Does the big rip happen in LQC?

[MTd2]

Does anyone know?

 

[tom.stoer]

As far as i know it doesn't.

LQC produces gravity-induces corrections to the matter interaction at high densities which may explain inflation rather generically w/o any inflation field, customized potential or special interaction term. At a few 10 - 100 Planck-length these effects should become invisible.

The big rip is due to a special feature of a specific dark energy model - which applies at low densities / in the vacuum / at large scales. Neither LQG nor LGC make predictions regarding DE.

There are some speculations from Smolin that LQG-like models could lead to an effect which looks like accelerated expansion and which could replace DE; the idea is that there is a mismatch between micro-causality (according to e.g. spin network links) and macro-causality (according to the derived smooth manifold). As far as I know this is really speculation as there are no detailed calculations available.

There are ideas that LQG could be based on a q-deformed SU(2) rather than standard SU(2). In these models there is a relation between the deformation parameter q and a cosmological constant (but keep in mind: the big rip cannot be generated by a standard cosmological constant!)

 

[francesca]

Yes, it does!

As far as I know it does

This result is well explained in a paper by Param Singh:
Are loop quantum cosmos never singular? http://arxiv.org/abs/0901.2750
The behavior of loopy universe is studied for an equation of state that has been used in literature to study quintessence and phantom dark energy.

Big Rip is a future singularity that emerge for a phantom-like equation of states, namely a scalar field with negative kinetic energy. At finite time, the scale factor go to infinity, but because of this wired EoS the energy density increase with the scale factor and go to infinity too. So, also Big Rip deals with high energy density and it's cured by LQG since the energy density is bounded by a certain critical density next to the Planck scale.

More puzzling is the situation with other kind of future singularity arising in this context: Big Rip is the number I, then you have the number II Sudden Singularity, the number III and the number VI, that differ depending on which/how they diverge scale factor, density, pressure, curvature and so on... One should notice that not all these singularities are so meaningful, since there could be a divergence even if the system is not "destroyed" and the equation of motion can be continued across the singularity.

Cheers, F

 

[MTd2]

Thank you for your answers. The purpose of my question is to make sense out of the initial bounce that is the big bang in LQC. It seems a crazy coincidence that our universe is the last in cycle of infinite cyclic universes.

Last night I remembered of the big rip. And I thought why not bouncing back? Extreme regimes means that quantum corrections become important just like in the very low energy limit. For example, String Theory does not have black holes, in principle, but fuzzy spheres. Like, you don't cross a black hole, as you enter it, you are dissolved and your strings are incorporated to a dense string gas.

String theory is not the only theory where that happens. See Matt Visser for a discussion:

http://xxx.lanl.gov/abs/0902.0346

 

[tom.stoer]

I have completely missed this paper!

Seems that singularity resolution is a rather generic feature of LQC. It is interesting that the big bang singularity and the big crunch, big rip, etc. are cured by the same mechanism. This comes somehow as a surpsise because the origin of the singularities is different:
- big bang is a generic feature of GR (Hawking / Penrose singularity theorems)
- big crunch, big rip etc. are not generic features of GR but are due to specific matter / energy content

So it seems that LQC can cure more than GR can be blamed for ...

 

[MTd2]

Just one thing. After the bounce in the big rip and bounce in the big bang several times, shouldn't the inhomogeneities become bigger and bigger?

 

[Dmitry67]

Dont forget that before the Big Rip cosmological horizons become closer and closer, and hence they emit more and more high-temperature radiation. So just before the Big Rip vacuum becomes filled with very dense radiation, which can prevent the Big Rip because of the positive energy density.

If LQG is consistent with Hawking radiation on the big scales, then it MUST happen.

 

[marcus]

... bounce in the big bang several times...?

I'm curious why you say "several times". One of the most common LQC models has only one bounce.

One cannot automatically assume there are several bounces, or that there are an infinite number.

In a given LQC model there might, for instance, be a contraction of infinite duration, followed by a bounce, then followed by an expansion of infinite duration. That's a common scenario in fact.

But the question of "what happens to the anisotropy?" is a good one! Likewise the question "what happens to the entropy?" At least I think they are good questions, and I think not fully answered yet. People are still studying very simple cases of non-singular cosmology.

 

[MTd2]

I'm curious why you say "several times". One of the most common LQC models has only one bounce.

...> 1 bounce for the big rip -> 1 bounce for the big bang -> 1 bounce for the big rip ->...

cyclic

BTW, it is in the paper posted by Francesca. A bounce in the big rip.

 

[MTd2]

If LQG is consistent with Hawking radiation on the big scales, then it MUST happen.

Hmm, nice heuristic thought! :D Never thought of that. Thank you.

 

[marcus]

The purpose of my question is to make sense out of the initial bounce that is the big bang in LQC. It seems a crazy coincidence that our universe is the last in cycle of infinite cyclic universes.
...

MTd2, this is what I am wondering about. Do you think that the LQC "initial bounce" occurs only in that infinite cyclic context?

BTW I think the answer to your main question is NO. Typically a big rip does not happen in the LQC model.
I think Francesca said that a big rip CAN happen (if you put in something to cause it) but I don't think she was saying that it must happen or that it always does happen.

If Francesca is still here, maybe she will clarify what she said.

You would have to put something special in by hand to make it happen.

If you really want a big rip to happen, you can probably set things up so that it will occur, but it is not a generic feature.

 

[MTd2]

No, I don't think it happens only that context of the cyclic model. But only 1 bounce is something as ugly as supersymmetry. I don't know how to explain right now, but it is disgusting. Fortunately, there is a big contracting bounce.

Alright Marcus, let me say that by big rip I meant that, instead of a big rip happening a big contracting bouncing happens, as it is shown in the paper pointed out by Francesca.

http://arxiv.org/abs/0901.2750
section 4.1, p.10

"The universe instead of ripping apart in finite time, recollapses and the evolution continues."

 

[marcus]

...> 1 bounce for the big rip -> 1 bounce for the big bang -> 1 bounce for the big rip ->...

cyclic

BTW, it is in the paper posted by Francesca. A bounce in the big rip.

No it is not in the paper (by Param Singh) that Francesca posted. The paper does not say that there is a bounce in a big rip.

Or did I miss something? If you think it says that, please find some discussion in the paper and paste it here so we can have a look.

Singh gives a unified treatment of singularities in LQC, he discusses the various possible kinds. He does not say that they are all the same

Let's look at sections 4.1:

4.1. Type I Singularities
If the value of α is chosen between 3/4 < α < 1 and A is positive, then the model gives a big rip (type I) singularity in GR. The scale factor, energy density and pressure diverge at a finite time and the DEC is violated (for all times). There is no big bang in the classical theory (since DEC is violated). The model is devoid of an initial singularity.
In LQC, the big rip singularity is avoided. The energy density initially grows as in the classical theory, however when it becomes comparable to ρ_crit , departures from classical trajectories become significant. Eventually, ρ becomes equal to ρ_crit and the Hubble rate vanishes with ä taking negative value. The universe instead of ripping apart in finite time, recollapses and the evolution continues. The Ricci scalar, its derivatives and higher curvature invariants are bounded in the entire evolution.​

This behavior is not generic. It can happen, according to Singh, if you make it happen. He does not say that it always automatically does happen.

 

[MTd2]

Meh, I posted before seeing your edition to the post. But the universe expands faster and faster, so I guess we live in a kind of universe that has a type I singularity in the future, since we classically perceive a big rip in the future.

 

[marcus]

... so I guess we live in a kind of universe that has a type I singularity in the future, since we classically perceive a big rip in the future.

No we do not classically perceive that. The standard cosmo model that virtually all professional cosmologists use is the LambdaCDM. It has slow steady acceleration without a big rip.

Observations do not favor the big rip prediction. Sure "maybe". But maybe a lot of things

You should get clear on some basic cosmology.
So far observational data is consistent with a constant Lambda. That kind of acceleration does not imply rip.
It just approximates a deSitter universe----nothing remarkable, no future singularity.
Just endless, slowly accelerating, expansion. Very smooth picture.

There is a key number w, called the "dark energy equation of state". Observations continue to narrow down the confidence interval for w around the value of -1. If w = -1 as an exact constant, then we are in the LambdaCDM case.
Back in 2003-2004 there was a lot of excited talk about "big rip", which appeals to popular imagination, but in the professional community you don't hear much about it any more. They were imagining that the dark energy density changes over time and/or the equation of state w changes over time---causing weird stuff to happen.
The observational cosmologists keep checking for signs of change and so far what they see favors exact constant dark energy parameters. If tomorrow they get new data and see something different, well, then we can start talking about big rip again

 

[MTd2]

What about the cosmological constant? As the universe expands, the matter content, and thus, the positive pressure, becomes proportionally null compared to the negative, leading to a big rip.

 

[Dmitry67]

Hmm, nice heuristic thought! :D Never thought of that. Thank you.

Don't forget to write me a small cheque when you get your future Nobel prize :)

I just wanted to say that for the same very reason Kerr singularity does not form: freely falling observers experience increasing tidal forces and become surrounded (in their frames) by the horizons. Singularity for them is in the future, as you know, exactly like in the Big Rip case. So Big Rip spacetime and kerr solution near singularity are very similar.

So Kerr singularity is not a 'point' but rather a 'cloud', constantly absorbing it's own Hawking radiation, smearing its mass around small, but not infinitely small space region.

 

[marcus]

As far as I can see, the section 4 of Singh that you point to does not go very deep or have much general significance.

Notice that it is using a 2005 classical model by Odintsov Nojiri and Tsujikawa (ONT).
http://arxiv.org/abs/hep-th/0501025

All the parameters like alpha, A, B, etc that he is talking about are not LQC parameters. They are from the ONT paper.
Singh says clearly at the beginning that he is using the ONT scheme which describes a "general dark energy scenario". This was developed in the classical FRW cosmology context.

So ONT supplies him with a schema or a format ( his equation #22) which has parameters alpha, A, B etc. that you can vary so as to get all kinds of weird dark energy that people used to talk about---phantom energy, quintessence, etc etc.

This is not LQC, it is the 2005 model of Odintsov, Nojiri and Tsujikawa. A convenient way to schematize a lot of different dark energy cases.

So then he plays around with the parameters in the ONT model and sees how the energy density changes. And he just uses isolated facts about LQC to see how they would affect the ONT model.

Like in LQC there is rho_crit energy density at which point gravity repels instead of attracts. He slips that fact in, and looks to see how things change.

All the time he is not solving any LQC equation or running any LQC model, he is using the ONT model. And seeing how an isolated fact about LQC might affect.

He doesn't talk about what these weird kinds of dark energy are, he doesn't put any of them into an actual LQC model, and run it. All those cases are just hidden under the rug of the ONT equation #22 scheme.

 

[MTd2]

So, at least, it is possible that LQC may allow a rip bounce.

 

[atyy]

Meh

Cantonese?

 

[MTd2]

Cantonese?

Lol wut?

 

[atyy]

Lol wut?

http://en.wikipedia.org/wiki/Singlish#Meh

 

[marcus]

So, at least, it is possible that LQC may allow a rip bounce.

In my humble opinion, YES DEFINITELY! I would not rely entirely on what Param Singh says in this one paper. He is a postdoc at Perimeter, used to be with Ashtekar at Penn State. The present paper could be said to be preliminary. The idea needs more work.

The main point is that it is not generic to LQC. And neither is the infinite series of bounces. The fact that a solution to the LQC equations has one bounce does not mean that it automatically will have more than one. Often a solution will have just one bounce.

And certainly one bounce does not imply the solution has an infinite number, or is "cyclic" in some sense. I want to emphasize that because it is a common mistake.

==============

My guess is that LQC definitely supports a "big rip" IF YOU PUT IN SOME WEIRD dark energy which has a density or equation of state that evolves over time IN SOME WAY THAT REAL OBSERVED DARK ENERGY seems not to. If you put into the LQC picture some field that is behaving in some way that hasn't been observed (at least yet) then you should be able to get a big rip. It's very hypothetical but I think you could.

And then within that case it might be possible to get a contraction (as Param Singh suggests). That would be quite funny. It starts out looking like a rip and then it suddenly contracts. I'm skeptical. I think that part needs further work. There are a lot of assumptions here. Singh makes ansätze that don't come out very clearly, because he is really using a classical model by Odintsov Nojiri Tsujikawa, based on the Friedman equations. I would want to see a paper where someone actually uses the LQC model and gets a rip to suddenly contract into a crunch.

And then assuming that contraction happens, it is plausible that one would get what is usually called a bounce. It is all pretty hypothetical though.

 

[marcus]

What about the cosmological constant? As the universe expands, the matter content, and thus, the positive pressure, becomes proportionally null compared to the negative, leading to a big rip.

No, that does not lead to a big rip. In the standard cosmo model, LambdaCDM, there is a cosmological constant Lambda. As the universe expands the matter density goes to zero. The remaining energy density is the constant one we estimate, corresponding to measured Lambda.

That does not lead to big rip, just to continued accelerated expansion.

It is so gentle does not even put our local group of galaxies apart.

One of the world's top cosmologists, Larry Krauss, has a paper in which he describes the prospects for the far future implied by the standard LambdaCDM model.
Our local group of galaxies gradually merges into one large elliptical galaxy. It has the mass of both our Milkyway and the Andromeda galaxies plus some other smaller ones.
The other galaxies, out beyond our local group, gradually recede until they can no longer be detected. Within our galaxy things go on pretty much as usual. Planets remain planets. Stars go on being stars, and gradually burn out. No rip.

To a large extent all that talk about rip is a useless distraction.

As I recall, the dark energy density is about 0.65 nanojoule per cubic meter, and the total average density including all kinds of matter and radiation is about 0.85 nanojoule per cubic meter.

As the universe expands the matter part naturally goes to zero, largescale average. So the total largescale average is gradually declining to 0.65 nJ/m³. Heh heh. That is not a recipe for rip! Or crunch or bounce or any of that exciting stuff.

I'll get a link to Krauss' article

http://arxiv.org/abs/0704.0221

I see it won a prize in the 2007 Gravity Foundation essay contest. Nicely written piece. Quite accessible to general readers.

 

[MTd2]

I will read that. But I don't get it. That density is negative, it is like inserting negative mass everywhere homogeneously, so that to keep energy density constant.

 

[marcus]

I will read that. But I don't get it. That density is negative, it is like inserting negative mass everywhere homogeneously, so that to keep energy density constant.

No, the dark energy density is not negative. It is measured at around + 0.65 nJ/m². Positive.

The measurement is indirect and there is some errorbar around it, but that is what it comes to.

Any time you have a constant positive energy, it creates a negative pressure.*
If you look at the Friedman equations you see that the one involving ä (the second time derivative of the scale factor)
depends on pressure. You can only get acceleration---that is ä > 0 ----if you have negative pressure.

The equations are actually very simple. A good place to start is Wikipedia "Friedman equations"
You will see one of the two equations has ä
and you will see both energy density and pressure. The key thing is the pressure.
That is why w, the ratio of energy density to pressure is important. w = -1 means that P = -rho.
The einstein equation of 1915 gen rel already tells us that positive pressure attracts just like mass does, and positive pressure can slow expansion. Negative pressure has the opposite effect. That is the message in the Friedman equations and it is the key to why a constant positive energy density (one way to look at Lambda) will accelerate expansion.*intuitively somewhat like the Casimir effect. Or think of a piston in a cylinder which has a constant positive energy density associated with the volume inside the cylinder. It will want to contract and pull the piston inwards because in that way it achieves a lower energy. This is in effect a negative pressure. If you want to pull out the piston you will make more volume inside the cylinder, and therefore more energy, because the density must remain constant. Therefore you must do work to pull out the piston. Again, this means there is negative pressure. Always a constant positive energy density has this.

 

[MTd2]

I was thinking negative as in negative potential, like changing the sign of a charge, except that the source is space-time itself and constant.

But I get what you mean. If you have a point mass, it would be attractive at small distances and repulsive at great distances. So, in the future, it is like the local group, or any denser concentration of matter, would stay forever inside the attractive part, and the rest of the universe would be repealed.

Friedman model just treats everything as dust, thus it doesn't quite match with what I wast trying to think.

 

[Dmitry67]

So can we say that in the Big Rip scenario:
1. Universe expands
2. Faster and faster.
3. It becomes crossed by too many event horizons
4. It becomes filled with Hawking radiation
5. When this matter becomes very dense and 'wins' over the quintessence the expansion stops, and Universe contracts.

 

[MTd2]

Hey, Marcus, wait a minute. What about the increasing negative pressure from the cosmological holographic horizon? What I mean is, LQC Black Holes fits the Bekenstein bound, so it should be expected that it LQC cosmology also fits the cosmological horizon in each frame. That means, the horizon of each particle would evaporate until nothing is left, there is a big rip/bounce. This kind of think is seen in desitter relativity, in which there is a maximum observable scale in each frame.

 

[John86]

http://arxiv.org/abs/0911.3140
Bohmian Quantization of the Big Rip
Authors: Nelson Pinto-Neto, Diego Moraes Pantoja
(Submitted on 16 Nov 2009 (v1), last revised 16 Nov 2009 (this version, v2))
Abstract: It is shown in this paper that minisuperspace quantization of homogeneous and isotropic geometries with phantom scalar fields, when examined in the light of the Bohm-de Broglie interpretation of quantum mechanics, does not eliminate, in general, the classical big rip singularity present in the classical model. For some values of the Hamilton-Jacobi separation constant present in a class of quantum state solutions of the Wheeler-DeWitt equation, the big rip can be either completely eliminated or may still constitute a future attractor for all expanding solutions. This is contrary to the conclusion presented in Ref.[1], using a different interpretation of the wave function, where the big rip singularity is completely eliminated ("smoothed out") through quantization, independently of such separation constant and for all members of the above mentioned class of solutions. This is an example of the very peculiar situation where different interpretations of the same quantum state of a system are predicting different physical facts, instead of just giving different descriptions of the same observable facts: in fact, there is nothing more observable than the fate of the whole Universe.

 

[MTd2]

Hmm, right on spot. Although this paper was not related to my question, it was what made me free associate with my question.

BTW, why Marcus is ignoring me? :(

 

[MTd2]

Look at what I found:

http://arxiv.org/abs/0907.5591v3

Non-singular Ekpyrotic/Cyclic model in Loop Quantum Cosmology
Authors: Thomas Cailleteau, Parampreet Singh, Kevin Vandersloot
(Submitted on 31 Jul 2009 (v1), last revised 23 Oct 2009 (this version, v3))

Abstract: We study the role of non-perturbative quantum gravity effects in the Ekpyrotic/Cyclic model using the effective framework of loop quantum cosmology in the presence of anisotropies. We show that quantum geometric modifications to the dynamical equations near the Planck scale as understood in the quantization of Bianchi-I spacetime in loop quantum cosmology lead to the resolution of classical singularity and result in a non-singular transition of the universe from the contracting to the expanding branch. In the Planck regime, the universe undergoes multiple small bounces and the anisotropic shear remains bounded throughout the evolution. A novel feature, which is absent for isotropic models, is a natural turn around of the moduli field from the negative region of the potential leading to a cyclic phenomena as envisioned in the original paradigm. Our work suggests that incorporation of quantum gravitational effects in the Ekpyrotic/Cyclic model may lead to a viable scenario without any violation of the null energy condition.