Even though we can make no observations beyond the cosmological horizon, I think people tend to picture a universe that is either homogeneous to infinity, or possibly having spacelike slices that are closed manifolds with homogeneous distributions of matter. Is there any reason other than the Copernican principle to think that this is true? Suppose an infinite universe, with all matter at the present Hubble time being contained in an exaparsec-radius ball. We would only see a part of that so small that any isotropy from density declining towards the boundary would be undetectable. I can't think of any way to distinguish that from an infinite universe.

I ask this question because, depending on your choice of coordinate system, such a universe would be precisely the "big bang as an explosion into empty space" model that many people have but is generally treated as wrong. And it would even be meaningful (although undecidable) to say that the center of the big bang was in a specific direction from here. Or is that wrong?

My take on this is that there really aren't any reasons beyond general considerations like the Copernican principle to reject the exaparsec ball, but that those are probably good enough. But I wanted an expert view.


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As far as I know, there is no published cosmology solution to the the General Relativity (GR) equations assuming a non-homogeneous configuration. I do not have the skills to tackle the math for creating such a solution with the assumptions of a sphere of stuff in an otherwise empty infinite universe, but my intuition is that there is no such GR solution for how such a universe could start. My guess is that a very small sphere with a lot of mass and a void outside would become a black hole, and it would not expand in the manner of a Big Bang.

On the other hand, I do not think it is theoretically impossible for an infinite universe to exist which is not homogeneous on a very large scale of the order of multiple spheres with different densities the size of our observable universe. The problem with assuming such a universe is that there is no way to observe whether our universe has this property, and the math for understanding its behavior is a lot more difficult, so why bother?

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    $\begingroup$ "a sphere of stuff in an otherwise empty infinite universe" is precisely what the Schwarschild solution describes. $\endgroup$
    – D. Halsey
    Oct 17, 2020 at 20:25
  • $\begingroup$ @D. Halsey The Schwarzschild metric does describe the sphere you mention, but it does not deal with a Big Bang, which is what I understand the original question was about. $\endgroup$
    – Buzz
    Nov 3, 2020 at 2:26

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