Is there reason to expect that the universe should conform to any simple geometric structure?
Geometry is a product of rational thought. Euclidean geometry is "real" as is Reimann (sp?). A sphere exists in Euclidean space just as a sphere can exist in Reimann or in a negatively curved space (it may "look" different but it satisfies a definition of a sphere in that space). BUT, "space" here does not mean space like the cosmos when we look up at it. Space is a very specificly defined mathematical term. I think that the problem is that the term is confused with space as in the cosmos. To think of the cosmos as possessing a certain geometry doesn't make much sense to me. To use geometry as a metaphor to make calculations about gravitational attraction is useful where it can make accurate predictions. But there are places where GR doesn't appear to predict things that actually exist so kludges keep being stuck onto the metaphor.