For myKK, in bounce models what drives prior contraction?

[marcus]

Big bounce cosmic models, as a research topic, shouldn't be confused with cyclic models where there is a recurrent bounce. The earlier thread by mykamakiri got a bit distracted because of that kind of confusion so I thought I would split off a separate topic just to focus on the question in the case of a one-time bounce.

There's a legitimate question here! It's not a hard one to answer, but it's reasonable to ask and it can get lost in an unfocused broader discussion.

Actually, in the earlier thread by myKK (BTW kamakiri means praying mantis) the question was already answered by Wabbit who pointed out that the Friedmann equation is time reversible----a cosmos with the same physics and same physical constants as ours would contract along the same curve (reversed) as ours is now expanding.

But let's look at that at a basic level and get some intuition for the role played in the collapse by the cosmological constant Lambda which we assume to be the same in the collapsing phase as it is in the expanding phase we are now in----just as we do with all the other physical constants.

 

[marcus]

We can see the effect of the Lambda constant in the shape of the scale factor curve that you get by solving the basic Friedmann equation for contraction and expansion. The scale factor a(t) tracks the size of cosmic distances compared with their present size---a(now) = 1.

When the slope of a(t) is down that means distances are contracting. When the a(t) curve is CONCAVE seen from above that means the collapse speed slows of any given distance you might be watching---the downwards slope is getting more moderate.
Or in the expansion phase, concave means the upwards slope is getting steeper.

this is characteristic of low matter density---early in the contraction phase and late in the expansion, e.g. where we are now. The present is t=0.8 on the timescale used in this figure. You can see that by t = 0.8 we are already in the concave (seen from above) increasing slope regime.

The intuitive point here is that where the density of matter and radiation is LOW the cosmological constant effect shows thru (slowing contraction and speeding expansion). But where the density of gravitating substance is high, gravity overwhelms the effect of Lambda so collapse speeds up and, after the rebound when expansion has been given an initial kick, gravity slows expansion down. This happens in the time interval from about t= - 0.4 to t= +0.4. You can probably see the convexity in that range.

According to recent Planck mission figures this changeover from deceleration to acceleration happened (on this timescale) at around t = 0.44. But I just gave it as 0.4 so as not to overstate the precision. If you look closely at the curve you can see the change taking place between 0.4 and 0.5.

There is more to discuss. This curve is a solution of the Friedmann equation for spatial flat case, with the standard cosmic model assumptions about Lambda and matter content (ordinary matter plus radiation plus cold dark matter). The standard model is usually denoted LambdaCDM or ΛCDM. We can give a simple statement of the Friedmann equation and get some intuition about how the curve is generated by the equation model. I'll pause here in case anyone is reading the thread and might have questions.

 

[slatts]

Aguirre & Gratton in 2003, shortly after the last revision in the Borde-Guth-Vilenkin Theorem that prohibits "past-eternal" inflation on "classical" (i.e., non-Quantum Mechanical) grounds, wrote the Arvix paper "Inflation without a beginning: a null boundary proposal". What they seemed to be describing was an exponentially expanding universe, that (if I was reading the text and diagrams between the equations correctly) is separated by a hyper-exponentially expanding region of totally empty space from an exponentially contracting region. In 2013, Vilenkin, in another Arvix paper called "Arrows of time and the beginning of the universe", associated their idea more with Hawking and Hartle's "wave function of the universe" than with the inflationary cosmology, but confirmed A & G's association of the expanding and contracting universes with dual arrows of time pointing in opposite directions, even while pointing out the fact that the opposition of their directions lacks a physical motivation. Since inflation has more predictive power than H & H's 1970's idea, and since I've heard that General Relativity allows no clear notion of time separate from space whereas Quantum Mechanics depends very heavily on one, I'm sort of guessing that the one-time bounce whose physical motor the quantum theorists are working on would be a sort of "Time Zero" forming a permanent and central feature of the landscape.

To a history major like myself, a central role for the concept zero, moving it from one end of the line to the center, would be real "timely" about now, but please let me know if I'm off the beam.

 

[Monsterboy]

Big bounce cosmic models, as a research topic, shouldn't be confused with cyclic models where there is a recurrent bounce.

Are cyclic models ruled out due to entropy ? I remember reading that somewhere , if that is the case why is it still under discussion? Maybe they are not ruled out completely , I don't know.

 

[slatts]

Are cyclic models ruled out due to entropy ?

I think Marcus broke this off from Mykamikiri's thread (which was kind of hard to find; it's in the "Cosmology" forum) to focus on the BIG bounce models. (Even so, since I've heard that it's the buildup of entropy density, rather than the buildup of entropy overall, which requires an origin even for cyclic models, it might be interesting if someone who really knows physics would relate that to the "matter density" of Marcus' OP: In Vilenkin's views, matter density is informally suggested as a time variable within the local or "bubble" universes of a multiverse, so that, if these two densities do correlate directly, it seems to me that the acceleration of cosmic expansion that was first detected in the late 1990's might put us in a rare period when entropy isn't increasing quite as fast as it usually has, and maybe some trillions of reruns of particularly old and common experiments could provide some faint confirmation of this.)

Just to put my own half-baked post into more comprehensible English, it appears to me that physics uses the verb "bounce" to refer to an action whose past and future are independent of it. (You can include the approach & departure of something like a ball in a colloquial English bounce, but not in a physics English bounce.) Also, the Aguirre-Gratton scenario implies that the one that they'd hypothesized is a "block universe" as far as time is concerned. (I know a lot of people find the block universe idea kind of annoying, but, if the motions in the endless repetitions of matter--each in a bubble universe physically inaccessible from any of the others within a multiverse--are averaged together, the cancellation of their motions in the spatial direction of one by their motions in the spatial direction of another would probably make it kind of inescapable.)

 

[marcus]

Are cyclic models ruled out due to entropy ? I remember reading that somewhere , if that is the case why is it still under discussion? Maybe they are not ruled out completely , I don't know.

Excellent question! The people who say "no" can point out that entropy is, as far as we know, observer-dependent. It is defined in various ways, for example, in terms of an observer's coarse-graining--the map that specifies the macrostates--collections of microstates which are indifferent/equivalent to that observer. Post-bounce observers are necessarily those for whom the conditions at the start of expansion had low entropy.

To apply the second law one would need an observer (and thus a definition of entropy) that persists thru the bounce. If entropy is not continuously well-defined, it is meaningless to ask if it is increasing thru the bounce, or if it is non-decreasing.

The situation is somewhat analogous to the issue of global energy conservation in GR. In GR there is no satisfactory definition of global energy. So one cannot say that it is conserved (If you haven't seen his article, google Sean Carroll "energy is not conserved in an expanding universe").

 

[spacejunkie]

There is a recent paper by Barbour, Koslowski and Mercati which seems to be a new approach to explain why the universe started with low entropy.
Here the bounce is a "Janus point" which is the origin of two arrows of time facing in opposite directions. There is no contraction from a previous phase and Janus points arise generically at the point of maximum disorder.

"Entropy and the Typicality of Universes"
http://arxiv.org/abs/1507.06498v2

" The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by inappropriate transfer of the traditional concept of entropy to the whole universe. Use of what we call the relational N-body problem as a model indicates the need to employ two distinct entropy-type concepts to describe the universe."

 

[Buzz Bloom]

Hi Marcus:

I find the concept of a single bounce history for our universe to be fascinating, but a bit confusing. Here are some questions.

1. Is there any possible scientific approach that could ever confirm that the history of our universe definitely included a bounce?
2. Is there any possible scientific approach that could ever confirm that the history of our universe definitely did not included a bounce?
3. If the history of our universe did include a bounce, could that be an alternative to inflation as a "solution" to the horizon problem?
4. For a universe in the state of collapsing rather than expanding, do you have any ideas about what the physical mechanism could be that could cause the bounce?

Regards,
Buzz Bloom

 

[marcus]

3. If the history of our universe did include a bounce, could that be an alternative to inflation as a "solution" to the horizon problem?

Yes. Google "LambdaCDM bounce" and have a look at the December 2014 article by Edward Wilson-Ewing and Yi-fu Cai.
They dispense with inflation. And they use a universe like our standard cosmic model (ΛCDM) except it is contracting. And they get results similar to what we see. (consistent with observation). If you have any trouble finding the article please ask for help--it is readily available to download free.
==quote==
3. If the history of our universe did include a bounce, could that be an alternative to inflation as a "solution" to the horizon problem?

4. For a universe in the state of collapsing rather than expanding, do you have any ideas about what the physical mechanism could be that could cause the bounce?
==endquote==
The bounce is a robust prediction of the most common line of research in quantum cosmology. It is normally what you get when you quantize GR along LQG lines and run the cosmic model back in time. Quantum effects dominate at extremely high density and you get a bounce rather than a 'singularity'.
('singularity' is where a model breaks down and no longer gives meaningful numbers---the quantized model does not blow up as the classical model did, so 'singularity' is avoided).

There are hundreds of research papers about this. Let's see what Stanford's Inspire database turns up if we do a search with keywords "quantum cosmology". Have to go briefly, back soon

 

[marcus]

http://inspirehep.net/search?ln=en&ln=en&p="quantum%20cosmology"%20and%20NOT%20d%201900->2008&of=hb&action_search=Search&sf=&so=d&rm=citation&rg=25&sc=0
(865 "quantum cosmology" since 2009)

http://inspirehep.net/search?ln=en&ln=en&p="quantum%20cosmology"%20and%20not%20"loop"%20and%20NOT%20d%201900->2008&of=hb&action_search=Search&sf=&so=d&rm=citation&rg=25&sc=0 (442 "quantum cosmology and not loop" since 2009)

Not all bounce quantum cosmology is Loop (LQG inspired) but basically all Loop QC models achieve a bounce.
Roughly half of all QC research includes the Loop approach. So at least half involves a quantum bounce at the start of expansion.
Again, Loop is not the only approach that gets a bounce---there are other types being actively researched ("matter bounce" e.g. by Brandenburger, teleparallel e.g. by Odintsov). Cosmology with quantum bounce has become POPULAR among researchers. There was always dissatisfaction with the 'singularity', considered unphysical, and a simple cure for that is to include quantum effects that resist infinite compression and cause a rebound. So it's naturally interesting to researchers.

You see this interest when you look not only at the publication numbers but also at CITATIONS. In the above listings each paper is shown with the number of "cites" received in other research. (The lists are ranked by cites so the most highly cited appear first.) You can see that in the list of 865 quantum cosmology papers the top 100 or so are mostly about bounce cosmology models. Bounce models get most of the cites in QC research.

If you are curious I'll try to explain in more detail why that is. Partly it is the concreteness and simplicity. When you quantize GR gravity quantum effects make gravity REPELLENT at high density so you get a rebound--you don't have to "make up" any hard-to-imagine exotic particle field or never-before-seen situation. You just crank a conventional model back in time and you get high density and gravity is repellent and then the universe is expanding as you go back further---and your are in a standard model universe like ours except contracting. You get avoidance of singularity for free. You get something you can calculate with.

A good example of the kind of research that comes out of this is the Wilson-Ewing paper I mentioned earlier.
http://arxiv.org/abs/1412.2914
A ΛCDM bounce scenario
Yi-Fu Cai, Edward Wilson-Ewing
(Submitted on 9 Dec 2014)
We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant. Furthermore, the modes that exit the (sound) Hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt, in agreement with observations. We assume that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, and this ensures that the big-bang singularity is resolved and is replaced by a bounce. We calculate the evolution of the perturbations through the bounce and find that they remain nearly scale-invariant. We also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter, the Hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation, and the curvature scale that the loop quantum cosmology bounce occurs at. Importantly, as this scenario predicts a positive running of the scalar index, observations can potentially differentiate between it and inflationary models. Finally, for a small sound speed of cold dark matter, this scenario predicts a small tensor-to-scalar ratio.
14 pages, 8 figures, JCAP03(2015)006
This does not need inflation in order to get the usual features that inflation was invented to produce.

 

[Buzz Bloom]

Hi @marcus:

Thank you very much for your helpful posts.

Except for one detail, I find the bounce scenario aesthetically much more satisfying than the inflation scenario. The one detail is the difficulty I have trying to imagine the beginning of the universe in its contracting state. If t = 0 is the time of the bounce, then I can sort of imagine the universe beginning at time t = -∞, but in that scenario, now would be an infinite time since that beginning.

Regards,
Buzz