>> Einstein postulated a finite universe as part of his formulation of
>> relativity. He said that, since space-time can curve, eventually if
>> you travel in a straight line far enough you will come back to your
>> starting point. This would mean that there is no well defined edge.
>
>  I understand how GR describes the curvature of space-time in relation
> to masses, and given the enormous amount of experimental evidence which
> corroborates this, I see no reason to doubt it.
>
>  However, I don't understand why GR would predict a curved universe
> where each geodesic line is closed. What would cause it? Certainly not
> the mass in the universe. I don't think it would be even nearly enough.
> (Because if it was caused by mass, it would mean that the entire universe
> is actually inside its own Schwarzschild radius, which is clearly not the
> case.)

If the universe is finite it must have a barycenter therefore
masses would tend to orbit. According to Wikipedia, "an object of
any density can be large enough to fall within its own Schwarzschild
radius", this leads to the question of expanding universe vrs collapsing
universe... if the universe has a finite mass, then the density of the
universe is very low, and the Schwarzchild radius is very
very large. Since by definition if a mass traveling outward is included
into the barycenter mass, the density of the universe could be
decreasing, and the Schwarzschild radius would be increasing...

>> Modern astronomers can find no evidence of such a large scale
>> warping of space-time. This is part of why the theories of parallel
>> universes are in vogue, if the universe is infinite, then if you
>> travel in a straight line far enough you might reach a region
>> that is very similar to earth, but isn't quite. It would be "parallel".
>
>  I don't find any kind of logic in that. Why would there be a "similar",
> "parallel" version of anything if you travel far enough? It doesn't make
> any logical sense.

If the universe is infinite, with infinite mass, then at some distance
the same patterns of atoms would be there. There are only a fixed
number of atom types, all the same laws of physics apply, and even
if the number of atom arrangements on a planet is very huge, it's not
infinite, so it must be repeated at some point in an infinite universe.

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