might our universe be a 4-sphere?

[dodecahedron]

Been reading about how the universe is a sphere, a saddle shape and may be flat but is there any evidence that says our universe isn't a hypersphere?

[IsaacKuo]

When you read about the universe being a "sphere", they do mean the surface of a "hypersphere". Just as the surface of a 3-d sphere is 2 dimensional, the surface of a 4-d hypersphere would be 3 dimensional.

[agingjb]

They do indeed mean the boundary of the hypersphere. If the universe is a hypersphere, then it's very big one since there isn't, I'm told, any detectable curvature in the bit we can see.

I suppose the best argument is that if space started out finite, then the hypersphere (S3) is a good a guess as any for the topology of the whole thing if, as seems reasonable, it remained finite.

S3 also has properties only shared by the circle (S1) and S7.

[mugaliens]

Been reading about how the universe is a sphere, a saddle shape and may be flat but is there any evidence that says our universe isn't a hypersphere?

You mean like a tesseract?

[dodecahedron]

You mean like a tesseract?

B-b-but a tesseract isn't round.