Question: Does space really go on forever?

Susan Cartwright answered on 14 Jun 2015:

According to our best observational evidence, probably (but not certainly).

The critical quantity that determines this is the curvature of space. If space is positively curved, that would be the 3D equivalent of the 2D surface of a sphere, say the Earth. The Earth’s surface has no edges – you can’t fall off – but it has a finite area: if you travel far enough, you wind up back where you started. A positively curved space has the same property, but in 3 dimensions (no, I can’t picture it either, our brains do not work in 4 dimensions). If space is positively curved, it does not go on forever.

If space is flat, or negatively curved (yes, that is possible), then it should go on forever, since the alternative would be for it to have an edge that you could fall off, which nobody is prepared to contemplate.

All the evidence to date is consistent with a flat universe, in which case space does go on forever. But the experiments are not absolutely precise, so it is possible that the universe has a small positive curvature. The most recent results I am aware of, from the Planck spacecraft, say that the curvature is less than 0.005, which implies that the radius of curvature is greater than 200 billion light years. So space probably does go on forever, and certainly goes on for a very very long way!