 billion years, when vacuum (dark) energy started another (milder) inflation epoch. This resulted in our present constant Hubble radius phase.[5]

The paper goes further and shows that both spacetime and gravity are phenomena that emerge from underlying (poorly understood) degrees of freedom, hidden in the mysterious quantum-gravity 'underworld'. It is pictured in broad terms on the right. For a better resolution graphic, check the main link in end note [6].

The circle represents the Hubble sphere in 2-D. The 'inside' area is called the 'bulk', essentially space that has already emerged. N is the number of degrees of freedom (independent variables) represented in that space - N is presently different for the bulk and the surface.[7] As matter density gets diluted with the increase in the Hubble radius, while vacuum energy density remains constant, Nsur will eventually equal Bbulk and the Hubble radius will become constant again.

As far as I understand, the mechanisms are similar to thermodynamics, where e.g. temperature and pressure are emergent phenomena that are useful without having to know the underlying decrees of freedom (e.g. molecular and atomic dynamics). Today we think we know the underlying facts for matter, but we do not understand the 'atoms' of spacetime yet. However, like with thermodynamics, we can quite confidently use the emergent spacetime phenomena, as long as we get results that agree with observations.

Amazingly, thermodynamics features strongly in present quantum gravity studies. The referenced paper shows how the entropy (hence the temperature) of flat spacetime can be determined, even in the presence of radiation and/or matter. Theorists say that gravity emerges from this entropy by means of quantum entanglement across any event horizon.[8]

The bottom line seems to be that nature dislikes an imbalance between degrees of freedom of the bulk and the Hubble surface, a situation essentially caused by the presence of radiation and matter. By creating more space inside the Hubble surface, the influence of these irritations will effectively be diluted away (energy density becomes smaller). Once this 'transient' is over and Nsur= Nbulk again, the vacuum may perhaps rule undisturbed forever.

One may perhaps ask: is this of any importance and if so, what is the use of it all? Well, since we do not really understand gravity, dark energy etc., any credible new angle on them should be taken seriously, I think.

-J

[1] T. Padmanabhan: Emergent perspective of Gravity and Dark Energy, http://arxiv.org/abs/1207.0505. There were some earlier works in this direction; see e.g. http://en.wikipedia.org/wiki/Entropic_gravity. It does however appear as if Padmanabhan expanded the ideas quite a bit further than previous treatments. His section 5 (page 28) illustrates the newer (AFAIK) insights and is IMO quite brilliant.

[2] The proper radius/distance is what one would measure if the expansion could have been stopped instantaneously. During inflation, proper distances between locations increase and less space falls within the constant Hubble radius. After inflation, the Hubble radius started to increase at a faster rate than the expansion and some of the space that was 'lost' during inflation emerged again (inside the horizon).

[3] There are theories that avoid inflation altogether, e.g. brane cosmology, de Sitter expansion, etc. None of them are without its own set of problems, so cosmologists tend to stick to the one making the fewest assumptions (Occam's razor), although they do not fully understand inflation theory either. Note that even in inflation theory, time did not necessarily start at 10-43 seconds; it is customary to start plots at the smallest time with any meaning, but the constant radius could have lasted for an arbitrarily long time. It simply enters as a time constant into the equations.

[4] Log-log graphic adapted from fig. 15.4 of Relativity-4-Engineers. You can read chapter 15 'Inflation', linked from here. Note that on log-log diagrams, curved lines represent an exponential law and straight lines represent a power-law of some sorts, not as linear law. The sharp changes in log-log slopes represent gradual changes in slope (change in expansion law).

[5] The present Hubble constant, H~70 km/s/Mpc (giving R_H~14 Gly) is still mildly decreasing, but it is already quite close to the final constant rate of H~60 km/s/Mpc (R_H~16 Gly).

[6] A much clearer picture is available in the source, Figure 1, page 19 of the pdf from http://arxiv.org/abs/1207.0505, also linked to in [1] above.

[7] This has to do with the way vacuum energy works - both pushing and pulling on the expansion rate. Radiation and matter only 'pulls' gravitationally and this causes the imbalance, which can only be restored by diluting the effects of their gravity through increase in the Hubble radius.

[8] This is similar to the gravity of a black hole, which emerges from the 'hidden inside', but can be observed from outside the surface (event horizon).

-=-

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#1

### Re: Our Observable Universe a Transient?

07/23/2012 1:46 PM

very interesting....

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#2

### Re: Our Observable Universe a Transient?

07/24/2012 12:36 AM

A very pretty work of art, but not to scale, for obvious reasons - they amplified the late times, where we are. In case someone wonders, my plot is technically to the correct (log) scale, amplifying the early times and compressing the late times.

-J

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#3

### Re: Our Observable Universe a Transient?

07/24/2012 12:31 PM

Are you saying space is contracting? beep...A bubble in the space-time continuum has connected your line to a channeler in the 23rd century. Any message you leave will be broadcast into the future.....beep....Oh damn another bubble.....say wouldn't that be the past?.....These cosmic concepts are confusing Jorrie, what might that mean in layman's terms?

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#4

### Re: Our Observable Universe a Transient?

07/24/2012 3:17 PM

"Are you saying space is contracting?"

Nope, "... compressing the late times" was perhaps a bad choice of words. I meant log-log is compressing the time scale at later times.

"Oh damn another bubble.....say wouldn't that be the past?"

If it is time symmetrical (or time reversible), would it matter?

A thought: every observer, wherever in the cosmos, lives at the center of his/her own observable bubble...

-J

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#6

### Re: Our Observable Universe a Transient?

07/24/2012 4:10 PM

Yes but all of our bubbles seem to be rather close together....So you're saying time is speeding up? or just has the appearance from our point of observation? or no nothing like that at all....

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#8

### Re: Our Observable Universe a Transient?

07/24/2012 5:08 PM

"So you're saying time is speeding up?"

Not quite. Time in truly empty space, e.g. intergalactic space, does go marginally faster than here on Earth, but the difference is insignificant in cosmic terms. Cosmological time is based on an average according to the average density of the observable cosmos. From observations of supernovae near and far, it appears that time has always progressed at this average rate.

The 'compression of time' that I mentioned has to do with the scale on the graph, i.e. just how time is represented, not how it flowed.

-J

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#5

### Re: Our Observable Universe a Transient?

07/24/2012 4:04 PM

Let us play a little mind game here. Some givens:

1. The velocity of electromagnetic radiation IN A VACUUM is observed to be constant over short time periods (i.e., human life-times, maybe even the age of the solar system). [Aside: many years ago, I read that one of the ancient relativity gurus suggested that the constant we call the "speed of light" was nothing more than the ratio of electrostatic and electromotive forces, whatever that means].

2. We have determined that a massive object will have an effect on a photon, or beam of photons. This is normally described as the curvature of space-time induced by the mass (which seems to me just another way of insuring we don't eventually have to assign a value for the "mass" of the photon).

Now, let us throw out this concept of curvature of space (easily done, since we don't really understand mass and gravity anyway, in spite of the recent excitement over the identification of a possible candidate for the Higgs). Let us also acknowledge that regions of space that are pure vacuums are actually quite rare.

Now, at some arbitrary time, let us designate it as t(0), we launch a beam of coherent photons at some arbitrary frequency into space. We know that, were we to launch this arbitrary beam of photons in the atmosphere of earth, the measured velocity of the light would be somewhat less than the theoretical maximum due to interaction with the medium through which it passes. In other words, THE MASS IN OUR MEDIUM IS ACCELERATING (negatively) THE PHOTONS.

Now, our beam of photons, travelling at near maximum velocity, is actually experiencing the universe as being more dense than we perceive it at our leisurely pace- given enough time and distance, the beam will have encountered the same quantity of mass in open space that a much shorter beam over a shorter period encountered here in the atmosphere. Ergo, it will have been negatively acceperated by some amount. Given enough time (or, MIT labs), this light can actually be brought to a standstill. In other words, the past seems to be compressed in time. Eventually, we reach the point in time where the light has lost all of it's energy and can no longer be detected.

Where does this lead us? Back to Einstein's "static universe". The big bang, inflation, the apparent age of the universe, even what we detect as the red shift, are all artifacts of how we chose to measure things, and what we chose to use as our reference point (i.e., the constant "c").

And it gets over the problems of requiring a singularity at the "Big Bang", and allows the universe to be a whole lot older than 13.7 billion years old...

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#7

### Re: Our Observable Universe a Transient?

07/24/2012 4:53 PM

"Let us also acknowledge that regions of space that are pure vacuums are actually quite rare."

Actually, I think the opposite: regions with anything in it are very rare. Empty space is the abundant feature and that's where the speed of light is c. So your beam of photons speeds up ever so slightly.

When the light from the cosmic microwave background (CMB) left the region where we observe it today, the ratio empty:occupied volume was similar to today. Mass concentrations en-route do affect the average speed of light, but because the average density is so low, it is negligible as far as we can tell.

There are evidence that the speed of light could not have changed significantly over time on cosmic scales - nothing compared to the 1000 times change in redshift that we can observe over those distances.

So, I'm afraid that your idea might not fly.

-J

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#9

### Re: Our Observable Universe a Transient?

07/24/2012 6:49 PM

Well, I had to try...Something's got to be done to give us a reasonable age for the universe...

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#10

### Re: Our Observable Universe a Transient?

07/25/2012 5:08 PM

"Something's got to be done to give us a reasonable age for the universe..."

According to the paper that I reported on, the universe could be of any age we like to give it. The problem is that theorists think that there was no matter before some 13.7 billion years ago. Except that is, if the matter sat in another 'bubble' that preceded ours, out of which our universe sprang forth in a region of empty space inside that bubble.

Sir Roger Penrose actually suggested such a scenario in one of those famous Penrose lectures. The final phase of constant Hubble radius essentially means matter has been diluted out of existence and the whole process can start over again - tiny regions of empty space may then collapse and start new matter building phases again, much like we observe today. It could also mean that ours is just one bubble in a Multiverse...

-J

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