Aekiel t1_iy7hyfh wrote

There's a lot of debate about this.

The prevailing theories at the moment are that the universe is either infinite or finite. If it is infinite then there is no question of whether it is bounded or not (it is unbounded as you can't name two points within the universe and have the distance between them encompass everything within it).

If it is finite then the question is whether it has an edge or not. If it has an edge it is referred to as a bounded universe and we have little idea what could be at or beyond the edge of such a universe.

If it is a finite but unbounded universe then there's a definable volume to the universe (that is growing all the time due to expansion), but it doesn't have an edge. This is where the common balloon analogy comes in (a balloon doesn't have an edge, but as it expands the surface area of the balloon and distance between two points expansions).

Current thought rules out a finite bounded universe as it violates homogeneity, but there's no settled consensus on whether we live in an unbounded infinite universe or an unbounded finite one.

EDIT: If we do live in a bounded finite universe there's also debate as to the geometry of it (is it like a sphere? a torus? something weirder?).