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<blockquote data-quote="freyar" data-source="post: 6730053" data-attributes="member: 40227">The energy density of the universe is (within measurement error) the amount that makes the universe spatially flat, yes.&nbsp; Due to the cosmological constant, the expansion is accelerating, again as mentioned earlier.&nbsp; [I am hesitant to use the phrase &quot;open universe&quot; since that had implications up until the discovery of the cosmological constant that no longer apply.]However, even a flat universe can have a nontrivial topology. Your example of gluing the edges of a square together is a good one --- that's the mathematical definition of a 2D torus.&nbsp; So (the spatial part of) our universe could be a flat 3D torus or one of several other alternatives.&nbsp; (That's assuming it's actually exactly flat; there are other alternatives if it's positively or negatively curved.)&nbsp; How do we know if the universe is infinite or a finite torus/other example?&nbsp; We actually have to go measure.&nbsp; There are several groups that have looked at the cosmic microwave background (the oldest visible light); if the universe is finite and small enough, we'd be able to see repeated patterns due to seeing the same spot in the early universe from several directions (think about different ways you can shoot the same area on the screen in the old Asteroids game).&nbsp; So far, we don't see any repeated patterns like that, which means that the universe is either infinite or else finite but so big we can't see all the way around it.This isn't really correct.&nbsp; There are finite, _flat_ spaces with nontrivial topology that solve Einstein's equations with _zero_ mass or energy density.&nbsp; A torus is an example.&nbsp; And our universe could have one of those spatial topologies.&nbsp; Black holes and wormholes do have curvature, though, so they require mass/energy.</blockquote>

[QUOTE="freyar, post: 6730053, member: 40227"] The energy density of the universe is (within measurement error) the amount that makes the universe spatially flat, yes. Due to the cosmological constant, the expansion is accelerating, again as mentioned earlier. [I am hesitant to use the phrase "open universe" since that had implications up until the discovery of the cosmological constant that no longer apply.] However, even a flat universe can have a nontrivial topology. Your example of gluing the edges of a square together is a good one --- that's the mathematical definition of a 2D torus. So (the spatial part of) our universe could be a flat 3D torus or one of several other alternatives. (That's assuming it's actually exactly flat; there are other alternatives if it's positively or negatively curved.) How do we know if the universe is infinite or a finite torus/other example? We actually have to go measure. There are several groups that have looked at the cosmic microwave background (the oldest visible light); if the universe is finite and small enough, we'd be able to see repeated patterns due to seeing the same spot in the early universe from several directions (think about different ways you can shoot the same area on the screen in the old Asteroids game). So far, we don't see any repeated patterns like that, which means that the universe is either infinite or else finite but so big we can't see all the way around it. This isn't really correct. There are finite, _flat_ spaces with nontrivial topology that solve Einstein's equations with _zero_ mass or energy density. A torus is an example. And our universe could have one of those spatial topologies. Black holes and wormholes do have curvature, though, so they require mass/energy. [/QUOTE]

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