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I have a question regarding the idea of eternal inflation happening in a multiverse and the topology of our universe.

Looking at the current data it seems plausible that our universe is flat or slightly negatively curved, i.e. has a non-compact topology. But the idea of eternal inflation tells us that our universe (every universe) was created from a small quantum fluctuation of a "mother-universe; therefore I would say that our universe created from a small region of cannot have a non-compact topology.

Is there an idea whether and how during eternal inflation something like a topology change can happen? Or is a local deformation of geometry sufficient to explain the shape of the universe we observe?