Posted: Nov 07, 2019 9:02 am
hackenslash wrote:Interesting.
I talk a bit about curvature and the shape of the universe here:
https://www.hackenslash.co.uk/2016/03/b ... art-i.html
Well worth noting - as newolder alluded to - that positive curvature measured locally doesn't rule out the possibility that space is flat or even open on larger scales. This observation aside, the universe has been measured to be remarkably flat on the largest scales we've been able to measure, with no curvature at all to within very small error bars.
Also, a 3-sphere isn't the only closed solution available. A 4-torus is also a potential solution.
Indeed it is, and without ruling out an extra, large dimension to space the Steinhardt & Turok double Klein bottle comes into play too...