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Pre-inflationary spatial curvature

  1. Dec 12, 2013 #1


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    Prior to expansion the inflaton field had a large potential energy. I wonder whether there are any considerations or calculations to evaluate how to this energy curves the space created by the big bang.

    Does it make sense at all to talk about critical vs. actual energy density, the value of the Hubble-Parameter, any time dependence of the scale factor, ... regarding that era?

    The big bang was hot and dense. Was does this mean, having in mind that the decay of the inflaton field into particles and radiation happened later? Naively but probaly wrong I would say hot and dense means positive curvature. But perhaps, as the nature of said scalar field isn't known, one can only speculate.

    Dense should mean pressure. Was there already negative pressure or only later, when the expansion was driven exponentially?
  2. jcsd
  3. Dec 12, 2013 #2
    I think you are asking questions that so far have mostly speculative answers......

    edit: seems so,
    from an earlier discussion in these forums [which I did not record]......

    Ivan Agullo, Abhay Ashtekar, William Nelson
    (Submitted on 7 Sep 2012)

    2009 perspective from Steve Carlip that may offer interesting possibilities:

    The Small Scale Structure of Spacetime
    http://arxiv.org/PS_cache/arxiv/pdf/...009.1136v1.pdf [Broken]

    Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional.

    Stephen Hawking and George Ellis prefaced their seminal book, The Large Scale
    Structure of Space-Time.......

    Last edited by a moderator: May 6, 2017
  4. Dec 14, 2013 #3


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    Naty 1, thanks for your answer and the quotations. I wonder whether some knowledge regarding the nature of said scalar field would help to determine the curvature of that era. Perhaps not, because that's Quantum Regime.
  5. Dec 14, 2013 #4
    Here are some other related notes I have:

    Wikipedia LQC: [Loop Quantum Cosmology]

    In quantum geometry a discrete formulation leads to a repulsive force at the Planck scale

    and there is a rather involved discussion here:
    [not too much on curvature...]

    Cycles of time--Penrose says his cyclic cosmology obeys thermodynamics.

    ....did not look to see who posted this:

  6. Dec 15, 2013 #5


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    Thanks again.

    Let's neglect for the moment any pre-inflationary spatial curvature, assuming it doesn't exist or isn't definable.

    Then another question arises:

    So, as the inflation is driven by vacuum energy (the decay of the inflaton field into matter happened at its end) the inflationary universe should be spatially flat, like the de-Sitter universe. Then however, if the inflationary universe is flat anyhow it seems there is no need to argue that due to inflation any pre-existing curvature is flattened out. What do I misunderstand?
  7. Dec 15, 2013 #6
    10-33 seconds is about the end of the inflationary era...by then things were apparently pretty flat....I don't know further details about how quickly they 'became flat' during infltion but from discussions in these forums I believe most cosmologists think things were rather highly gravitational, that is spacetime as best we can describe it, was highly curved....asymptotically 'infinite'.....before inflation. As already posted, it seems it can be repulsive....maybe two dimensional.....whatever that means.....

    Another view:
    Wikipedia LQC: [Loop Quantum Cosmology]

    In another paper, Guth, Ashtekar say:

    You can interpret this as well as me....
    I take it to mean,
    "perhaps space and [emergent] time are not at all what we classicaly think they are" or

    "we didn't even find time, all we could find was a scalar field that can be interpreted to act as such..."

    "Our model ends up with a finite start [bounce] but still appears to replicate current large scale cosmological observations...."

    I checked Alan Guth's INFLATIONARY UNIVERSE, my copy 1997...Epilogue

    He goes on to say he worked with Lisa Randall, Harvard, and they had trouble naming a new version of inflation she invented...several names they tentatively picked were already taken and they didn't even know it....[LOL]

    I checked Lisa Randalls Book WARPED PASSAGES, 2005 [ which has discouraged me from reading further about particle physics....goodbook, but just too many particles, I got indigestion]

    All I could find of direct interest [not very illuminating] :

    I'm concluding others haven't posted because [a] it's somewhat unsettled science, I haven't said anything too crazy yet......so I better stop.
  8. Dec 15, 2013 #7


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    The vacuum energy of the inflaton field drives the universe towards flatness. The general idea being that the curvature prior to inflation is unimportant; once the inflaton potential energy comes to dominate a region of spacetime, that region inflates and approaches flatness.
  9. Dec 16, 2013 #8


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    In this view which is the usual one the 'flattening-out' develops over time due to the exponential growth of the scale-factor.

    In the other view, mentioned by Wikipedia the inflationary universe behaves like de-Sitterer (empty with a positive cosmological constant only) and thus is spatially flat per se, no development over time.

    Is this just a semantic difference?
  10. Dec 16, 2013 #9


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    Pure de Sitter is flat, but inflation is not quite pure de Sitter. In order for inflation to be a dynamical process (start, proceed, end), the vacuum energy must vary (so, not a cosmological constant.)
  11. Dec 16, 2013 #10
  12. Dec 16, 2013 #11


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    Just to make sure that I understand you correctly. Provided the energy density consists exclusively of vacuum energy, then the space is flat during the whole dynamical process, you mentioned . Because flatness depends on the existence of vacuum energy in this case, not however on it's amount. Would this be correct?
  13. Dec 16, 2013 #12


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    Yes. A universe filled with nothing but cosmological constant is flat regardless of the magnitude of this constant.
  14. Dec 17, 2013 #13


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    Ok, thanks.
  15. Dec 17, 2013 #14
    Just to confirm what I think bapowell is implying, that's a misleading statement...not very accurate...in fact it seems refuted by comments later in the article...and that article is critiqued by wikipedia itself.....

    seems a lot more accurate to state the final stage of the universe will be asymptotically deSitter.
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