If the universe has no boundaries, then there are eight possibilities, or seven, if the possibility that would be the eighth isn't possible. I'm going to argue that all eight are possible, however, argue against it if you'd like.

The possibilities are a composition of three possibilities: The universe is/isn't finite, the universe is/isn't flat, and the universe is/isn't metaisotropic.

By finite I mean simply that, excluding black holes, and assuming that the universe is not fractal, there exists a finite amount of space.
By flat, I mean as flat as possible given the other two conditions, even if this means I can be only locally flat and not globally flat, or vice versa.
By isotropic I mean that for each point in that universe, there exists a velocity for which universe, by that frame of reference, is radially symmetric.

These definitions really don't work that well, but please do the best you can with them, and don't just assume that they don't work, even if your judgment is backed up with evidence. Just assume that I didn't word them correctly. Don't assume that I don't understand what I'm saying either.

Imagine, for each universe, I go a certain distance, and with minimum curvature. I return to where I started. Aside from acceleration with respect to local curvature, how am I going to be affected by global curvature?

Imagine a non-flat, finite universe, whether it is metaisotropic doesn't matter but sometimes it's easier to get the full impact of this question if it's metaisotropic. Two twins go on journies. One travels from their home planet, and goes around in a figure eight or an infinity. At the same time, the other travels from their home planet and goes around the entire universe. Then they both go home. Their departure and arrival time is the same. Now this is a relatively small universe and the twins are practically immortal. Let's assume they both accelerate the same amount. Which one ends up older and which one ends up younger?