Ok, I will assume that space has a positive curvature, where space is the "surface" of this sphere, and time is the radius from the center, so the universe is a 4D hypersphere. Under these assumptions, this would mean that the "center" of the universe is the big bang. Now back to my question. if these assumptions are correct, does this mean that in order for time to progress, everything must have a greater distance from the center, and so space expands, or is there something that I am missing?
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1$\begingroup$ There is absolutely no observational evidence for the universe being closed. Instead, everything so far points towards an open, flat universe. $\endgroup$– paulinaCommented May 26 at 17:19
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1$\begingroup$ also, there is nothing stopping you from using the time coordinate to parametrize the expansion of the universe, indeed, this is done in the Friedman-Lemaitre-Robertson-Walker metric. This does not imply that time causes the expansion. $\endgroup$– paulinaCommented May 26 at 17:22
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General relativity doesn't work like that. Space doesn't need a place to put itself. It is the place.
In many cosmologies with positive spatial curvature, the universe recollapses, so it passes through the same values of the scale factor a second time in reverse order. There isn't any overlap between the two times when the scale factor has the same value. They're different times, and therefore they're different places in spacetime.
