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I am a mathematician with an undergrad understanding of physics. I recently learned of topological defects in quantum fields. It is an intriguing idea that there could be regions in our universe that, to say it mathematically, behave like submanifolds of spacetime. Now, the following thought came to my mind:

Question: Is it conceivable that our universe actually lives on a (3+1)-dimensional topological defect in some higher dimensional space?

Is this exactly the idea of brane cosmology (our universe lives on a 3-dimensional brane in "the bulk")? I read that branes are in the same category as strings (from string theory), and that strings are not to be confused with cosmic strings, which are topological defects. So this left me confused.

Some related thoughts within this hypothetical:

  • could it be that the bulk is some sort of good old actually flat "Minkowski hyperspacetime", and the curvature of our universe comes from the fact that it is actually curved as a submanifold of the bulk? Would this give plausible scenarios for changing the topology of spacetime (which, as far as I know, can't be done via general relativity).
  • are the quantum fields that we observe some "remnants" of the fields in the bulk (perhaps some high-energy versions of those), or are they completely new properties of the subspace we live in?
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    $\begingroup$ Your first bullet point is closely related to the DGP model. $\endgroup$
    – Andrew
    Commented Aug 24, 2023 at 23:12

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