The implications of a spatially infinite universe is profound, but so are the implications of a finite universe. What we know about this issue?
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As far as we know the spatial sections of our spacetime, the ones comoving with big objects (galaxies and clusters of them), are flat. Hence, assuming that, we have two possibilities related to the topology of those spatial sections.
- These sections are 3 planes, and in that case the volume is infinite.
- These sections are quotients of the 3 planes wit respect to discrete groups of isometrics. In this case, the volume may be either finite or infinite depending on the case.
However, I am not an expert, but I guess that the second case would imply some correlations between the apparent positions of very far objects. I do not know if there is any experimental evidence of similar correlations.
Another issue is whether or not that spatial topology may change in time. On the ground of FLRW model it should not.
Valter Moretti
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