When the mass fills all of space in almost uniform density, can it sustain its state?

When the mass (wood, hardened sand, iced water, stone or whatever but is not so fluid) fills all of space (especially in a volume of infinite size) in almost uniform density, could the mass sustain its state/structure?

I'm afraid about that it will collapse into a planet or something. I think it could create a gravity equilibrium (?) state, but with my limited understanding of physics I cannot be sure of this situation.

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When the mass fills all of space in almost uniform density, can it sustain its state?

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