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Super inflation in LQC again

  1. Nov 22, 2013 #1
    I was under the impression that the super inflation generated by the LQC was not enough to give us the 60 minimum e foldings for inflation to solve the horizon problem. However I have just noticed this paper on the arxiv today and Im wondering now if that conclusion is too hasty, any thoughts?

  2. jcsd
  3. Nov 22, 2013 #2


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    Hi Skydive,
    The Xiao-He-Zhu paper takes a little getting used to for several reasons. You notice that what they call "the e-folding number" is very different from what we usually mean by "e-folds" when we say that inflation must produce around 60 e-folds.

    If you look at where they define the "e-folding number" you see it involves an additional factor, the ratio of the initial and final Hubble rates. In the bounce, H changes from negative to positive, so it goes thru zero. This makes the "initial" Hubble rate be around zero. So the ratio can be very large. This makes "e-folding number" much larger than the simple number of e-folds.

    Also you can see immediately from the abstract of the paper, and just by glancing at the introduction, that they are studying a special case where there is assumed to be two fields (radiation and a massive scalar field) in play already at the very start---and these fields are interacting. They explain up front that this is a special case that they are studying.

    At this point I have no insight to share. I have only a very superficial reaction based on a brief glance at the paper. But you asked for "any thoughts", so FWIW I'll tell you my preliminary reaction.

    J-Y Zhu is the senior author. Of the three, he is at the more prestigious institution: Beijing Normal. Beijing Normal hosted the Loops 2009 conference and has a long-standing active program in Loop gravity/cosmology.
    J-Y Zhu is not the most prominent Loop guy there but he has published over 30 papers and a lot of them are Loop.

    Personally I was INTERESTED by the paper. I think that the Horizon problem is not the ONLY thing that inflation has to solve, so this is not the only criterion of how much inflation is ADEQUATE. However J-Y Zhu et al have focused on this criterion and they have come up with a different measure (see also their reference [18]) that they call "the e-folding number". This can be very large even if the actual number of e-folds is small and the period of superinflation is brief. Personally I find this intriguing. I'd like to understand it better.

    I'd like to understand why the "e-folding number" is the relevant measure of adequacy (with regard to the Horizon problem.) I'd like to understand the role played by the special assumptions about the interacting fields (massive scalar and radiation.

    I'm definitely going to be watching out for more papers by J-Y Zhu. This looks like a resourceful creative guy with a strong interest in Loop cosmology. Let me get the Inspire profile.
    Here are his published paper ranked by numbers of cites:
    Last edited: Nov 22, 2013
  4. Nov 22, 2013 #3


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    In the Xiao-He-Zhu paper the reference [18] is very prominent. they say they are using the method of reference [18]. Maybe we have to look at that paper---it may be the key:

    Bouncing Loop Quantum Cosmology from F(T) gravity
    Jaume Amorós, Jaume de Haro, Sergei D. Odintsov
    (Submitted on 10 May 2013)
    The big bang singularity could be understood as a breakdown of Einstein's General Relativity at very high energies. Adopting this viewpoint, other theories, that implement Einstein Cosmology at high energies, might solve the problem of the primeval singularity. One of them is Loop Quantum Cosmology (LQC) with a small cosmological constant that models a universe moving along an ellipse, which prevents singularities like the big bang or the big rip, in the phase space (H,ρ), where H is the Hubble parameter and ρ the energy density of the universe. Using LQC when one considers a model of universe filled by radiation and matter where, due to the cosmological constant, there are a de Sitter and an anti de Sitter solution. This means that one obtains a bouncing non-singular universe which is in the contracting phase at early times. After leaving this phase, i.e., after bouncing, it passes trough a radiation and matter dominated phase and finally at late times it expands in an accelerated way (current cosmic acceleration). This model does not suffer from the horizon and flatness problems as in big bang cosmology, where a period of inflation that increases the size of our universe in more than 60 e-folds is needed in order to solve both problems. The model has two mechanisms to avoid these problems: The evolution of the universe through a contracting phase and a period of super-inflation (H˙>0).

    EDIT: here is the Inspire entry on that
    It has 4 cites already. One of the cites is by Jaime Haro (in different dialect = Jaume)

    Cosmological perturbations in teleparallel Loop Quantum Cosmology
    Jaime Haro
    (Submitted on 2 Sep 2013 (v1), last revised 18 Nov 2013 (this version, v3))
    Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator.
    In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation.
    In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.
    18 pages.

    THIS MAY BE THE CLEAREST EXPOSITION. We have to put UPC-Barcelona on our map. Universitat Politècnica de Catalunya. "Cat Poly" :biggrin: , Catalonia Polytechnic University. I like the simple way Jaime presents this. Now I see. It is an initiative to make inflation UNNECESSARY. Why not!!! Always good to check out alternative routes to resolving problems.

    Catalan is a slightly different language from Spanish, that they speak around Barcelona. Jaume is how you say Jim in Catalan. So Jaime Haro would be registered at UPC-Barcelona as Jaume de Haro. And inflation never was necessary to explain the signal characteristics of the cosmos. It all makes sense now :biggrin:
    Last edited: Nov 22, 2013
  5. Nov 22, 2013 #4


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    Skydive, I think it's important to point out that this leads us into a very different version of Loop cosmology, that Sergei Odintsov calls "F(T)" where T stands for "Torsion" and one of the keywords is "teleparallel".
    It looks to me as if Odintsov is strongly promoting this and that it is a different brand of Loop.
    I think of it as "F(T) brand Loop cosmology" so as to make the distinction clear. Here is a quote from the introduction of the paper I just linked:

    "...A possible solution to the big bang singularity could come from a modification, at high energies, of Einstein’s General Relativity. Since this theory could be understood as a linear teleparallel theory (recall that Einstein used teleparallelism in an unsuccessful attempt to unify gravitation with electromagnetism [1]), because its Lagrangian is a linear function of the spacetime scalar torsion, namely T , one can assume that our universe could be described by non-linear teleparallel theories (F(T ) theories) [2, 3, 4, 5], that become nearly linear at low energies.
    It is known that F(T) gravity can realize both inflation [6] and the late-time cosmic acceleration [7, 8, 9], revealed by recent observations for example, Type Ia Supernovae [10], baryon acoustic oscillations (BAO) [11], large scale structure (LSS) [12], cosmic microwave background (CMB) radiation [13], and effects of weak lensing [14] (see [15] for a recent review of current cosmic acceleration). In fact, a very large number of recent papers are devoted to investigate diverse properties of F(T) gravity in order to check whether it could be a veritable alternative to General Relativity [16]. Moreover, models of F(T) gravity in which the finite-time future singularities appear have been reconstructed [17].
    When one considers an homogeneous and isotropic space-time, i.e., when one considers the Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, the scalar torsion is given by T = −6H2, where H is the Hubble parameter [7], as a very remarkable consequence, F(T) cosmologies entail that the modified Friedmann equation depicts a curve in the plane (H, ρ), where ρ denotes the energy density of the universe. That is, the universe moves along this curve with its dynamics given by the so-called modified Raychaudhuri equation and the conservation equation...
    Our main result is to show that, for the flat FRWL geometry, choosing as F (T ) theory the effective formulation of Loop Quantum Cosmology ..., the modified Friedmann equation that
    includes holonomy corrections gives, at early times, a universe in an anti de Sitter phase, which after leaving this phase starts to accelerate leaving the contracting phase to enter in the expanding one (it bounces), then it starts to decelerate and passes trough a radiation and matter dominated phase. Finally, at late times it enters in a de Sitter phase (late time cosmic acceleration). Our model does not suffer the flatness and horizon problem that appear in big bang cosmology, because it has a contracting phase and a super-inflationary period (H ̇ > 0), then in principle, making unnecessary an inflationary epoch such as that of big bang cosmology, where the scale factor increases more that 60 e-folds in order to solve these problems.

    Moreover, the evolution of the universe at early times, in a contracting matter-dominated phase, could produce an scale-invariant spectrum of cosmological perturbations that agrees whit current observations. Finally it is important to stress that our viewpoint of LQC as a F(T) theory…"

    This is something I, as non-expert, cannot dismiss out of hand, nor can I leap headlong into the unknown territory of a new "brand" of quantum cosmology. I have to apply patient open-minded attention.
    Let's see if we can find some mainstream Loop papers that have CITED Odintsov's F(T)-brand papers. Let's see if we can find where he or co-workers have presented talks at Perimeter or at major conferences. Has there been anything yet about it at ILQGS?

    Sorry I can't supply anything more definite by way of response.
  6. Nov 22, 2013 #5
    Very interesting stuff , thanks MArcus, will try and look over this through the weekend,
  7. Nov 27, 2013 #6
    Interestingly , this paper just came on the arvix claiming that super inflation can explain the Planck anomalies , its from a string perspective though but could be interesting:
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