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Time direction in LQC bounce

  1. Feb 13, 2015 #1

    wabbit

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    My understanding is that, in the standard GR BB model, an expanding universe starts with infinite spacetime curvature but zero space curvature; but a collapsing universe ends with a diverging, spagghettifying spatial curvature - very different animals.
    The LQC bounce however connects, through a very tiny, very fleeting high density QG phase, a collapse to an expansion. If they both look like their respective GR counterpart, the amount of work the QG phase has to do to forget everything about the horribly distorted collapse geometry and produce the smooth expansion geometry seems staggering.
    But if the origin of time is at the bounce for both sides, then both geometries are spatially flat and the gluing is easy.
    So my question is: are there articles discussing this possibilty in LQC or related approaches? Thanks
     
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  3. Feb 16, 2015 #2

    marcus

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    LQC predicts a single-time-direction bounce. Here's a good example of a recent paper, which bases its analysis on the current ΛCDM standard cosmic model.
    http://arxiv.org/abs/1412.2914
    A ΛCDM bounce scenario
    Yi-Fu Cai, Edward Wilson-Ewing
    (Submitted on 9 Dec 2014 (v1), last revised 28 Jan 2015)
    We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant. Furthermore, the modes that exit the (sound) Hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt, in agreement with observations. We assume that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, and this ensures that the big-bang singularity is resolved and is replaced by a bounce. We calculate the evolution of the perturbations through the bounce and find that they remain nearly scale-invariant. We also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter, the Hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation, and the curvature scale that the loop quantum cosmology bounce occurs at. Importantly, as this scenario predicts a positive running of the scalar index, observations can potentially differentiate between it and inflationary models. Finally, for a small sound speed of cold dark matter, this scenario predicts a small tensor-to-scalar ratio.
    14 pages, 8 figures

    GR breaks down and fails to apply at extreme density. The divergence you point to stems from following GR where it does not apply. In LQG, quantizing GR results in a discrete area spectrum---hence a minimal measurable non-zero area---and a maximum curvature. If you run the model forwards in time, a collapse leads smoothly to a rebound and expansion. If you explore back in time, instead of a singularity you reach a peak density and beyond that a contracting phase. So it provides an interesting framework to add content to, like radiation, dark matter, cosmological constant---to get something fairly realistic that you can compare with observations.
     
  4. Feb 16, 2015 #3

    wabbit

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    Thanks, so no need for time direction shenanigans : ) These scenarios also seem closely analogous to the Planck star scenario, which to me is a little easier to grasp, and it would seem quite silly to pretend time runs backward in the contracting phase of a BH.

    Still, what I find surprising is the huge smoothing effect the bounce has as it transforms a highly asymetrical collapse into a very homogeneous expansion. Is this not a large entropy decrease ? Presumably it isn't and a clarification might come from an analysis of the BH information paradox in the context of Planck stars ?
     
  5. Feb 16, 2015 #4

    marcus

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    Good questions, good points! You know that a collapsing regime that starts out matter-dominated becomes radiation-dominated because radiation energy density goes as the inverse fourth power of scale (instead of third). matter radiation equality in our expanding universe occurred around z = 3300, they think. Back in much higher z, the matter becomes negligible or boils away into something like radiation.
    So personally I don't think of the collapse as "highly asymmetrical"

    I think of the visible U as highly homogeneous at large scale. Visually like the oval CMB map you sometimes see without the blue red exaggeration. The temperature variation in reality is around 10-5, basically a uniform-tone oval. Just my mental picture, people's imagery varies.

    The point to mention about entropy is that it is an observer-dependent concept. Who or what the observer is determines what macroscopic variables the observer interacts with. And therefore partitions the map of phase space into macrostate regions consisting of many indistinguishable (to the observer) microstates. Whose map do we use, going thru the bounce?

    In Lqc the bounce happens because (with GR quantized) quantum corrections that dominate at extreme density make gravity repel instead of attract. Black holes and other structures are not stable. Structure gets wiped and, upon rebound, one starts with a blank, or nearly blank, slate. There is lots of research to be done here, and you can see, in the Cai&Wilson-Ewing paper, how people like C&E-W are getting started on it. There are plenty of open questions, which they enumerate and discuss towards the end of the paper.
     
  6. Feb 16, 2015 #5

    wabbit

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    So observers might not be allowed to cross the bounce (perhaps a particle as such cannot ? because a particle state becomes undefined at the planck density ? ) thus the bounce might act as a barrier which resets any "entropy of the universe"...

    http://arxiv.org/0805.3511 [Broken] seems to suggests that in some cases an entropy calculation could be made across the bounce, but that paper is exploratory and they do caution in particular that "[some] approximations [they use] are suspect especially in the Planck regime."

    The Planck star case is a bit different since we do have external observers who can assign an entropy to both the black and white hole phases - it will be interesting to see how this develops.
     
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