High School How can the Universe be infinite and yet have a finite age?

[PeterDonis]

Is that, "topology $S^n$ plus constant curvature", restricted to a FRW universe or generally to a universe which obeys the cosmological principle?

It's restricted to a spacetime that has spatial topology $S^n$ and constant spatial curvature. Such spacetimes are a subset of FRW spacetimes or spacetimes that obey the cosmological principle (since there are other topologies besides $S^n$ that allow constant spatial curvature).

 

[kimbyd]

Point of pedantry - an octopus at least has a digestive tract, so is topologically a torus (or possibly something more complex if it has something like gills as well - I'm no marine biologist) since it effectively has a hole right through it. A stuffed toy octopus, though, lacking such biological messiness, would be topologically a sphere.

Ah, yes, you're right. I didn't realize it had a full digestive tract. I misremembered.

 

[Fervent Freyja]

If the universe does indeed bounce in between cycles of beginning and ending, then it can be considered infinite, with a finite "time" in between each cycle. Conceptually, this makes sense, more so than one universe having a single beginning and end, and nothing else existing after that one cycle. With so many possible combinations with particles at each beginning, each new cycle can be different than prior.