The wave function of quantum mechanics at a fixed point in space-time is simply a set of complex numbers. How does the set of these numbers relate to the geometry of the universe?
Nothing. The geometry of the Universe is described by classical gravity. How to describe it, when quantum effects become relevant, isn't known.
Classical gravity determines only the internal geometry of space-time, and the geometry of the universe is something else.
For simplicity, take 1-dimensional space and wrap it around a torus as an irrational coil or around a sphere as a spiral. What does the general theory of relativity say about this?
After all, what can general relativity say about the geometry of the Universe if it is a foliation on a seven-dimensional sphere with a typical layer R^3×S^3? And quantum mechanics says that this is so.
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