Anisotropic LQC bounce: Bianchi-I case (Chiou and Vandersloot)

[marcus]

It turns out that this work has a timely significance. In reacting to Martin Bojowald's bounce article in July 2007 Nature Physics one or more blog personalities spoke as if they understood LQC to deal only with the homogeneous and isotropic case. It doesn't. Current LQC does not only deal with that case. Here is work dealing with the ANisotropic case, and not the first paper either. Some of the crit we heard was based on lack of information.

Actually there are a lot of interesting issues around the quantum-cosmological bounce--much more work needs to be done and IS being done. The effect of inhomogeneities is being investigated and several papers are out about that.
I think it would improve the quality of discussion if we could get the message out concerning recent LQC directions and results.

In any case, Dah-Wei is a UC Berkeley PhD who went to Penn State for postdoc barely a year ago and is already in the thick of things. Kevin V. is a recent Ashtekar PhD who won a coveted European postdoctoral fellowship and chose to enjoy it at Roy Maarten's institute at Portsmouth UK. This work shows how quickly new PhD's can get important results in this field. Congratulations to both.

http://arxiv.org/abs/0707.2548
The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
Dah-Wei Chiou, Kevin Vandersloot
15 pages, 10 figures
(Submitted on 17 Jul 2007)

"In homogeneous and isotropic loop quantum cosmology, gravity can behave repulsively at Planckian energy densities leading to the replacement of the big bang singularity with a big bounce. Yet in any bouncing scenario it is important to include non-linear effects from anisotropies which typically grow during the collapsing phase. We investigate the dynamics of a Bianchi I anisotropic model within the framework of loop quantum cosmology. Using effective semi-classical equations of motion to study the dynamics, we show that the big bounce is still predicted with only differences in detail arising from the inclusion of anisotropies. We show that the anisotropic shear term grows during the collapsing phase, but remains finite through the bounce. Immediately following the bounce, the anisotropies decay and with the inclusion of matter with equation of state w < +1, the universe isotropizes in the expanding phase."

By the way, on a related subject, Kevin Vandersloot gave what I thought was one of the more interesting contributed talks at the Loops 07.
http://www.matmor.unam.mx/eventos/loops07/cont_abs.html
It appears to confirm BLACK HOLES bounce in certain cases. I will get the abstract.

Kevin Vandersloot: Dynamics of Loop Quantum Schwarzschild Interior · slides (pdf)

"We discuss dynamics of the Schwarzschild interior using an effective semi-classical description of the loop quantization. We will consider the effects of an improved loop quantization using techniques from loop quantum cosmology."

The talk was based on a paper by K.V. with Christian Böhmer (also a postdoc at Portsmouth) which is in preparation.
The paper's title is Loop Quantum Dynamics of Schwarzschild Interior
The conclusions said in part:"Each phenomenological study indicates singularity resolution of Schwarzschild black hole analogously
to LQC results. Detailed consequences dependant on quantization scheme..."

 

[marcus]

I think sometimes it's possible to learn more easily from the work of beginning researchers because they are not so cautious.
so there is a kind of clarity that comes from daring

For example there were many posts by Carroll on CV-blog that said essentially the same thing: "it is reasonable to expect that inhomogeneities get worse and worse during the collapse, so how can a bounce result in the nice smooth universe that we see coming out of our big bang?"
He was dismissing the possibility of a bounce in our universe's past on theoretical grounds essentially because of CRUMPLING.

During collapse all the chaotic irregularities of the world are exacerbated.

Everybody knows this, but people like Ashtekar have the (perhaps intuitive, perhaps rigorously supported) view that when you get down to Planck scale where you can't crumple any more then SMOOTHNESS IS RESTORED IN THE PLANCK REGIME by a kind of phase transition. So the new world can start out with a clean slate.

Alejandro Satz (a PhD student at Nottingham) asked Ashtekar about that during coffeebreak, and reports Ashtekar said that entropy is LOW at the Planck regime before expansion starts. I suppose this means entropy as seen by an observer looking back in time to the beginning of his world's expansion. One has to pin down who the observer is.

Anyway this is currently a live issue and Chiou-Vandersloot result is RELEVANT, because in their model the universe SELF-ISOTROPIZES during, or immediately after, bounce.

You start with some anisotropy (lopsided irregularity) and during collapse it gets WORSE in their model, and then there is a bounce and it somehow gets better again and is somehow SMOOTHED OUT.

I think this must be unintuitive to a lot of people and all I can say is read their paper and also I think they are doing what it is great if first year postdocs do which is to take risks. Openly contradict entrenched ideas. maybe that is what firstyear postdocs are for---what they are supposed to do, in the grand scheme of nature

Anyway I like it, so i want to quote from their introduction.

 

[marcus]

from the Chiou Vandersloot introduction

==quote==
Recently, the investigation of loop quantum cosmology (For a review see [1]) in homogeneous and isotropic universes has indicated that the classical big-bang singularity can be replaced with a big-bounce [2, 3, 4, 5, 6]. In these scenarios gravity can be interpreted as becoming repulsive in the Planckian high energy regime, implying that our current expanding universe would have been preceded by a contracting phase. The presence of a big-bounce has been shown to be a rather generic and genuine feature of the quantum gravitational effects of loop quantum cosmology and does not require any exotic matter which violates energy conditions [7]. An exciting fact of bouncing cosmological models is that the scales measured in the cosmic microwave background (CMB) can be in causal contact if the current expanding phase is preceded by a contracting one, thus opening the possibility for a replacement of the standard inflationary scenario.

In order to more fully develop this scenario, one must go beyond the assumption of homogeneity and isotropy. It is both the inhomogeneities and anisotropies that are expected to grow in a collapsing phase and thus a proper accounting of these fluctuations is required. One particular
question that immediately arises is whether the presence of the bounce is stable under the inclusion of inhomogeneities and anisotropies. A proper description of the inhomogeneous perturbations and anisotropies would then provide an answer to the question of whether a suitable alternative to inflation can be constructed, and/or what possible cosmological signatures may result.

In this paper we do not seek to answer all these questions as work on including inhomogeneities in loop quantum cosmology is in its infancy (initial progress can be found in [8, 9, 10, 11]). Instead, we will focus on the behavior of anisotropies, studying the dynamics of the anisotropic Bianchi I model in the framework of loop quantum cosmology. In the classical Bianchi I universe sourced with matter with zero anisotropic stress, the anisotropic shear term behaves as an effective matter component with energy density that scales as a^−6 in the Friedmann equation with a being the mean scale factor. Thus for matter with equation of state w < +1, the anisotropies will dominate the collapsing phase as the singularity is approached. If the current expanding phase of the universe was preceded by a collapsing phase, the inclusion of anisotropies can be expected to have significant results near the bounce.

The loop quantization of the anisotropic Bianchi I model was initially studied in [12] and more recently in [13]. In this paper, we will study the dynamics of the model at the level of effective classical equations of motion that incorporate quantum effects arising from the loop quantum Einstein equations. At the level of the effective equations we study, we show that the big bounce is indeed robust under the inclusion of non-linear anisotropies. We will show that the anisotropic shear remains finite through the bounce and that if matter with equation of state w < +1 is included, the universe isotropizes in the expanding phase.

The results represent evidence that the bouncing scenario of loop quantum cosmology is robust when the assumptions of homogeneity and isotropy are relaxed and gives hope that the same can be said when inhomogeneous perturbations are properly...
==endquote==

 

[marcus]

I think as a rough generalization that in science you tend to get major developments when one model challenges another, or several others.

So knowledgeable people are going to be pricking up their ears when they hear talk like this challenging INFLATON scenarios.

Conventional inflaton scenarios assume EXOTIC negative pressure MATTER, that doesn't obey energy conservation----that is how they get an early episode of accelerated expansion.

this is similar to the creation myths of primitive people----you observe certain things about the world so you propose a fanciful being that acts in a certain way. In one creation myth I remember the world was created by a Beaver that swam down to the bottom of a big pond and brought up some Mud, out of which she fashioned people and everything.
===========

in the case of the Inflaton Myth, the things that needed explaining were the uniform temperature, the flatness, the structure.

But you don't necessarily need an exotic inflaton field to explain these things.

Chiou and Vandersloot arent the first to point this out. Earlier this year there was a paper that did by Magueijo and Singh. But Mr. C and Mr. V do it clearly. You can see in that passage I quoted.

In LQC it seems that you naturally get a BOUNCE and that takes care of prior causal contact between different regions of the sky===does away with the "horizon problem"

Another thing you get automatically in LQC is a period of INFLATION that does not require an exotic inflaton field. It just happens because of quantum corrections to gravity at high density.

It's not very MUCH inflation compared with what you can get with an exotic inflaton field, but it might be enough to explain the smooth flat appearance of space which seems to have had its creases and blemishes expanded away.

Mr. C and V talk about how the early universe SELF-ISOTROPIZES at the start of expansion. that is one thing their analysis showed.
they were running a BIANCHI-ONE bounce and the Bianchi-one model has the ability to develop a lot of anisotropy in the form of shear---non-uniformity---chaotic squash and stretch problems. And they were noticing that the model automatically GOT RID OF SOME OF ITS NON-UNIFORMITY as it started to expand.

 

[marcus]

So what Mr. Chiou and Vandersloot paper (and some other recent work) is telling me is that the exotic inflaton field is maybe NOT THE ONLY way to explain
what we call the 'horizon problem' and the 'flatness' or smoothness problem.
And it may also not be the only way to explain the observed largescale structure at the cluster supercluster level or in the spectrum of bumps in the CMB. Magueijo and Singh had some discussion of structure formation without inflation.

this is the kind of thing that is likely to alert researchers and arouse interest, because it has the prospect of CHALLENGING a common assumption.

Basically what C and V paper tells me is that if an Inflaton is not the only way to explain the uniform sky temperature, or the near-flat geometry, or the spectrum of bumps, then the Inflaton is looking more like a made-up BEAVER MYTH.

So this is something for smart people to study and try to resolve and indeed they certainly might end up resolving it in favor of the Beaver!

Or they might resolve it in favor of some entirely different thing nobody thought of yet. Whatever happens it's likely to be interesting.

 

[marcus]

Here's the start of Chiou and Vandersloot's concluding section, where they discuss their findings:

==quote==
Let us restate the main results presented. We have consider the anisotropic Bianchi I model with loop quantum corrections to the classical equations of motion. We have shown that a bounce occurs under rather generic conditions in a collapsing universe. The anisotropic shear term Sigma²/a⁶ which classically grows during collapse and blows up at the singularity, remains finite through the bounce. After the bounce, the universe behaves more and more classically and can isotropize at later times. This is thus evidence that the bouncing scenario of the isotropic models of loop quantum cosmology is robust when the symmetries of the isotropic model are relaxed...
==endquote==

In the Bianchi-one model there are three different Hubble parameters====different rates of expansion or contraction in three different directions. So spatial geometry can get really messed---with expansion in one direction and contraction in another.
If you look in their APPENDIX where they plot results of numerical studies you will see where they plot the RATIOS of the different Hubble parameters with each other. And as they run the model on past the bounce at first these ratios get crazy and go plus or minus off the chart, and then they somehow get a grip and all CONVERGE TO ONE.
So that is back in the isotropic situation where the Hubble expansion parameter is the same in every direction. this happens of its own accord. neat.

Sean Carroll was asking on CV about this kind of thing. He didn't seem to think that a bounce could cure irregularities.
During the crunch, in this model, nonuniformities DO keep getting worse and worse, and then they abruptly start smoothing out of their own accord. Have a look at the graphs plotted in the appendices to the paper.

So maybe a bounce CAN cure the irregularities inflicted during the prior collapse.
And this opens the way for bounce to challenge inflaton because the bounce is then able to offer an alternative answer to the issues of "horizon problem", flatness, structure that an exotic inflaton, violating energy conditions, is usually invoked to explain.
One can't say which explanation will ultimately prevail but I do expect that bounce will give inflaton a hard run-for-the-money before it's settled.