Could an infinite Universe ever end?
No. By definition.
If by "end" you mean "end in space", then obviously not, as DaveC426913 pointed out.
If by "end" you mean "end in time", i.e., "come to an end", then according to GR, no; any spatially infinite universe must keep expanding forever.
I didn't know that. Care to elucidate?
There are no solutions in the FRW family of spacetimes that are spatially infinite and recollapse; all of the spatially infinite solutions expand forever. The only solutions that recollapse are spatially finite (closed universes--but not even all of those recollapse, some, with positive cosmological constant, expand forever).
I'm not sure that's true. You could have universe with a negative cosmological constant and open curvature that recollapses. However, it might not "end" in the sense that quantum gravity might demonstrate that something happens after the recollapse.
Hm, yes, you're right. (I think a flat universe could also recollapse with a negative cosmological constant.) AFIAK, nobody has proposed that such a model might describe our actual universe, so it would not be relevant in a practical sense, but as a matter of theory, yes, such a model could be spatially infinite and recollapse.
Yes, agreed; this would be true of closed models that recollapse as well.
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