I just finished readying Sean Carroll's book, "From Eternity to Here", and have a question about reversibility and inflation:
Assume inflation allows random quantum fluctuations to produce high energy density regions that pinch off from the original spacetime and grow into disconnected baby universes. If we slice spacetime a while after this disconnection has occurred, how would the time-reversed dynamics know to spontaneously connect the two separated regions of spacetime together? Would this situation necessarily violate time reversibility (or render it undefinable)?
In particular, assuming that the entire multiverse is infinitely large, and each baby universe spawning can be described by a finite number of variables, there would be an infinite number of completely indistinguishable spawning events. Slicing spacetime a short while after each one, they could be reconnected arbitrarily without violating the dynamics.