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(Im)probability of Inflation (Ashtekar Sloan 1003.2475)

  1. Jul 16, 2011 #1

    marcus

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    The likelihood or actually the UNlikelihood of a satisfactory inflation episode---assuming various beyond-standard-model pictures of cosmology---has recently become a major issue.

    The discussion revolves around the difficulty of putting a MEASURE on the range of possible initial conditions at the start of expansion. And in models involving a BOUNCE there is the issue of ENTROPY. How can the entropy of the gravitational field (the geometry of the universe) be defined? Assuming a satisfactory definition of entropy, what role might be played by the Second Law of Thermodynamics? Do observers before and after the bounce has different perspectives on the states of the universe and apply fundamentally different coarse-graining, and so on?

    A conference on Challenges for Early Universe Cosmology was recently held at Perimeter and the talks wrestled again and again with the topics of Measure, Bounce, Geometric Entropy, Probability of Inflation.

    At the end of the first talk of the conference (by Turok 12 July) a very interesting point was raised by someone in the audience (at time 1:07:40) who pointed out that Loop cosmology addresses these issue in a comaratively simple way. They referred to this paper of Ashtekar and Sloan:

    http://arxiv.org/abs/1103.2475
    Probability of Inflation in Loop Quantum Cosmology
    Abhay Ashtekar, David Sloan
    34 pages, 3 figures
    Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically or does it require a careful fine tuning of initial parameters? In recent years there has been considerable controversy on this issue. In particular, for a quadratic potential, Kofman, Linde and Mukhanov have argued that the probability of inflation with at least 65 e-foldings is close to one, while Gibbons and Turok have argued that this probability is suppressed by a factor of ~ 10-85. We first clarify that such dramatically different predictions can arise because the required measure on the space of solutions is intrinsically ambiguous in general relativity. We then show that this ambiguity can be naturally resolved in loop quantum cosmology (LQC) because the big bang is replaced by a big bounce and the bounce surface can be used to introduce the structure necessary to specify a satisfactory measure.
    The second goal of the paper is to present a detailed analysis of the inflationary dynamics of LQC using analytical and numerical methods. By combining this information with the measure on the space of solutions, we address a sharper question than those investigated in the literature: What is the probability of a sufficiently long slow roll inflation WHICH IS COMPATIBLE WITH THE SEVEN YEAR WMAP DATA? We show that the probability is very close to 1.
    The material is so organized that cosmologists who may be more interested in the inflationary dynamics in LQC than in the subtleties associated with measures can skip that material without loss of continuity.
    =========

    One of the main points of this paper is that the Loop bounce is simple enough that the universe forms a spacelike hypersurface at the moment of the bounce---making it straightforward to define a probability measure on the range of initial conditions.

    Models suffering from a singularity at the start of expansion, or where something more elaborate happens (which may involve more complicated assumptions) seem to have a harder time establishing a plausible measure on the initial conditions. We saw a lot of that in the talks at the "Challenges" conference. With some models one had to put a measure not on initial conditions at bounce, but on hypothetical limiting states in the far distant future.

    Here are videos of all the conference talks:
    http://pirsa.org/C11008
    The opening one, by Turok, at the top of this iist is the one that had the interesting comment towards the end (at time 1:07:40) referring to the Ashtekar et al result in arxiv 1103.2475.
     
    Last edited: Jul 16, 2011
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  3. Jul 16, 2011 #2

    marcus

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    The essential thing to note here is that IF you assume gravity/geometry is quantized in the style of LQG, this does away with the unlikelihood of adequate inflation---under Ashtekar's assumptions, problem solved. On the other hand if you assume some other early universe model it seems to be much more difficult to match the available data with high probability.

    Speakers coming from various other models mentioned this problem of unlikely or inadequate inflation time and again.

    Sir Roger Penrose gave a talk in which he needed to "transcend" the Second Law of Thermodynamics, to the things to work out. And in which assumed that over 100s of billions of years electrons would become massless----along with all the other particles. Mass itself would decay. His talk was very charming, but illustrates how people were going through contortions to address the issues that I mentioned---the challenges facing early U cosmo.
     
  4. Jul 16, 2011 #3

    marcus

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    Perhaps the best talk to watch on these topics is one given by Abhay Ashtekar in May 2011 at the Madrid Loops conference. At time 27:00, or slightly before that, he starts a new topic
    WMAP AND THE PROBABILITY OF INFLATION.

    If you are interested in this topic you can save time by pausing the talk, dragging the time-button along the timebar until the clock says 26:00 or so, and then unpausing.

    I'll get the link for downloading the Madrid video files. They play on "VLC", a free piece of software that is easy to get off the web.
    Here's the listing of all the Madrid talks:
    http://loops11.iem.csic.es/loops11/index.php?option=com_content&view=article&id=75&Itemid=73
    Plenary talks have links to both slides PDF and video. Having the slides handy in a separate screen can sometimes help you follow the video.
    Scroll down to Wednesday and click on Ashtekar's talk (Recent Advances in Loop Quantum Cosmology) or try this direct link:

    http://loops11.iem.csic.es/loops11/...-Cosmology&catid=35:plenary-lectures&Itemid=1
     
    Last edited: Jul 17, 2011
  5. Jul 17, 2011 #4

    marcus

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    The second link in the preceding post was wrong, sorry. I gave the link to Rovelli's talk instead, by mistake. Too late to edit. Here's the link to Ashtekar's talk (I hope this is right now):
    http://loops11.iem.csic.es/loops11/index.php?option=com_content&view=article&id=181
    Yes! That goes directly the abstract page for Ashtekar's talk, which has further links to the slides PDF and to the video.

    And I gave the time as 27:00, which was off by a minute. The section starts around 28:00. Drag the time button to 28:00 and the slide will say "WMAP and the Probability of Inflation".
     
    Last edited: Jul 17, 2011
  6. Jul 17, 2011 #5

    bcrowell

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    Interesting. I didn't know the relevant background for the Ashtekar-Sloan paper, so I found this helpful: Bojowald, Inflation from Quantum Geometry, http://arxiv.org/abs/gr-qc/0206054

    "Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present-day cosmological acceleration is so tiny."

    Marcus, maybe you could help me to figure out whether I'm understanding correctly.

    I thought LQG had problems incorporating matter fields. Is this now a solved problem?

    Bojowald describes a scalar field (like the traditional inflaton), but one that doesn't have to have a self-interaction potential with any specially cooked up properties. Is he just using a scalar field because it's easy to calculate with, or is LQG's inflation similar to traditional inflation in that you need a matter field that's a scalar? In other words, does LQG still produce inflation if you instead put in some other field such as a photon?

    The Ashtekar-Sloan paper refers to "super-inflation." What's that?
     
  7. Jul 17, 2011 #6

    atyy

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    As far as I understand, it is better to treat LQC separately from LQG. LQC does have matter and gravity. It seems like a framework (But maybe one should read only papers after 2006 first to figure out what that is). LQG has not yet been shown to exist, nor to contain gravity or matter.
     
  8. Jul 17, 2011 #7

    bcrowell

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    Hmm...how can LQG not contain gravity if it's a theory of quantum gravity?
     
  9. Jul 17, 2011 #8

    atyy

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    It may or may not, it's still work in progress. (Or as we know from string theory and AdS/CFT - theories without gravity can contain gravity;)

    LQC, on the other hand does seem to have matter and gravity. However, it is background dependent (requires symmetry of the spacetime).

    It would be nice to have a link between LQC and LQG, but I think that's also work in progress.
     
  10. Jul 17, 2011 #9

    bcrowell

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    I'm sure you know what you're talking about, but I can't make sense of this statement.
     
  11. Jul 17, 2011 #10

    MTd2

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    What is the justification for a quadratic potential and not other kind of potential?
     
  12. Jul 17, 2011 #11

    marcus

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    Hi Ben,
    at present there seem no serious obstacles to including matter in LQG AFAICS. Many of the current papers do include matter. In particular there was that landmark paper around December 2010 called "Spinfoam Fermions".
    I suppose how one thinks about this depends on one's sense of the momentum or progress of research in the field. No responsible expert has identified any reason why it should be impossible to include matter in a fully satisfactory way. Meanwhile plenty remains to be done, and plenty is getting done.
    It's a rapidly developing field, so to gauge the current status and rate of progress one has to watch the latest overview presentation.
    http://loops11.iem.csic.es/loops11/index.php?option=com_content&view=article&id=76

    Inflation is understood to be (near) exponential growth of the scale factor. Super-inflation is a phase of super-exponential growth. The hubble parameter, instead of being large and nearly constant (as in usual inflation) is increasing rapidly.

    Before the bounce the H is negative, and at the bounce H = 0.
    During the extremely brief period of superinflation, H increases from zero to nearly the Planck frequency.

    Then you get inflation with H staying nearly constant and gradually declining.

    The Hubble time 1/H we think of as a long time, like 14 billion years. But by the end of super-inflation H has increased to 93% of Planck frequency so that the Hubble time is around 10-43 second. The bounce is what causes this rapid increase in H.

    If anyone is new to the discussion and wants background, this is OK:
    http://en.wikipedia.org/wiki/Inflation_(cosmology [Broken])
    you will see that during inflation the scale factor ~ eHt with H approx constant.
    In the paper Ben referred to, superinflation is described in section B-1 starting around page 16 or 17.
    You will see that the bounce causes H to increase abruptly from 0 to near Planck scale.
    So in that brief episode the growth is much much faster than exponential! This brief episode is what drives the (hypothetical) inflaton up its potential---gets it all charged up and prepared for a longer satisfactory period of ordinary inflation. Super-inflation itself may be too brief to afford much increase in the scale factor, so you need it to be followed by usual inflation.
     
    Last edited by a moderator: May 5, 2017
  13. Jul 17, 2011 #12

    atyy

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    A regular QFT without gravity in a lower dimension holographically specifies a theory of gravity in a higher dimension. It's one of the most amazing things to have emerged in quantum gravity, not yet proven, but lots of evidence in its favour.

    http://arxiv.org/abs/0909.0518
    http://arxiv.org/abs/gr-qc/0602037
     
  14. Jul 17, 2011 #13

    bcrowell

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    Thanks, atyy and marcus, for the explanations!
     
  15. Jul 18, 2011 #14

    MTd2

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    What is the justification for a quadratic potential and not other kind of potential?
     
  16. Jul 18, 2011 #15

    marcus

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    Quadratic is a common type of inflaton potential which has traditionally been used in constructing inflation scenarios.
    I think this probably goes way back---perhaps to the 1980s---to do the analysis, just for the sake of definiteness inflation scenarists would have needed to specify some type of potential.
    So maybe you should ask that question of Alan Guth or Andrei Linde. :biggrin:

    The point is that IF you assume inflaton with (for the sake of argument) that common type of potential THEN with other approaches YOU STILL HAVE PROBLEMS. As speakers at the Perimeter conference were explaining, adequate inflation is still improbable. But with LQC, making the same assumption, you do not have a fine-tuning problem.

    You might find it interesting to listen to what Ashtekar has to say at around time 28:00 concerning the motivation for taking the possibility of inflation seriously. He emphasizes the observed large-scale structure (clusters of galaxies, superclusters, filaments, voids...). Numerical models of structure formation based the initial density fluctuation spectrum that would have arisen from inflation predict structure resembling what is observed.

    It is an impressive match of theoretical model with observation. I don't think the "quadratic vs non-quadratic" issue is important here. It is just one common type of potential which one traditionally assumes. You have to introduce some potential and that is one which theorists have used for inflation for a long time. Think of it as "generic". It is the choice you don't have to explain. If you pick anything else, it would seem fancy, like a deliberate complication, and then you would need to give a reason.

    The point is not "quadratic vs non-quadratic". It is that inflation (with a wide range of choice for the potential) gives a good match with observed largescale structure. I remain skeptical---I would like to see other possible explanations that do NOT involve inflation. But if you want to have inflation, and you assume the usual generic inflaton field, then getting the right amount of inflation is STILL improbable (unless, as Ashtekar points out, you base the analysis on Lqc.)
     
    Last edited: Jul 18, 2011
  17. Jul 18, 2011 #16

    MTd2

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    It could be a discussion of quadratic vs. non-quadratic. What if the quadratic function is the peak value of an ensemble of eigenfunctions of LQG?
     
  18. Jul 18, 2011 #17

    marcus

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    MTd2,
    Re your question, I suggest you read the last paragraph on page 28. The paragraph which ends "...will continue to hold for a wide class of physically interesting potentials."
     
  19. Jul 18, 2011 #18

    bapowell

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    One important distinction is between potentials that are local attractors and those that aren't. Quadratic inflation is one such potential, one that generically leads to eternal inflation. The other popular potential -- inverted, Mexican hat-type -- are not generically attractors, and without presupposing thermal equilibrium in the pre-inflationary universe, it is difficult to understand how the inflaton would find itself in the false vacuum.
     
  20. Jul 18, 2011 #19
    As a dilettante:

    1. The entropy issue seems like an old (and solved?) problem of time in general relativity (quantum doesn't necessarily add any new problems). It seems possible that current LQC is simply using a coordinate time and not in any sense a measurable time. This might be the perfect testing ground for Rovelli/Connes thermal time hypothesis, and show that time itself becomes poorly defined around the bounce, but away from it definitely flows *away*.

    2. Aren't all potentials quadratic at the bottom? :-p I seem to remember thinking this when the paper first came out and this issue was raised --- was the suggestion was then (as now?) that their analysis needed the lack of higher order terms to remain true because one does get pushed very far away from the bottom of the well?
     
  21. Jul 18, 2011 #20

    marcus

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    Hi Genneth! Yes, this was one of the points made in that paragraph I referred to on page 28 of the paper. I don't think there is any serious issue here---the results hold qualitatively for a wide class of potentials.

    In his Madrid talk Ashtekar explains how to view the results.
     
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