# Magueijo-Singh: observational LQC prospects

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This new paper by Magueijo and Singh discusses prospects for observational Loop Quantum Cosmology

http://arxiv.org/abs/astro-ph/0703566
Thermal fluctuations in loop cosmology
Joao Magueijo, Parampreet Singh
10 pages
from the abstract:
"Quantum gravitational effects in loop quantum cosmology lead to a resolution of the initial singularity and have the potential to solve the horizon problem and generate a quasi scale-invariant spectrum of density fluctuations. We consider loop modifications to the behavior of the inverse scale factor below a critical scale in closed models and assume a purely thermal origin for the fluctuations. We show that the no-go results for scale invariance in classical thermal models can be evaded even if we just consider modifications to the background (zeroth order) gravitational dynamics. Since a complete and systematic treatment of the perturbed Einstein equations in loop cosmology is still lacking, we simply parameterize their expected modifications. These change quantitatively, but not qualitatively, our conclusions. We thus urge the community to more fully work out this complex aspect of loop cosmology, since the full picture would not only fix the free parameters of the theory, but also provide a model for a non-inflationary, thermal origin for the structures of the Universe."

the next is from the conclusions section:
Loop quantum cosmology has the potential to relate observational physics and quantum gravity, allowing concrete calculations to be made in the quantum gravity regime as long as a minisuperspace approximation is assumed to be valid. The approach is known to modify the equation of state of ordinary matter, thereby permitting a solution of the horizon problem without resorting to scalar fields. It is then natural to ask whether in such scenarios thermal fluctuations could be behind the observed structure of the Universe. In order to analyze this issue we have assumed in this paper that physics learned in the mini-superspace approximation (in the sense of modifications to inverse volume terms) will not change qualitatively.

There are positive indications for this hope from ongoing work [28], but we stress this important caveat in our analysis.
We showed that prima facie we are confronted by a no-go result in classical physics...

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scalar field = unicorn

the scalar field "inflaton" is the unicorn of our period in history

Magueijo-Singh remark that one can do without this unicorn

they mention that LQC modifies the equation of state of ordinary matter in such a fashion that it solves the horizon problem

the main direction is towards getting testable predictions about structure formation in the universe----stuff that we can go to the CMB and look to see if it is there, or the galaxy surveys.

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Magueijo-Singh mention a radical improvement in LQC made in 2006 and associated with work by Ashtekar, Bojowald---sometimes called "new dynamics" sometimes called "new quantization". Bojowald describes what happened as an unplanned convergence* from different directions of work by himself, Ashtekar, Thiemann. The relevant 2006 papers are all from Ashtekar's Penn State group.

This has a lot of relevance to what Magueijo-Singh are saying in this paper---possibly essential to their idea.
Here's a quote:

===quote M-S===
With Cgrav and Cm written in form of holonomies and triads, we quantize the theory and are led to a nonsingular difference equation with uniform discretization in eigenvalues of volume operator [14]:
...
...
Unlike the old quantization [PRIOR TO 2006] in LQC (where the difference
equation was of uniform discretization in eigenvalues of triad [32, 33]), the evolution has the correct classical limit for arbitrary matter content and quantum gravitational effects set in when curvature becomes of the order Planck. Study of backward evolution of semi-classical states peaked at late times on trajectories of a large classical universe shows a generic bounce when
$$\rho = \rho_{crit} = 0.82\rho_{planck}$$
[14]. In this quantization (for j = 1/2) modifications originating from Fiab terms dominate over those containing 1/√detE in both gravitational and matter parts of the constraint. Investigations of closed models yield similar results [16].
===endquote===

a couple of recent papers where Bojowald remarks on this convergence are gr-qc/0609034 and gr-qc/0701142

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In line with what Magueijo said about Loop's correct classical limit there is something from a recent Bojowald paper also remarking on the appearance of this classical limit---in cases sufficient for what he was working on

this is in gr-qc/0611112

Effective constraints of loop quantum gravity

from the abstract:
Our results demonstrate that loop quantum gravity has the correct classical limit, at least in its sector of...etc etc. [in the cases they needed for what they were doing, in other words]

Bojowald's take on it is distinct in one specific detail: he attributes crucial importance to work with Skirzewski at Berlin

from page 41 of the same paper:
This demonstration of the correct classical limit crucially rests on a new understanding of effective theory [12]. .....(see [14)

references [12] and [14] are to a paper of Bojowald and Skirzewski
math-ph/0511043
and to Skirzewski's thesis Effective Equations of Motion for Quantum Systems

I cant say what this might be, not having looked at the Bojowald-Skirzewski paper

hellfire
Thanks for bringing this into our attention. I found the paper very interesting and enlightening, however, the relevance of the conclusion ("a model for a non-inflationary, thermal origin for the structures of the Universe") is very unclear to me.

The cosmological scenario described by loop quantum cosmology consists of three different phases, a pure quantum gravitational one with discrete equations, a semiclassical one with effective equations and a classical one as usual. The semiclassical approximation should still capture the most relevant quantum effects of the theory, and it already becomes similar to the classical regime at length scales of order of the Planck length.

On the other hand, the origin of structures in the standard model of cosmology is assumed in the inflationary period, during which density perturbations arise as a consequence of quantum fluctuations in a de-Sitter background. The quantum effects of the gravitational field are assumed to be negligible. This mechanism would be therefore part of the third phase.

In the paper, they analize the behaviour of matter in the semiclassical regime (second phase) of a minisuperspace model. They find some features of matter (e.g. the modified equation of state) that arise due to the quantum nature of space-time in which matter exists, but they neglect the possibility that matter acts on space-time making the minisuperspace approximation invalid. To my naive understanding, if the quantum effects of the gravitational field are not negligible, then, neither is the backreaction of the gravitational field to fluctuations or inhomogeneities.

The paper may contain interesting insights about loop quantum cosmology, but I must doubt about the relevance of the result. In the abstact they mention this fact, but I am surprised to read that they consider that the treatment of perturbed equations may change their conclusions quantitatively, but not qualitatively.

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Thanks for bringing this into our attention. I found the paper very interesting and enlightening, however, the relevance of the conclusion ("a model for a non-inflationary, thermal origin for the structures of the Universe") is very unclear to me.
you're welcome, glad you found it interesting
It IS unclear at present. more needs to be worked out. we do have the material here, I would say, for an alternative to the more farfetch aspects of the inflation scenarios and it is an alternative that CAN POTENTIALLY BE TESTED. that is the important thing. with a new theory the first question to ask is not "is it right?" but "can it be tested?"
The cosmological scenario described by loop quantum cosmology consists of three different phases, a pure quantum gravitational one with discrete equations, a semiclassical one with effective equations and a classical one as usual.
That sounds like the papers that Bojowald was writing in, like, 2004. It is an OK way to look at it but in the 2006 work of Ashtekar et al you get a lot of overlap.
A semiclassical approximation will run smoothly back to before the bang and also forwards into the classical. The picture is not so cut and dried three stages as it used to be. They even modeled a cyclic universe case amd ran the computer model thru many cycles with many bounces

... This mechanism would be therefore part of the third phase.

In the paper, they analize the behaviour of matter in the semiclassical regime (second phase) of a minisuperspace model. ...
Your reasoning seems to depend on this artificial division into stages. I don't find it convincing.
but I must doubt about the relevance of the result. ...

Well I do not doubt the interest of the result and that it will stimulate considerable followup research and in that way be highly relevant. About the ultimate validity I can of course not guess. It is an initial paper. There are places where they say very clearly they are making simplifying assumptions in order to get started, and more work needs to be done.

Like the backreaction of matter on geometry during structure formation, just as you mentioned and they mentioned!

this could turn out to be wrong. But Magueijo is one of the world's top QG cosmologists and he knows what he is doing. If he things this is a relevant possibility to look at, i'm inclined to give him benefit of doubt.

Also Singh has been collaborating with Ashtekar with some 3 years and has a lot of background in the QG bang, his sideline has been related phenomenology, so he is an ideal one for Magueijo to work with.

Basically we can only guess. You guess it will NOT go somewhere. I guess it WILL go somewhere. And we will see what kind of followup research results.

hellfire
I have a hard time to understand this claim:

Since a complete and systematic treatment of the perturbed Einstein equations in loop cosmology is still lacking, we simply parameterize their expected modifications. These change quantitatively, but not qualitatively, our conclusions.

Is this based on some clear criteria or is this some kind of faith about the minisuperspace approximation? I was not able to read this out of the paper.

Minisuperspace models are dubious, because with symmetry reduction they simultaneously fix canonically conjugate variables in some coordinate axes violating the uncertainty principle. There is an old paper by Karel Kuchar analyzing this in detail.

Regardless of this, they are the only approximation available to study the quantum universe and they predict some interesting features. This probably lead to believe that the symmetry reduction might make sense somehow.

Now, Magueijo-Singh go a step forward and strecht the validity of the minisuperspace model for gravity to describe perturbations of matter... Intuitively it seams to me that the effect of matter perturbations on space-time should be only negligible on a classical regime. Of course I may be wrong.

The definitive verdict should be given by a cosmological model that describes inhomogeneities from the full quantum theory. In any case I agree with you that the paper is interesting, readable, and a great new idea in the inflationary paradigm.

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...
The definitive verdict should be given by a cosmological model that describes inhomogeneities from the full quantum theory. In any case I agree with you that the paper is interesting, readable, and a great new idea in the inflationary paradigm.

Hellfire thanks for reading and commenting on M-S paper! it is so great to hear an intelligent knowledgeable reaction and know someone else has seen the paper. makes the day!
for sure this is iffy. but it is a new gambit and may start a fruitful line of investigation

I hope you or somebody votes for it in the MIP prediction poll.