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How has LQG resolved the Big Bang Singularity

  1. Jan 5, 2013 #1
    I get the impression from the following material that LQG models have 'resolved'
    the divergent big bang singularity into a finite big crunch....
    If so, what changed and is this a generally accepted 'new start' at the front end of the FLRW model which follows??

    I may have missed some discussions in November/December as I was away,
    but I did skim this discussion from that time frame:

    Penrose's argument that q.g. can't remove the Big Bang singularity
    https://www.physicsforums.com/showthread.php?t=649836


    From that discussion, papers linked to by Marcus were discussed, so I read them and was surprised to find this in the Introduction:

    An Extension of the Quantum Theory of Cosmological
    Perturbations to the Planck Era
    Ivan Agullo, Abhay Ashtekar, William Nelson

    http://arxiv.org/pdf/1211.1354v1.pdf



    Can someone explain what has been 'resolved'?

    From the other paper by the same authors,

    A Quantum Gravity Extension of the Inflationary Scenario
    Ivan Agullo, Abhay Ashtekar, William Nelson
    (Submitted on 7 Sep 2012)
    http://arxiv.org/abs/1209.1609

    the early text says this:



    In layman's terms, did truncating [the author's term] continuous spacetime somehow eliminate the associated divergences??
     
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  3. Jan 5, 2013 #2

    marcus

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    ==Naty's question more in context, quote==
    ...
    ...
    An Extension of the Quantum Theory of Cosmological
    Perturbations to the Planck Era
    Ivan Agullo, Abhay Ashtekar, William Nelson

    http://arxiv.org/pdf/1211.1354v1.pdf


    An Extension of the Quantum Theory of Cosmological
    Perturbations to the Planck Era
    Ivan Agullo, Abhay Ashtekar, William Nelson

    http://arxiv.org/pdf/1211.1354v1.pdf


    ".....Loop quantum gravity (LQG) provides a promising avenue to meet this goal because by now the big bang singularity has been resolved in a variety of models in LQC. It is therefore natural to use LQC as the point of departure for extending the cosmological perturbation theory."

    Can someone explain what has been 'resolved'?

    From the other paper by the same authors,

    A Quantum Gravity Extension of the Inflationary Scenario
    Ivan Agullo, Abhay Ashtekar, William Nelson
    (Submitted on 7 Sep 2012)
    http://arxiv.org/abs/1209.1609

    the early text says this:

    "...Loop quantum gravity (LQG) offers a natural framework to address these issues because effects of its underlying quantum geometry dominate at the Planck scale…The key difference from standard inflation is that quantum fields … now propagate on a quantum geometry represented by Ψo (a, φ) rather than on a classical Friedmann solution (a(t), φ(t)). These quantum geometries are all regular, free of singularities. Thus, by construction, the framework encompasses the Planck regime…., we use the conceptual framework of quantum field theory on cosmological quantum geometries"
    ...
    ...
    ===endquote===

    It will be interesting to see what other people have to say! One simple thing to mention is that "resolve" singularities just means that in your model you get rid of singularities because in your model the singularities in question do not occur.

    The model still has to be tested against observation. Nothing has been "resolved" in a general sense until the model has passed whatever tests people can devise and has become accepted.

    What they mean is they have constructed a number of LQC models (both equation models and computer models) and they all show a bounce from a prior contraction, rather than stopping at a singularity as you go back in time.
    By now they have constructed LQC models with a lot of non-uniformities, unevenness, not-homogeneous, not-isotropic, more degrees of freedom than just one or two. So far the conclusion that in LQC there is a bounce is fairly "robust". This does not mean that it happened in Nature. That is still controversial and has to be checked.

    that is what it means to say the singularities have been resolved in LQC.

    We already knew that in 2005 or 2006 but then it had only been checked in a few of the simpler cases, with a comparatively few computer simulations etc. Since then it has been checked and rechecked in more different cases with varying the parameters, changing details, putting in the little non-uniformities and so forth.
     
  4. Jan 5, 2013 #3

    marcus

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    Naty, if you have a question about the word "truncating" which you say the authors used, could you find a passage and quote it and tell us the page so we can find the context?

    I think what you are referring to could have to do with the discreteness of the spectra of geometric operators in LQC. There is a GAP between zero volume and the lowest positive volume that can be measured. Space might be continuous but when it comes to making measurements and defining operationally meaningful quantities there are limits, in the theory.

    In the theory (which may or may not agree with Nature) there are limits to how small you can measure and how dense something can be. This might be what they were talking about. I'm not thoroughly versed in this but if you can find the passage, and give a page reference, I'll take a look.
     
  5. Jan 5, 2013 #4
    oh, Boo.....big disappointment.....if this all there is:

    Marcus:

    TRUNCATE COMES from the page two, second paragraph of this paper, Introduction,

    An Extension of the Quantum Theory of Cosmological
    Perturbations to the Planck Era
    Ivan Agullo, Abhay Ashtekar, William Nelson

    http://arxiv.org/pdf/1211.1354v1.pdf


    TRUNCATING caught caught my attention because earlier space-time discussions in these forums suggested maybe, based on information theory for example, 'quantized' and 'continuous' space-time might be indistinguishable. So imagine my surprise when "TRUNCATING the classical theory" eliminates Big bang divergence....if that's what happens.

    edit: I see TRUNCATING is explained in Part III of the same paper...
    TRUNCATED HAMILTONIAN FRAMEWORK....oh boy, is THAT above my pay grade....except if it IS a popular approach now, maybe a non mathematical explanation of the motivation could be helpful.

    edit:

    Marcus: "Space might be continuous but when it comes to making measurements and defining operationally meaningful quantities there are limits, in the theory."

    How would you interpret this from the same paper Introduction

    "This paper …. provides a detailed extension of the cosmological perturbation theory to the Planck regime...Specifically, we will consider gravity coupled to a scalar field and study the dynamics of quantum fields representing scalar and tensor perturbations on quantum cosmological space-times. "

    I took this to mean they quantized Einstein continuous spacetime at Planck scale.....I think they said as much somewhere....Maybe I am reading too much into the explanations...
     
    Last edited: Jan 5, 2013
  6. Jan 5, 2013 #5

    atyy

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    The big bang singularity is not resolved in LQG.

    It does seem to be resolved in several versions of LQC. The difference between LQC and LQG is that LQC only allows solutions with a high degree of symmetry - this is essentially what is meant by "truncate" - the solutions with low or no symmetry are not allowed. For this reason, LQC is not considered a full theory of quantum gravity as LQG aims to be. In these papers, there is some degree of inhomogeneity allowed in LQC, but these are assumed not to backreact on the quantum geometry, so LQC is still symmetry restricted.
     
  7. Jan 5, 2013 #6
  8. Jan 5, 2013 #7

    atyy

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  9. Jan 5, 2013 #8
    Key insights from the Wiki link:

    Sounds like quantum geometry repulsion effects prevent classical space-time divergence???


    Rereading the Penrose thread, Marcus posted there:

    "
     
    Last edited: Jan 5, 2013
  10. Jan 5, 2013 #9
    atyy:

    Lol/////you know I never looked!! Thanks....

    from Wiki:

    This description is maybe 2/3 correct!!! Not overprotective: our Schnauzer mix is more so, some Yorkies show LOTS 'SOFT temperament'...when THEY want; NOT always so easy to train...not mentioned: VERY smart, BIG vocabulary, strong willed, gotta watch what you say..because THEY KNOW....and are especially sensitive to cues....All I have to do is take my travel bag out of the closet, and my two are READY to travel!!!!

    No wonder I can't follow some of Wiki's physics!!!!
     
  11. Jan 5, 2013 #10

    atyy

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    Ha, ha - actually I looked it up because I didn't know what "Yorkies" were. Big vocabulary - as in English (or whatever language you speak to them)?
     
  12. Jan 5, 2013 #11

    atyy

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    Reading one of the earlier Ashtekar papers with Pawlowski and Singh, he comments that this is consistent with Asymptotic Safety (p37):

    "The modified field equations (B6) and (B7) can be interpreted as saying that the effective Newton’s constant is given by Geff = G(1 − ρ/ρcrit), where G is the low energy Newton’s constant and ρcrit ≈ 0.82ρPl. Now, the renormalization group analysis based on Euclidean quantum gravity [33] strongly suggests the existence of a non-trivial fixed point at which the theory becomes asymptotically free. The behavior of Geff in LQC is in qualitative agreement with that picture."

    I recently came across another piece of evidence supporting this view - unexpected for me, because I don't think these guys generally work on asymptotic safety: Marunovic & Prokopec, On antiscreening in perturbative quantum gravity and resolving the Newtonian singularity.
     
    Last edited: Jan 5, 2013
  13. Jan 6, 2013 #12
    ok, no more 'Yorkie jibber jabber'....back to the papers:

    So the behavior of G in LQC is consistent with asymptotic safety according to Ashtekar.
    Fine.

    Wikipedia has a qualitative explanation about asymptotic freedom in the Standard Model:

    Fine. [Apparently the interaction behavior of the vacuum and virtual particles changes at high energy and short distance.]

    Is there a similar qualitative explanation for what's happening in LGC that goes a step or two further than Marcus' explanation and the overview from Wiki:


    edit:
    I skimmed the earlier Ashtekar paper with Pawlowski and Singh,
    but did not find much in the way of physical interpretations as to what causes a bounce....but here are some physical interpretations of the math...

    Mathematically "..., to obtain the expression of the quantum constraint, one has to first introduce an operator representing curvature of the gravitational connection....An improved Hamiltonian constraint operator is introduced..... while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities,with the new Hamiltonian constraint it occurs only at a Planck-scale density....the scalar field was shown to serve as an internal clock, thereby providing a detailed realization of the ‘emergent time’ idea....Models discussed so far are too simple to be physically realistic.."
     
    Last edited: Jan 6, 2013
  14. Jan 6, 2013 #13

    marcus

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    There is a superb paper about the bounce on the current MIP poll.

    I assume you believe the Heisenb. uncer. princ. (nature resists being pinned down) and accept that this has physical effects, so there can be quantum corrections e.g. to the Friedmann equation which are due to these (quantum) physical effects.

    So in most of the papers you find a quantum corrected Friedmann equation---Friedmann eqn is derived from Einstein eqn so that is talking about quantum effect on the geometry and that is ENOUGH to cause a bounce because of the term ρ/ρcrit in the corrected Fr. eqn. When it dominates it changes the sign of the Hubble constant H from neg to pos---ie. bounce. contraction changes to expansion.

    But this new paper goes further and considers quantum effect on the matter, which also does not like to be pinned down. And a correction to another equation. This contributes extra springiness so that the bounce occurs earlier, at a substantially lower density. It's important work, and really still in progress. This is the first Loop paper of this type, there will be more along these lines. So this will change the relevant physical intuition IMHO.
     
  15. Jan 6, 2013 #14
  16. Jan 6, 2013 #15

    julian

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    A paper which had an impact on me with regard to the true nature of singularity avoidance in LQG (rather than LQC) was the paper arXiv:gr-qc/0505032 by Thiemann and Brunnemann.

    Would like to hear Francesc's opinion as she has experience with understanding inhomogeneous fluctuations in LQC.
     
    Last edited: Jan 6, 2013
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