> How does something infinite "expand" though? Infinite things don't work like our ordinary intuitions expect. > I always hear "space itself is expanding" but

> How does something infinite "expand" though? Infinite things don't work like our ordinary intuitions expect. > I always hear "space itself is expanding" but how does that work with topology? The topology doesn't change as the universe expands. "Expanding universe" just means that a particular metric (geometry) is imposed on the topology. If you think of the spacetime of the universe as a stack of 3-dimensional spatial slices, "expansion" just means that a given pair of points in space gets further and further apart as you advance from slice to slice into the future. That is perfectly well-defined for infinite slices, even though it's hard to imagine intuitively. The math works just fine. > When you travel in a given direction you will arrive back where you started? No. That would be the case for a spatially finite universe with the topology of a 3-sphere. But our spatially infinite universe has the topology of Euclidean 3-space. > Surely that "shape" or "object" or topology or whatever you want to call it has a volume The spatial 3-volume of the universe is infinite. > relative to something else, or it wouldn't be able to be calculated? Not at all. The universe doesn't need to be embedded in anything else to have a well-defined volume.