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I Finite universe models

  1. Jan 20, 2017 #1
    Hi guys,

    Based on what I know about the status of modern cosmology the question whether the universe is infinite or finite in extent is still open.

    Are there any plausible models in which the universe is finite and closed, despite the curvature being close to flat?

    Thanks in advance.
     
  2. jcsd
  3. Jan 20, 2017 #2

    Chalnoth

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    Certainly. I don't know what to say beyond that: closed is not outside current observational bounds, and there's a good chance it never will be.
     
  4. Jan 21, 2017 #3

    Chronos

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    Einstein definitely preferred a close universe in the spirit of Mach's principle, In both an open and closed universe, there must be boundary and/or initial conditions, but, the question is if the distribution of mass-energy is sufficient to fully define the field, or if independent boundary conditions are necessary to seal the deal. In a closed universe boundary conditions can be clearly defined by the mass-energy distribution, but, in an open universe they are quite independent. Therefore a closed universe can satisfy Mach's principle, whereas an open universe definitely cannot. Of course the relevance of this hinges on the validity of Mach's principle. Since we can regard a field as an actual component of the universe, and given spacetime itself is a field under GR, one can argue Mach's dualistic view is irrelevant. However, the devil is in the details. If the distribution of mass-energy plus boundary conditions at infinity yield a unique solution - and which they do under Maxwell's equations (which are linear), but do not under Einstein's equations (which are non-linear). This is probably the point made by Misner, et al, when they comment that "Einstein's theory...demands closure of the geometry in space ... as a boundary condition on initial value equations if they are to yield a well-defined (and, we now know, a unique) 4-geometry".
     
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