I think special relativity would disallow our universe from having the structure similar to an ant on a sphere. What I mean is that it can't be possible to travel in a constant direction and to come back to your original location. Suppose there is an observer S on a planet and an observer S' in a spaceship having a relative speed v. (These are the only things in this hypothetical universe and the gravity is ignored.) Suppose when S' moves past S they synchronize their clocks, so they both read zero at the instant of the first passing. Now suppose S' moves "around the surface of the sphere" and comes back to S (without ever needing to accelerate). Then we will have a paradox, because these two events will occur at the same place in both frames, and so each frame will say they measured the proper time and the other frame's clock was ticking more slowly between the events. (There is no acceleration as in the resolution of the twin "paradox"). We can't have both clocks show a lower reading than each other, so this set up seems paradoxical. Is this a justified reason to disallow universes with such structure?