I am mostly interested in how global spacetime geometry might effect local physics. Similarly to Mach's principle, different global boundary conditions yield different solutions to the differential equations of local problems (where the geometry itself is governed by general relativity)
In particular I would like to ascertain whether some of the local physical principles we take for granted might not be a result of such boundary conditions. Should that be the case such principles would not do well (or rather not lend themselves to being used ) in arbitrary geometries. Because quantum mechanics does not lend itself to meshing nicely with general relativity( is does not subscribe to a full covariant formulation) I have come to wonder if some of its properties might not stem from a particular set of boundary conditions for the universe.