Scale of perturbations re entropy, in quantum bounce

[slatts]

In Bojowald's 2010 popularization of Loop Quantum Cosmology Once Before Time, there's a sketchy diagram (on his p.125) showing quantum perturbations in a transitional phase between contracting and expanding universes as widest at earlier times of decreasing volume, narrowing at the singularity-averting bounce, and remaining narrow in later times at smaller volumes. I've read in older books, and in some stuff on the web, that bouncing cosmologies require an increase in volume with each bounce, to absorb entropy. Consequently, it surprised me to see a depiction of the perturbations as being more prolonged during earlier times, although I'm assuming that the increase in their volume is needed to generate repulsive gravity as a response to the negative pressure associated with the contraction of matter due to cooling. I may be making a wrong assumption by figuring that the perturbations are analogous to the burbling drops in air pressure produced by Bernouilli's Principle in such situations as the passage of air over an airplane wing, but, assuming I'm not, does mainstream LQC currently see the proportion of each iteration of the universe that's occupied by the lower density portions of the quantum perturbations/fluctuations as increasing between each bounce and the next? (If it doesn't, the odd thing is that the sketched band representing the perturbations remains at constant width after its closest approach to time zero, which, to me at least, suggests a one-shot bounce rather than an endless sequence of expansions and contractions. Is some imperceptible subtlety in the post-bounce widening of the perturbations implying an LQC bypass of the BGV Theorem?)

 

[marcus]

Hi Slatts, I somehow missed seeing your post earlier. Must have been distracted by other matters when you posted it on Friday. I don't have Bojowald's book but if I understand what you are asking about in a more general sense it is definitely an interesting question! It calls attention to fundamental issues like the definition of entropy in GR context. Robert Wald, who is a prominent relativist (you may know of him) famously made the point that entropy is not absolute, it is observer-dependent. There is a paper by Don Marolf and others that picks up on this, cites Wald, and goes further with it.

You ought to be able to get Marolf et al by googling "marolf entropy" . Yeah. I just googled those two words and got the paper:
http://arxiv.org/abs/hep-th/0310022
Notes on Spacetime Thermodynamics and the Observer-dependence of Entropy
Donald Marolf, Djordje Minic, Simon Ross
(Submitted on 2 Oct 2003)
14 pages
I think there are some unresolved issues here---FWIW I'll just give you my very personal perspective on it and perhaps others will give theirs.

An observer defines a map of state space based on what he cares about and what makes a difference to him. He divides the state space into "macrostate" regions each of which comprises many "microstates" among which he can't distinguish. Like he cares about the temperature and pressure in the room but not the location and speed of every molecule. He's indifferent to which micro state it happens to be, and indeed ignorant which it is. The entropy of a macro, for him, is the log of the number of micros in it. A measure of his ignorance and indifference, if you like.

One problem, I find, is that I can't imagine an observer living through a bounce and (if somehow an observer did, coming out with the SAME MAP of states, caring about the same macroscopic things)

In the LQC bounce gravity becomes in effect repellent for a brief period during extreme density. If gravity repels, how would a black hole keep its shape? Wouldn't it just dissolve into uniform blank high density? Wouldn't any gravitationally bound structure dissolve, be erased? Repellent gravity seems to turn the definition of entropy on its head.

People have different opinions about this. One thing to notice is that with the universe there is no "outside observer". I can imagine a pre-bounce observer and a post-bounce observer, but I think they have different maps. I think there is a problem defining the second law. It could be that the bounce just wipes the slate clean, boils away all matter, dissolves and erases all structure, and starts you off with uniform high energy density together with whatever primordial fluctuations nature provides.

 

[wabbit]

Marcus, I can't seem to find the references now but I also remember seeing several papers (at least some from your bibilo thread) that discuss the spectrum of perturbations in a LQC bounce, ie starting with a FLRW+perturbations contracting universe and looking at what emerges; the general theme seemed to be as you say, that perturbations are washed out as they pass through the bounce, except maybe for the longer wavelengths - and the details depended on the kind of inflation assumed after exit if any... pretty vague but if I find those references I'll post them as they seem relevant to what slatts is asking.*

Also, regarding black holes during the bounce: Usually the bounce has ~planck density, so the Schwarzschild radius is the Planck length - this seems to imply that nothing like a semiclassical black hole could even be defined in these conditions? Actually spacetime as a 4D manifold is probably not a very useful description of what happens "inside the bounce".

* One of them is Wilson-Ewing : Primordial quantum nonequilibrium and large-scale cosmic anomalies

 

[wabbit]

which, to me at least, suggests a one-shot bounce rather than an endless sequence of expansions and contractions.

Sorry this is just a very pedestrian comment, not to do with the substance of your remarks - but most LQC bounce scenarios do seem to involve a single bounce - well I suppose that's just because they are built to fit our current expectation of a non-recollapsing universe so it's not a matter of principle, and it doesn't affect what you're saying...

 

[marcus]

Marcus, I can't seem to find the references now but I also remember seeing several papers (at least some from your bibilo thread) that discuss the spectrum of perturbations in a LQC bounce, ie starting with a FLRW+perturbations contracting universe ...".

Yes! I didn't get into that. Ashtekar and Agullo have a bunch of papers. I'll get links. My post was not responsive enough to slatts, too much my own personal thoughts. You are right, too, about most LQC scenarios being single bounce, too. Why bother with more, just try to understand what was happening around OUR start of expansion and immediately before.

OK, perturbations. Here is an Ashtekar Agullo search
http://arxiv.org/find/grp_physics/1/AND+au:+Ashtekar+au:+Agullo/0/1/0/all/0/1
An Ashtekar Nelson search would do equally well or better, he coauthored all of these, I just happened to pick those two names to search with
Here is some of what it brings up:
2. arXiv:1302.0254 [pdf, ps, other]
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
Ivan Agullo, Abhay Ashtekar, William Nelson
Comments: 64 pages, 15 figures. Published version
Journal-ref: Class. Quant. Grav. 30, 085014 (2013)
3. arXiv:1211.1354 [pdf, ps, other]
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era
Ivan Agullo, Abhay Ashtekar, William Nelson
Comments: 50 pages, no figures. This is first of the two detailed papers which form the basis of Phys. Rev. Lett. 109, 251301 (2012). A few references and clarifications added. Version to appear in Phys. Rev. D
Journal-ref: Phys. Rev. D87, 043507 (2013)
5. arXiv:1204.1288 [pdf, ps, other]
Perturbations in loop quantum cosmology
Ivan Agullo, Abhay Ashtekar, William Nelson
Comments: ICGC (2011) Goa Conference proceedings

Wabbit as you probably know I'm kind of a fan of that very recent paper by Cai and Wilson-Ewing. they are two post docs. It is easier to read than the Ashtekar papers. He is a major authority and the papers are lengthy and thorough. Wilson-Ewing is an Ashtekar PhD, co-authored with him quite a bit, and now is off on his own (LSU, MPI Potsdam). The Cai and W-E paper addresses the issues of what spectrum of perturbations their bounce model predicts, but it is easier to read IMHO.
Their model is basically the essentials of the LambdaCDM standard cosmic model, both collapsing and expanding with a LQC bounce
To get Cai Wilson-Ewing all you need to do is google "LambdaCDM bounce" it will be the first hit:
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
Published JCAP 1503 (2015) 03, 006

Beautiful paper. Ed W-E has been presenting the work at various conferences/workshops since it came out.
In case anyone is interested here is the Stanford-SLAC database author profile.
http://inspirehep.net/author/profile/E.Wilson.Ewing.1

At such extreme density it makes sense that the "Hubble radius" that matters (for freezing perturbation modes when they expand outside that radius) would be the speed of sound Hubble radius and not the speed of light Hubble radius. We are talking near Planck density, what medium is not opaque? I hadn't thought of that until I saw the Cai W-E paper.

 

[wabbit]

Ah nice, thanks!... Now I don't have an excuse anymore not to re-read those papers and try to understand a little bit more of them:)
Yes I also find this line of inquiry quite fascinating (but then again as you know from our recent exchange about Smolin's trialities, I'm easily fascinated - as befits a wabbit)

I was disappointed recently however when looking at LISA etc capabilities that it seemed observational quantum cosmology through (direct detection of) gravitational wave background still seems rather far off, so the signature read off CMB might be the best we have for a while - I know, one shouldn't get greedy, who'd have said 10 years ago that such a thing as observational quantum cosmology might even be within reach? I suppose Ashtekar might have, but to me it was a rather well kept secret then.

 

[slatts]

Thanks, guys; I was just about to give up and turn the TV on instead.

The articles you've cited will definitely give me quite a bone to chew on (-usually the only way to shut me up, as you can see by my last post, elsewhere).

What I'm getting at, on the one-shot-bounce question, is whether there's any principle in physics that rules out the endless regression, kitties-in-kegs, Russian dolls, picture-of-a-girl-on-the-cereal-box-looking-at-the-picture-of-the girl-on-the-cereal-box kinds of scenarios, at least in cosmology. (To relate it to my mode of infinite pre-postponement, I almost picked ProCrAssTinator for my Forum name, but went with Slatts instead.) It sounds like both of you know enough physics to give me a read on that; if so, I'd appreciate it. (In case you think it might be of greater interest to put the question out as a new thread, have at it; I'll be looking for something like "Endless Regression", and you're welcome to cut-&-paste any of this into its start; if you'd rather I declassify MYSELF with such a move, just let me know.)

 

[wabbit]

I don't know physics, I'm just a tourist - but that hasn't stopped me from replying so far and it won't now : ), so -

As far as I know, no, there's no principle that rules out a succession of expansion-collapse-(bounce)-expansion-collapse... And as you know such scenarios have in fact been considered in the past.

However, I believe the reason we don't see such scenarios studied now is that our current observations in cosmology indicate that our universe is on a path to perpetual expansion, not recollapse, so such scenarios don't seem relevant to our universe.

The conclusion that our universe isn't going to recollapse is not one of principle either, it is just the result of fitting our best cosmological observations to our best models - but my understanding is that as we speak it is quite robust, and would require fairly big changes in model and/or observations, to disappear. This conclusion is also fairly recent, though I can't recall now when exactly that was.Note - i may be misinterpreting your question though, because there are no russian dolls here - no universe-within-a-universe or anything like that, just a long series of ups and downs. And there are exotic theories that do propose fancier things such as multiple universes and such, perhaps even nested ones, but I neither know them nor do I have much interest in learning more about them.

 

[wabbit]

At such extreme density it makes sense that the "Hubble radius" that matters (for freezing perturbation modes when they expand outside that radius) would be the speed of sound Hubble radius and not the speed of light Hubble radius. We are talking near Planck density, what medium is not opaque? I hadn't thought of that until I saw the Cai W-E paper.

And the meaning of those references to the sound radius hadn't struck me till you pointed it out here. Thanks!

With so many papers discussing various aspects of this, it would be great if someone were to put together a book on (perturbative) quantum cosmology that catered to the non-technical audience (I haven't read Bojowald, maybe that's what I'm looking for?). - perhaps a bit of a niche market though:)

Edit: reading Martin Bojowald : Quantum cosmology: a review now.