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Karami's Loop cosmology talk Tuesday at ILQGS,

  1. Oct 24, 2013 #1


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    Karami's talk is scheduled for Tuesday 29 October in just a few days.
    The title has not yet been posted. It is a good bet that it will be about one or more of the active topics in Loop cosmology of which there are quite a few. Karami's recent work co-authored with Alejandro Corichi has been about generalizing the Loop "big bounce" to models that are not isotropic and/or not homogeneous.

    But there is also a chance that the talk will bear on the apparent high probability of adequate inflation after the Loop bounce.

    In 2008 Gibbons and Turok found a problem with inflation, namely that using what they thought was a natural probability measure and a widely-assumed inflation mechanism the probability of enough inflation happening was extremely low.
    G.W. Gibbons and N. Turok, Phys. Rev. D 77, 063516 (2008)

    Then in 2009 Ashtekar and David Sloan found that in the Loop cosmology context the probability, by contrast, was nearly one! After the Loop bounce, enough inflation was virtually certain (with the same basic generic assumptions.)
    Loop quantum cosmology and slow roll inflation
    Abhay Ashtekar, David Sloan
    (Submitted on 21 Dec 2009)
    In loop quantum cosmology (LQC) the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. Rather than growing unboundedly in the past, the Hubble parameter vanishes at the bounce and attains a finite universal maximum at the end of super-inflation. These novel features lead to an unforeseen implication: in presence of suitable potentials all LQC dynamical trajectories are funneled to conditions which virtually guarantee slow roll inflation with more than 68 e-foldings, without any input from the pre-big bang regime. This is in striking contrast to certain results in general relativity, where it is argued that the a priori probability of obtaining a slow roll with 68 or more e-foldings is suppressed by a factor e−204.
    5 pages, 1 table. Physics Letters B (2010)

    Then in 2010 a former student of Ashtekar's, Alejandro Corichi, and his student Karami posted a result that seemed to explain the conflict.
    On the measure problem in slow roll inflation and loop quantum cosmology
    Alejandro Corichi, Asieh Karami
    (Submitted on 18 Nov 2010)
    We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to one in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.
    14 pages, 3 figures. published in Physical Review D (2011)

    So Asieh Karami has taken part in this rather lively exchange of views (along with Gibbon, Turok, Ashtekar, Sloan, and Corichi) and just today another paper two of the authors was posted:
    Inflationary Attractors and their Measures
    Alejandro Corichi, David Sloan
    (Submitted on 23 Oct 2013)
    Several recent misconceptions about the measure problem in inflation and the nature of inflationary attractors are addressed. We show that within the Hamiltonian system of flat Friedmann-Lemaître-Robertson-Walker cosmology coupled to a massive scalar field, the focussing of the Liouville measure on attractor solutions is brought about by a spread in a gauge degree of freedom - the spatial volume. Using this we show how the Liouville measure formulated on a surface of constant Hubble rate induces a probability distribution function on surfaces of other Hubble rates, and the attractor behaviour is seen through the focussing of this function on a narrow range of physical observables. One can conclude then that standard techniques from Hamiltonian dynamics suffice to provide a satisfactory description of attractor solutions and the measure problem.
    6 pages, 1 figure

    As I said, the title of Karami's seminar talk has not yet been posted and since 2010 he has collaborated on several Loop cosmology papers that are not concerned with the probability of inflation. But there is a chance some part of the talk will have a bearing on this interesting issue.
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  3. Oct 25, 2013 #2


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    The title of Karami's talk was posted today. It is:
    Bianchi IX LQC: Quantization ambiguity and effective description

    So this will not be about the high probability of getting enough inflation if nature uses Loop bounce cosmology. It will be about recent contributions to generalizing Loop cosmology to NON-ISOTROPIC cases, where the bouncing universe does not look the same in all directions.

    The Bianchi IX case was studied extensively, along with Bianchi I and II, in this recent paper:
    Loop Quantum Cosmology: Anisotropy and singularity resolution
    Alejandro Corichi, Asieh Karami, Edison Montoya
    (Submitted on 26 Oct 2012)
    In this contribution we consider the issue of singularity resolution within loop quantum cosmology (LQC) for different homogeneous models. We present results of numerical evolutions of effective equations for both isotropic as well as anisotropic cosmologies, with and without spatial curvature. To address the issue of singularity resolution we examine the time evolution of geometrical and curvature invariants that yield information about the semiclassical spacetime geometry. We discuss generic behavior found for a variety of initial conditions. Finally, we show that the modifications which come from Loop Quantum Cosmology imply a non-chaotic effective behavior in the vacuum Bianchi IX model.
    12 pages, 4 figures, To appear in the Proceedings of the Relativity and Gravitation 100 Years after Einstein in Prague conference

    Bianchi IX is where you have three separate Hubble rates for contraction and then expansion in three separate directions.

    So the universe is anisotropic. The rate geometry is changing depends on which direction you look in!
    Last edited: Oct 25, 2013
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