Is it possible, or in any way related, that a small but non-zero curvature could be responsible for the accelerated expansion of the universe? I don't know, it's hard to picture. But I'm thinking the idea that you can look at a sphere as a 2 dimensional space that curves and eventually wraps around such that things going opposite directions on its surface eventually can run into each other again.
That would probably be more easily measured though. I don't know.
A small non-zero curvature would correspond to a non-zero cosmological constant, which is precisely what seems to be driving the accelerated expansion of the universe (there are other explanations but this is the simplest one).
That would probably be more easily measured though. I don't know.