> "If the universe is expanding, that implies an edge which implies a centre of mass."
Current theory says that it's space itself that is expanding, and there is no "outside" for it to expand into. I gather that if you could travel long enough in a "straight" line you'd find yourself back where you started, but even that is impossible because space is expanding faster than light speed. In fact we can only ever observe a small portion of the whole thing.
Basically the universe is very weird, but we knew that.