Spacetime curvature is given by the cosmological constant, that produces a De-Sitter spacetime. It is non-zero

But space curvature is nearly zero (how close to zero, compared to the cosmological constant?)

If we accept Kaluza-Klein derived theories (I like to believe that that encompasses string theory and M-theory as well, but one is never sure these days), then one would expect that curvatures of hidden dimensions are huge to be able to stay hidden (by the way, one can conceive high curvature manifolds that are not bounded, hence is not clear how high curvature helps hidden dimensions to stay hidden in all cases)

I'm wondering if one can think of individual dimensional curvatures as cosmological variables, and time was the last one to expand exponentially, while space dimensions where older than time (in some mathematically yet unrealised sense), and electromagnetic gauge U(1) is just the higher inner dimension

Can we compare the curvature of a typical Kaluza-Klein theory compactification with the curvature of the cosmological constant? what about the curvature of the U(1) electromagnetic gauge dimension? can one express the 1/137 coupling constant of electromagnetism as a curvature?

I'm aware that there is no evidence for the electromagnetic dimension to budge or expand in spectroscopic analysis of light from the farthest observed galaxies, but I think that's still an interesting scenario to think about

Spacetime curvature is given by the cosmological constant, that produces a De-Sitter spacetime. It is non-zero.

But space curvature is nearly zero (how close to zero, compared to the cosmological constant?)

If we accept Kaluza-Klein derived theories (I like to believe that that encompasses string theory and M-theory as well, but one is never sure these days), then one would expect that curvatures of hidden dimensions are huge to be able to stay hidden (by the way, one can conceive high curvature manifolds that are not bounded, hence is not clear how high curvature helps hidden dimensions to stay hidden in all cases)

I'm wondering if one can think of individual dimensional curvatures as cosmological variables, and time was the last one to expand exponentially, while space dimensions where older than time (in some mathematically yet unrealised sense), and electromagnetic gauge $U(1)$ is just the higher inner dimension

Can we compare the curvature of a typical Kaluza-Klein theory compactification with the curvature of the cosmological constant? what about the curvature of the U(1) electromagnetic gauge dimension? can one express the 1/137 coupling constant of electromagnetism as a curvature?

I'm aware that there is no evidence for the electromagnetic dimension to budge or expand in spectroscopic analysis of light from the farthest observed galaxies, but I think that's still an interesting scenario to think about