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A topological question

  1. Dec 20, 2004 #1
    The critical density determines the Universe evolution along time. So, by measuring this density, we could know about the finite or infinite age of the Universe.

    But we don't know from General Relativity if our Universe is spatially finite or infinite.

    As far as I know, such question could be only answered from Topology.

    If so, are there enough observational evidences to sustain any topology?

    What would be the observational keys to elucidate this topology?
     
  2. jcsd
  3. Dec 20, 2004 #2

    Garth

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    If repeated patterns, "circles in the sky", were to be found in the CMB radiation that would be evidence of a closed universe.

    Actually we don't even know the future of the universe by simply measuring its density. That would have been true in a plain Friedmann universe, without a cosmological constant or dark energy, but as today it is generally accepted that the universe is accelerating in its expansion and that acceleration (due to dark energy?) switches itself on and off, nothing can be said about the future. Big crunch, Big sigh, big rip????
     
  4. Dec 20, 2004 #3

    Chronos

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    If I may expand on what Garth said, repeating patterns in the cosmic microwave background [CMB] would be evidence the universe is finite, which is to say it wraps around on itself [something akin to seeing the back of your head through a telescope]. Scientists have looked for evidence of this in the CMB and came up empty. For details see
    "The universe is at least 156 billion light-years wide."
    http://www.space.com/scienceastronomy/mystery_monday_040524.html
    For a general discussion of topology and means to detect see:
    Cosmic Topology: a Brief Overview
    http://arxiv.org/abs/astro-ph/0402324
     
    Last edited: Dec 20, 2004
  5. Dec 20, 2004 #4
    There was some months ago a proposition by some people that the Universe could have the shape of a horn, a horn of finite volume. This kind of universe, called Picard Universe, is explored in this paper that has appeared this month
    http://arxiv.org/abs/astro-ph/0412407
    Can one hear the shape of the Universe?
     
  6. Dec 20, 2004 #5

    Garth

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    A horn? Try a cone, not only is it spatially finite, and so explains the large angle anisotopry deficiency but if of a large enough size would not necessarily show any detectable "circles in the sky", and is conformally flat, so it would be concordant with all the major WMAP features.

    Garth
     
  7. Dec 21, 2004 #6

    Chronos

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    Agreed, although I think the jury is still out on the large scale anisotropy deficiency. It does not necessarily mean the universe is spatially finite. The universe is, however, observationally finite. I therefore suspect observational evidence will indicate it is exactly as large as it appears to be.
     
  8. Dec 22, 2004 #7
    If we are going to talk about geometry, we can also mention the Poincare dodecahedron
    http://arxiv.org/abs/astro-ph/0412569

    I find enticing the finite topologies. The concordance model says that the universe is infinite, but infinites are strange things. You can barely deal with them in maths... Why should them exist in real life...?
     
  9. Dec 22, 2004 #8

    Garth

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    I thought the Poincare dodecahedron has now been eliminated?
    From NewScientist, 11 October 2003 "Does the universe go on forever?"


    Garth
     
    Last edited: Dec 22, 2004
  10. Dec 28, 2004 #9
    But our universe could be also multiply-connected in absence of circles in the sky if the "cell" size were higher than our observable (horizon) universe. Is that o.k? If so, we couldn't know its topology.

    And... what do you think about the possibilities of repeated patterns in distribution of quasars (or other 3D distribution) as a method to solve topology ?
     
  11. Dec 28, 2004 #10

    Garth

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    True
    In the absence of such repeated patterns in the sky it might seem a little extravagant to invoke multiple-connected topologies, when a simply connected cone - the freely coasting closed universe - would do just as well.

    Garth

    [Note: the cone topology would be closed yet conformally flat and so it would be one way of explaining the WMAP data]
     
    Last edited: Dec 28, 2004
  12. Dec 29, 2004 #11

    Chronos

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    That is pure balogna. Show a single pattern that defies probability. Your turn. I said it does not exist, you said it did. Prove me wrong. That is a bunch of crap.
     
  13. Dec 29, 2004 #12
    In my last post, I only posed two questions. I didn't any affirmation as you seems suggest with your "elegant" reply.

    Now, I ask you these other questions:

    1. Do you really think that your answer is scientific? Are terms as "balogna" and "bunch of crap" solid arguments?

    2. Do you think that your answer is respectful?

    I believed that this forum was scientific and respectful. With your "answer" you show me that I was mistaken.

    Best wishes.
     
  14. Jan 13, 2005 #13

    Phobos

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    Chronos - That response was inappropriate. Keep the discussion civil.

    Given that this thread has been inactive for 2 weeks, I'm locking it up rather than restarting any arguments.
     
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