QM in a very small universe.

[Mike2]

How is QM modified in a small universe? Usually we have path integrals that consider every possible path throughout infinity. But what about the early universe that may have been about the size of an atom or smaller? Do we continue to consider all paths throughout infinity? Or are the paths constrained to the size of the universe, which may be quite small?

Thanks.

[Mike2]

If the dimensions of the very early universe were curled up and flatten out with expansion, then can QM be formulated in these curled up dimensions? Thanks.

[MathematicalPhysicist]

How is QM modified in a small universe? Usually we have path integrals that consider every possible path throughout infinity. But what about the early universe that may have been about the size of an atom or smaller? Do we continue to consider all paths throughout infinity? Or are the paths constrained to the size of the universe, which may be quite small?

Thanks.
this field you are asking the question in is quantum cosmology.
try this link (if you havent tried it already):
http://www.damtp.cam.ac.uk/user/gr/public/qg_qc.html

although it's not technical overview so i dont how much can it help you.

[Mike2]

If the dimensions of the very early universe were curled up and flatten out with expansion, then can QM be formulated in these curled up dimensions? Thanks.
Isn't this precisely how one would connect QM with GR... by determining how to do QM in curved space-times? It sounds like a change of coordinates. But I'm probably being naive about it.