Why does the balloon analogy not accurately describe the universe? Common sense would say that an expanding isomorphic homogenous space would have to be curved in a higher, infinite, spatial dimension. Astronomers seem unsure if the universe is finite or infinite. Physicists seem to, according to wiki, wish to avoid the concept of infinity. Mathematicians are a little opaque, for me, on most issues; so, I don't know if they are saying infinity can expand. Can anyone tell me what the "official" teaching on the balloon analogy is?