>At one moment, it was believed that space curved back on itself - like the surface of a sphere, but with one more dimension. I am not sure what is the current view on this.

(Super)string theory proposes 10 dimensions - prior to the Planck time (10**-43 seconds) all were of similar size, after that time only the 4 dimensions we are familiar with expanded, the remaining 6 remained compacted to below the Planck length (10**-34m) and consequently are not directly detectable.

There is also M-theory (membrane), which proposes 11 dimensions.

There was a recent theory of the creation of the universe based around parallel 4-dimensional membranes in a 5th dimension in collision, called something like the "Ekpyrotic" theory. I'll try & find a reference for you.