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I understand why the expansion of the universe is believed to be caused by the expansion of vacuum space, i.e. the Hubble flow.

I understand that if the universe had mass/energy in excess of its critical density, then it would be a "closed" universe which would eventually start contracting (potentially after a long expansion phase). I understand that it is believed that in a contracting universe, space itself would be contracting (shrinking), bringing galaxies, etc. closer and closer together.

Something strikes me as odd about such a contraction of space. If the universe has more mass/energy density than its critical density, won't normal gravitation cause the galaxies, etc. to clump together through peculiar motion (i.e., motion through space), first in many small clumps, then a few large clumps, and perhaps eventually in a single clump containing all of the mass/energy of the universe?

If the latter were true, then at some point during the contraction, couldn't the single clump have a volume much smaller than the volume of space in the universe? Leaving an island of mass/energy surrounded by a potentially large (or infinite?) void of empty space? This seems entirely contradictory to the standard concept of a homogeneous, isotropic universe.

Perhaps the answer is that the closed universe will eventually reach a spatial contraction rate far faster than the peculiar velocities of the mass/energy clumps, thus overtaking their gravitational clumping rate and, ultimately, reaching a singularity (whatever that means) before mass/energy has been able to concentrate in a single clump. I guess the question is whether that is mathematically compelled to be the case, or whether at some selected density value (as a factor of time), the "ultimate clump" could form, as I described. On the other hand, the faster space itself contracts, the more the rate of gravitational clumping through gravitation should also accelerate, due to the ever shrinking distances between clumps.

Related question: Could the additional clumping occurring during the contraction phase cause the universe to become sufficiently inhomogeneous at large scales that the Friedmann equations no longer apply?

Thanks, Jon

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# Closed Universe

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