On the relation between causality and topology in the semiclassical universe

Abstract

We systematically derive a series of validity conditions for semiclassical gravity and deduce a strong restriction on the possible topology of the semiclassical universe founded on the path-integral formalism. We begin with the investigation of the fundamental setting of quantum gravity. We show that, in order to obtain the causal semiclassical Einstein equation at the later stage of the universe, we have to regard the in-in path-integral formalism as fundamental in quantum gravity. We then perform the stationary phase approximation for the gravity mode. From the first variation of the phase , we obtain a series of validity conditions of semiclassical gravity in a completely general manner.