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Algebra closure in LQC(eff.) w. 1/V and holonomy corrections

  1. Aug 2, 2013 #1


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    Anomaly-free perturbations with inverse-volume and holonomy corrections in Loop Quantum Cosmology
    Thomas Cailleteau, Linda Linsefors, Aurelien Barrau
    (Submitted on 19 Jul 2013)
    This article addresses the issue of the closure of the algebra of constraints for generic (cosmological) perturbations when taking into account simultaneously the two main corrections of effective loop quantum cosmology, namely the holonomy and the inverse-volume terms. Previous works on either the holonomy or the inverse volume case are reviewed and generalized. In the inverse-volume case, we point out new possibilities. An anomaly-free solution including both corrections is found for perturbations, and the corresponding equations of motion are derived.
    19 pages.
    ==quote from Conclusions, p, 18==
    In this work, we tried to sum up all that is currently known on the issue of the closure of the algebra in effective LQC and to address the question of a full resolution taking into account both corrections simultaneously.
    ==end quote==

    The PIRSA plenary talk videos from Loops 2013 are a remarkable information resource! and some especially noteworthy, I believe, were the first two talks of the conference. These concerned application of LQG to cosmology and confrontation with observations---and were given by Ivan Agullo and Aurelien Barrau. Both talks went considerably outside what we usually think of as typical LQC: i.e. the framework established by Ashtekar Pawlowski Singh in 2006.
    An important part of Barrau's talk was based on the above July paper. The talk evoked a series of probing questions at the end, by Rovelli, Freidel, Ashtekar, Lewandowski, Dowker, and Unruh, so it is worth watching not only the talk itself but also the Q&A which followed.

    Some Possible Ways to Observe Consequences of Loop Quantum Gravity
    Aurelien Barrau
    In this talk, I'll briefly review some possible observational consequences of loop quantum gravity. I will first address the issue of the closure of the algebra of constraints in holonomy-corrected effective loop quantum cosmology for tensor, vector, and scalar modes. I will underline some unexpected features like a possible change of signature. The associated primordial power spectrum and the basics of the related CMB analysis will be presented. The "asymptotic silence" hypothesis will be mentioned as a promising alternative. Then, I'll address the issue of the probability for inflation and the prediction of its duration from a new perspective. Finally, I'll present some prospect about the evaporation of black holes in LQG.
    22/07/2013 - 9:55 am
    Last edited: Aug 2, 2013
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  3. Aug 3, 2013 #2


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    In connection with Barrau's talk it's interesting to note that of Jon Engle. To quickly scan the slides, open http://pirsa.org/13070039 select "PDF" and scroll to slide 46/60. If you decide to watch, Engle's talk begins at minute 83 of the video recording. That means waiting 7 or 8 minutes for the buffer to fill, so one can start the video, mute the sound, and work at another window for a few minutes. Here's Engle's abstract:
    Jonathan Engle, Florida Atlantic University
    Quantum isotropy and dynamical quantum symmetry reduction
    We give a diffeomorphism and gauge covariant condition equivalent to homogeneity and isotropy which in principle can be quantized yielding a definition of a diffeomorphism-invariant homogeneous isotropic sector of LQG without fixing a graph. We specialise this condition to Bianchi I cosmologies yielding a condition for isotropy. We show how by quantizing and imposing this condition in the Bianchi I LQC model one recovers isotropic LQC with standard 'improved dynamics.'

    A second talk about this was given by Engle's student Matt Hogan, treating the Bianchi I application in detail. The paper these talks are based on is supposed to appear shortly on arxiv. It is by Engle with Beetle, Hogan, and Mendonca.

    In effect they restrict to an "LQC sector" within the full LQG theory, using quantum operators defined on the LQG Hilbert space. The phrase "improved dynamics" means the formulation of LQC by Ashtekar Pawlowski Singh which became standard in 2006. (A flaw in the earlier formulation was pointed out by Bill Unruh.)
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