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Lets imagine you have a universe where the average matter density is extremely close the the boundary between one that will expand forever and one that will eventually re-collapse. Now lets imagine that there are very large scale fluctuations in density at the Gpc/Tpc scale and above. Could this result in differences in the rate of expansion between some parts and others, causing parts of the universe to collapse and parts to expand forver? If yes what would this look like near the boundary?

What if the region was non simply connected. (E.G. a torus, or hollow ball.)

How about a universe with bee marginally above the critics density with some very large under dense regions, perhaps ones large enough for the centre to become causally disconnected form the edges.

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    $\begingroup$ Isn't this exactly what a black hole is? i.e. it's an overdense region of the universe that collapsed. $\endgroup$
    – John Rennie
    Commented Jul 31, 2023 at 16:46
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    $\begingroup$ In fact the Oppenheimer-Snyder metric models the interior of a collapsing star using the exact same equation that describes a collapsing universe. $\endgroup$
    – John Rennie
    Commented Jul 31, 2023 at 16:47
  • $\begingroup$ This question was already answered at physics.stackexchange.com/q/756980/24093 $\endgroup$
    – Yukterez
    Commented Jul 31, 2023 at 20:32

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As John Rennie said in comments, yes this can happen, and the result is a black hole. It would be surrounded by a void that would grow in size as the matter that escaped collapse continued to move away.

If the region that collapsed was spherical then the collapse wouldn't have much effect on the larger-scale expansion, since the black hole's distant field is the same as that of the matter that collapsed into it. If the region was irregularly shaped then the collapse might generate huge gravitational waves that might wreak havoc elsewhere; I'm not sure.

If there were an overdense region near us, whether it collapsed or not, we would see inhomogeneity in the cosmic microwave background.

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  • $\begingroup$ What about a non simply connected region larger than the observable universe. Would be difficult to get a single black hole out of that. $\endgroup$
    – blademan9999
    Commented Jul 31, 2023 at 19:32
  • $\begingroup$ @blademan9999 I'm not sure what would happen. You could get a ring of smaller black holes, or a large black hole that included encircled matter that wouldn't have collapsed on its own. $\endgroup$
    – benrg
    Commented Aug 1, 2023 at 7:02
  • $\begingroup$ What about a slighty above critical density universe with a large underdensity region? $\endgroup$
    – blademan9999
    Commented Aug 1, 2023 at 7:23
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I'm sorry that I can't remember the reference, but that claim was made in one of my astrophysics review texts. The basic idea was that the local value of omega varies according to the local mass density. In places where it is > 1, the "local universe" is collapsing and where it is < 1 it is expanding.

This was the only time I had ever seen this state of affairs described in this way, and I do not know if it is a useful concept in cosmology.

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