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Flat vs finite universe

  1. Jul 11, 2003 #1

    Hurkyl

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    What exactly is the problem with a flat, finite universe?

    I've often heard it quoted that a flat universe must be infinite... but it's easy enough to design space-times that are perfectly flat yet are bounded. For example, S^1*S^1*S^1. What additional information is used to suggest a flat, finite universe is not feasible?
     
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  3. Jul 11, 2003 #2

    jcsd

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    No your correct a flat finite universe is perfectly feasible in the shape of a torus. It's just observational evidence for a torus shape universe is non-existant (that's not to say tere's evidence against it).
     
  4. Jul 11, 2003 #3

    Hurkyl

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    But is a torus the only possible shape?
     
  5. Jul 11, 2003 #4

    jcsd

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    Your stretching my knowledge of cosmological models, but it's the only one I've heard tht meets observational evidence but is bounded and finite.
     
  6. Jul 11, 2003 #5

    jcsd

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    bounded???? I meant unbounded.
     
  7. Jul 11, 2003 #6

    marcus

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    this came up earlier at PF---astronomy forum I think.
    someone posted a link to a paper by some folks who
    were looking for evidence (I think it was repeated galaxies
    but my memory is not clear about this) of some finite flat shape.

    I wonder how careful one should be? Maybe one should only
    say "spatially flat" and never mention infinite extent as probable consequence. I've noticed one cosmologist Michael Turner being careful about this---but others, like Ned Wright IIRC, being
    unrigorous about it and talking as if flat implied infinite.
    (my sympathies are with the unrigorous but I will pull the socks
    up on this if you all think it best)
     
  8. Jul 11, 2003 #7

    Hurkyl

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    The reason I bring it up is that when I've read up on big bang theory, it is terribly "obvious" to me that it is describing a finite expanding universe... so obvious that I once read something on the horizon problem and thought that it actually said the above! (I just recently found it again and discovered it was claiming an infinite universe, which prompted this post)
     
  9. Jul 12, 2003 #8

    marcus

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    delicate issue
    the main thing is that the classical singularity
    is thought of as having spatial extent
    (it is not a point)

    if space has a toroidal topology
    (a cube where when the little guy goes out the top
    he reappears at the bottom, and when he goes offstage
    on the right he reappears coming in at stage left, and
    front and back)
    then I guess, tell me if I'm making an unjustified leap)
    that the topology was probably like that at the time of
    the classical singularity.

    Do I really suffer any downside if I go on thinking of
    the classical singularity as infinite in extent?

    I'm ready to consider informed advice on this. Maybe
    there is some way the singularity could be finite!

    But so far it seems simplest if I assume it infinite in extent.

    My experience with what I've read agrees with yours. The
    authors tend to assume space is flat and infinite. I instinctively
    go along with the crowd---but am not quite sure why.

    So if the classical singularity is resolved it would (by this assumption) be across a spatially extended front.
    the resolution would not be localized to a point.
    divergence would be controled throughout an extended 3D volume [?] which could however have a compact topology
    along the lines you suggested
     
  10. Jul 14, 2003 #9
    Hurkyl, as I recall, Eh posted this same question on the old PFs. It was side-tracked, but one of the points that was brought up was this:

    If the Universe is flat and infinite, then there could be many (possibly infinite) "little" Universes popping up all over the place; while, if the Universe altogether is finite, and expanded from a smaller point, then it would take on a spherical shape.

    I don't know how consistent this is with current cosmological models (which discard the idea of expanding from one point, for the idea of all parts of spacetime expanding), but it's all I can remember from the thread (I'll have to look it up again on my trusty Archive C.D. :smile: (that is, as soon as I get my home computer working again ).
     
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