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On the topic of curved spacetimes

  1. Jul 13, 2003 #1
    Hurkyl's thread on why it is useful to study curved spaces as well as some discussions with a friend have led me to pose this question:

    There is a current theory that the universe could be torus shaped because the intrinsic curvature of a torus would be zero, much like that of a flat space. Currently there are observational studies underway to try and determine if there are signature repetitions in the sky that would indicate light has made a curcuit around the universe. Such an idea is possible in theory, but I'm interested in debate on the subject of the implications if the universe turns out to be a torus shaped object, or if there are possibilities for other objects with zero intrinsic curvatures that could be a possible shape of the universe.

    On a side note, I posted this topic in this forum because it is a cosmology issue, and even though it is theoretical, it is not so much of the same breed as M-theory or LQG for example.
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  3. Jul 13, 2003 #2
    An interesting post topic

    that you have. I've always tried to hold an open mind on the topic of the global properties of space and space-time, simply because the data we have is so scant and our imaginations are so limited as to the possibilites.

    The same thing can be said about the local properties to some extent. Instead of space just expanding and contracting, the only two possibilites presently being considered, how about it twisting and turning in various ways? This might be the solution to the vexing problem of galactic rotation instead of dark matter or the MOND hypothesis.
  4. Jul 14, 2003 #3


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    There was an article in Sci American a while back on the possible shapes a finite flat universe could take. Of course, the article is dumbed down but it had lots of nice pretty pictures to get the point across. It is probably still in the Sci American archives, or floating around the net somewhere.
  5. Jul 19, 2003 #4
    Brad_Ad23 -

    I'm one of the few apparent fans of the Hyperbolic universe, of which I believe you are describing. The Torus is not the only minimal surface shape that a Hyperbolic universe could exist in.

    In fact, I still have a site open in my browser window that covers all sorts of possible minimal surfaces that could be applicable for any form of Hyperbolic universe.

    Check out the gallery for some great pictures, and imagine yuorself looking down on the universe. :)

  6. Jul 22, 2003 #5


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    There is an observational problem connected with distinguishing between different possible topologies that flat (zero curvature, Euclidean-seeming) space can have. Undoubtably you've thought about it.

    It might take a billion years of waiting before we detect the "signature repetitions" you mention.
    A flat 3D finite space with very large spatial period is for all practical purposes indistinguishable from an infinite flat 3D space.

    According to the "concordance model" cosmology that Lineweaver describes (or Ned Wright or Michael Turner, there is essential agreement on the parameters of accelerating expansion) objects more than 62 billion LY distant at present will NEVER be visible even if we wait til infinity. So if the universe is toroidal in the sense of being a repeating Euclidean cube but the spatial modulus is bigger than 124 billion LY then we will never know.

    the toroidal flatspace idea has the frustrating feature of not ever being disprovable, even with infinite time.
    If "signature repetitions" have not shown up yet, at age 14 billion years, why should they show up even in the next billion? And yet the universe might still be flatly finite and repetitions due to show up at age 20 billion years. Or it might be flatly finite and because of accelerated expansion the repetitions never show up at all, ever.

    Brad you made it clear at the outset of the thread that you were discussing (not hyperbolic models which have negative spatial curvature, but) zero spatial curvature, spatially flat, models. If you continue to be interested in the flat case (which the observations support) there is a lot to investigate in that connection like "what made it flat". Say if you want to delve deeper---it would apply equally to the infinite and finite flat 3D cases.
    Last edited: Jul 22, 2003
  7. Jul 22, 2003 #6
    Indeed. I posted a thread somewhere awhile ago inquiring about people's thoughts about the limitations of observation. Essentially, we have cosmological event horizons a certain distance out because space expands far too fast. I would agree that this is a very frustrating thing about the universe.
  8. Jul 23, 2003 #7


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    From what you say I'd guess you read-up on this some, maybe have read Lineweaver's recent overview of cosmology as I have, or else something equivalent. So you know the upside--there is a lot that can be inferred from observations.

    About spatial flatness, I am impressed with equations 29-32
    on page 11 of lineweaver about how expansion magnifies any slight deviation from flatness. The ordinary reasonably flat flatness we see today implies an *extreme* flatness back in the old days when expansion was only 1 second or 1000 years old.

    this is true under matter-dominated conditions and even more true for a universe where radiation is the dominant form of energy. An implication that interests me is that running the equations backwards shows that as long as matter and/or radiation are dominant contraction favors extreme flatness.

    Maybe you have looked at lineweaver page 11 or something comparable to that and know what I mean. A prior contracting phase explains the Euclidean flatness of space at least as well as the 'inflation scenarios' offered to expain it.
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