Minkowski vs deSitter: hyperbolic vs spherical?

[nomadreid]

I am a bit confused over the shape of matterless spacetime: on one side Minkowski space is described as hyperbolic, and deSitter space is (hyper)spherical. Both are used, yet how can you have spacetime being both hyperbolic and spherical?

 

[nomadreid]

Wait. I just found the following from another thread:"de Sitter space is... a (3+1) 4-dimensional hypersurface in a 5-dimensional (4+1) Minkowski space." I think that answers my question, but this poses another, rather elementary question: in discussions of expanding spacetime, which one are we referring to?

 

[Amanheis]

De Sitter space is not a physical model. It is a solution of the Einstein equations but doesn't make much sense.
In discussions of expanding spacetime, we usually mean the Robertson-Walker-metric.

 

[nomadreid]

Thanks for the tip about the Robertson-Walker-metric. That gives me something to work through.
When you say that de Sitter space "doesn't make much sense", I presume you mean that its physical interpretation remains only useful on a cosmic scale.