# Does inflation predict a closed universe?

I read somewhere that both a closed and a finite flat universe would have zero total energy in General Relativity (On the Zero-Energy Universe). But the best evidence shows that the universe is flat and infinite: "We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent" (NASA).

In this video, at 1:09:59, Lawrence Krauss says: "[Inflation] tells us, remember, that in the largest scales the universe isn't flat. It's actually closed." But the whole point of his argument is that the universe is flat and, because of that, its total energy is exactly zero (e.g., from 53:32 to 54:23).

So, I'm confused. Does inflation really predict a closed universe? If so, how is that compatible with the evidence that the universe is flat?

• Inflation predicts that the size of the whole universe is many orders of magnitude greater than the observable part, so it could be spherical on the large scale but still appear perfectly flat to any measurement we could do. – Nathan Reed Dec 14 '14 at 6:22
• For one thing, the arxiv document you cite does not seem to be a peer-reviewed publication. I would not give it too much credibility. The question of the global geometry of the universe is tied to the question if general relativity is the correct theory. Personally I would not put too much belief in that, either. Since everything else on this matter derives from there, my personal suggestion would be to treat this as a completely open question, which will probably not get resolved sufficiently in this century. – CuriousOne Dec 14 '14 at 6:26

• So it's actually closed if you consider the whole universe, but "flat" in the sense that you can't really measure $\Omega-1$ in the observable universe? Did I get it right? – Wood Dec 14 '14 at 12:00