Old Black Holes in LQC: Entropy & Information During the Bounce?

[maline]

According to LQC, did the universe before the bounce contain black holes? If so, would they still be around?

What I'm getting at is this: I've read that LQC predicts that the high densities around the bounce tend to smooth out inhomogeneities. If I understand correctly, this is quite promising because it explains the (near) homogeneity of the early universe, and thus the Second Law of Thermodynamics (according to Penrose in "The Emperor's New Mind"). But what about entropy & information during the bounce itself? If there was nothing special-a macrostate with very many microstates- going in, doesn't conservation of information imply that all that entropy should still be present in our universe?

I don't know much even about thermodynamics, & certainly not about BtSM science. That's why I'd like an answer that addresses black holes specifically- hopefully that will be concrete enough for me to think meaningfully about. I'm using black holes as a specific instance of high entropy, because I take from Penrose that they would represent the major component of the entropy in a collapsing universe.

 

[marcus]

The distinction between macrostate and microstate depends on the observer--he defines the map of macrostates each consisting of those microstates which are indistinguishable from his standpoint. Entropy and 2nd law are meaningless unless you have a continuously existing observer, or IOW a well-defined macro-microstate map. I don't see how the 2nd law can be violated at the LQC bounce since entropy is not defined there. One version of entropy can be defined from the perspective of a pre-bounce observer, and another can be from the standpoint of a post-bounce observer.

In LQC gravity repels at extremely high density--which is what causes the bounce. AFAIK horizons and observers are not defined at the bounce.

I do not see how a black hole could continue to exist through the LQC bounce, given that gravity becomes repellent instead of attractive. Any black holes that were present in the collapsing universe would be exploded and their horizons would cease to exist, wouldn't they?

It is just a special case of what I said. Their horizons would cease to exist, their entropy would cease to be defined.

Here's a recent paper on LQC co-authored by Ashtekar. It doesn't address your question directly, but discusses what I was talking about by quantum correction and repellent force at high density. Ashtekar might be someone to ask about entropy and the second law over the course of the bounce.
http://arxiv.org/abs/1509.08899
Generalized effective description of loop quantum cosmology
Abhay Ashtekar, Brajesh Gupt
(Submitted on 29 Sep 2015)
The effective description of loop quantum cosmology (LQC) has proved to be a convenient platform to study phenomenological implications of the quantum bounce that resolves the classical big-bang singularity. Originally, this description was derived using Gaussian quantum states with small dispersions. In this paper we present a generalization to incorporate states with large dispersions. Specifically, we derive the generalized effective Friedmann and Raychaudhuri equations and propose a generalized effective Hamiltonian which are being used in an ongoing study of the phenomenological consequences of a broad class of quantum geometries. We also discuss an interesting interplay between the physics of states with larger dispersions in standard LQC, and of sharply peaked states in (hypothetical) LQC theories with larger area gap.
21 pages, 4 figures. Version to appear in PRD

==quote page 15==
In LQC, the standard effective description [28, 34] has proved to be a powerful tool for un- derstanding the physics of the bounce [11, 28]. As explained in sections I and II, the effective Friedmann and Raychaudhuri equations, (2.10) and (2.11), incorporate the key quantum correc- tions to Einstein’s equations. They bring out the fact that quantum geometry effects lead to a new repulsive force. They show that the force is completely negligible in situations where general relativity is known to be successful. However, they also show that the repulsive force grows rapidly in the Planck regime, overwhelming the classical attraction and replacing the big bang with a big bounce. Thus, the effective equations make the physical origin of the quantum bounce transparent. They have also played a role in the investigations of pre-inflationary dynamics of cosmological per- turbations. In particular, they have helped us understand why the ultraviolet modifications of the background FLRW dynamics can leave imprints on observable modes with longest wave lengths [31, 32].
=endquote==

Equation (2.10) is a key one, it shows the quantum corrections at extreme (near Planckian) density. It is on page 6.

 

[kodama]

how does LQC bounce due to repulsion compare with asymptotic safety UV fixed point?

 

[maline]

I don't see how the 2nd law can be violated at the LQC bounce since entropy is not defined there. One version of entropy can be defined from the perspective of a pre-bounce observer, and another can be from the standpoint of a post-bounce observer.

So you're saying that a pre-bounce observer would describe a very high entropy, including plenty of black holes & whatnot, while the post-bounce observer will describe a homogeneous and low-entropy universe? And this doesn't contradict the 2nd law, because of the change of perspective between observers?
This result doesn't sound very time-symmetric. What am I missing?

observers are not defined at the bounce.

Why shouldn't we postulate an idealized observer who can survive the bounce?

 

[marcus]

Kodama, the last

how does LQC bounce due to repulsion compare with asymptotic safety UV fixed point?

K, you realize I'm not an expert and don't speak with any authority but I think there is a really interesting analogy to investigate. The last time I looked at AsymSafe QG what runs to a UV fixed point are the DIMENSIONLESS versions of G and Λ
In Reuter's notation, k is like a wave number (reciprocal length) so we approach the UV fixed point by letting k→∞
and the dimensionless (pure unitless number) versions are
g = Gk²
λ = Λ/k²

So in practical terms, as k→∞ these two to approach finite non-zero limits (i.e. some point (g*, λ*) on the g,λ plane in that figure Reuter is always drawing) and that obviously means you have to have G→0 and Λ→∞.
In other words, intuitively at least, gravity becomes repellent at high density.
One corresponds to attractiveness (it goes to zero) one corresponds to expansiveness (it gets infinitely large).

It sounds like a bounce, doesn't it?

AsymSafe QG does not have a prior contracting phase, so it does not explain where the expanding geometry "comes from". It does not AFAIK say how expansion from a high density state started, but the very early expansion does look rather much like the second half of the LQC bounce (in which quantum corrections at high density cause gravity to be repellent).

So at least on an intuitive level there is a curious kind of agreement between ASQG and LQC.

 

[marcus]

So you're saying that a pre-bounce observer would describe a very high entropy, including plenty of black holes & whatnot, while the post-bounce observer will describe a homogeneous and low-entropy universe? And this doesn't contradict the 2nd law, because of the change of perspective between observers?
This result doesn't sound very time-symmetric. What am I missing?
...

I don't think you are missing anything. The existence of an observer (e.g.imagine something able to remember the past and predict the future) breaks time reversal symmetry.
AFAICS you summarized the situation accurately.

 

[marcus]

...Why shouldn't we postulate an idealized observer who can survive the bounce?

That's an interesting question! I think the answer may have something to do with the fact that geometry becomes Euclidean at the bounce. In LQC there is a signature change right at the bounce, Lorentzian signature is lost and then recovered.

There are a bunch of recent papers about this. It would be a good thesis, IMHO, to address this question based on the signature change body of research.
If you want to look into it let me know if you have any trouble finding the papers. Aurélien Barrau coauthored one or more, IIRC.
I'm just speculating but I think anything you would consider an observer must be able to interact with its environment. must consist of causal diamonds. must have welldefined lightcones past and future. This structure is nullified by signature change, I believe, and then restored.

There should actually be several explanations why it leads to self-contradiction to postulate an observer (1) who is part of the universe, not outside it, and (2) whose identity persists through the bounce. Signature change could be one possible approach to explaining that. Anyway it's an intriguing question.

 

[kodama]

Kodama, the last

K, you realize I'm not an expert and don't speak with any authority but I think there is a really interesting analogy to investigate. The last time I looked at AsymSafe QG what runs to a UV fixed point are the DIMENSIONLESS versions of G and Λ
In Reuter's notation, k is like a wave number (reciprocal length) so we approach the UV fixed point by letting k→∞
and the dimensionless (pure unitless number) versions are
g = Gk²
λ = Λ/k²

So in practical terms, as k→∞ these two to approach finite non-zero limits (i.e. some point (g*, λ*) on the g,λ plane in that figure Reuter is always drawing) and that obviously means you have to have G→0 and Λ→∞.
In other words, intuitively at least, gravity becomes repellent at high density.
One corresponds to attractiveness (it goes to zero) one corresponds to expansiveness (it gets infinitely large).

It sounds like a bounce, doesn't it?

AsymSafe QG does not have a prior contracting phase, so it does not explain where the expanding geometry "comes from". It does not AFAIK say how expansion from a high density state started, but the very early expansion does look rather much like the second half of the LQC bounce (in which quantum corrections at high density cause gravity to be repellent).

So at least on an intuitive level there is a curious kind of agreement between ASQG and LQC.

do you know at what energy/scale ASQG gravity goes to zero, and what scale this happens in LQC/LQG?

Would it be safe to say gravity in LQC is AsymSafe where the gravity pull exactly balances gravity repulsion hence G=0