I don’t know where you heard that, but the short answer is that no-one knows. There are models of space that curve back in on themselves, and thus have finite extent, even without any kind of hard boundary. But astronomical observations thus far indicate that spacetime is pretty flat, or we’d have seen distortions of scale in the distance. What we know to available observational precision, last I heard indicates that even if the universe does curve in on itself, it must be so slight that the total Universe is at least thousands of times larger (in volume) than the observable part, which is still nowhere near big enough for Tegmark Level I, but that’s a lower bound and it may well be infinite. (There are more complicated models that have topological weirdness that might allow for a finite extent with no boundary and no curvature in observable dimensions that might be smaller.)
I don’t know if it makes any meaningful difference if the Universe is infinite vs “sufficiently large”. As soon as it’s big enough to have all physically realizable initial conditions and histories, why does it matter if they happen once or a googol or infinity times? Maybe there are some counterintuitive anthropic arguments involving Boltzmann Brains. Those seem to pop up in cosmology sometimes.
I don’t know where you heard that, but the short answer is that no-one knows. There are models of space that curve back in on themselves, and thus have finite extent, even without any kind of hard boundary. But astronomical observations thus far indicate that spacetime is pretty flat, or we’d have seen distortions of scale in the distance. What we know to available observational precision, last I heard indicates that even if the universe does curve in on itself, it must be so slight that the total Universe is at least thousands of times larger (in volume) than the observable part, which is still nowhere near big enough for Tegmark Level I, but that’s a lower bound and it may well be infinite. (There are more complicated models that have topological weirdness that might allow for a finite extent with no boundary and no curvature in observable dimensions that might be smaller.)
I don’t know if it makes any meaningful difference if the Universe is infinite vs “sufficiently large”. As soon as it’s big enough to have all physically realizable initial conditions and histories, why does it matter if they happen once or a googol or infinity times? Maybe there are some counterintuitive anthropic arguments involving Boltzmann Brains. Those seem to pop up in cosmology sometimes.