# The curvature of our universe?

When someone says that the universe is flat it should be infinite. But, this contradicts the Big bang because infinity can never be reached from below. If the universe is in fact infinite then shouldn't it be infinite always, I mean all the 'time'? Is Big bang a lie or universe does have a curvature?

• It seems to me that you're missing a third option, which is that it's you who is wrong and not everybody else. See physics.stackexchange.com/q/136860. – Javier Sep 23 '17 at 12:46
• Also related: physics.stackexchange.com/q/9419/2451 – Qmechanic Sep 23 '17 at 12:57
• The flat FLRW universe is infinite in space, but not in time. Time still starts 13.8 billion years ago when the universe is infinitely large and has an infinite density. This way the universe does not grow from small to large, but only stretches into a lower density. This model IMHO has no physical meaning, because it is singular (infinite) in size and mass in addition to density and beyond the zero time. Ironically this model is viewed as "correct" by the consensus while in fact it only shows the failure of the FLRW model. – safesphere Sep 23 '17 at 15:38

• @safesphere: take a sheet of paper and roll it up into a tube, connecting the longer edges; if you could also connect the shorter edges by bending the tube into a ring, you'd get a torus which still had the same flat intrinsic geometry as the sheet; in the real world, you of course cannot do so because such a flat torus can't be smoothly embedded into $\mathbb R^3$ – Christoph Sep 23 '17 at 16:41