Time in semiclassical gravity

Some questions concerning the existence of time and the validity of Einstein’s equations as a quantum-mechanical mean have arisen in the development of semiclassical gravity applied to cosmology. The first is a technical question which concerns the choice of a certain class of solutions. We here show that this is a ‘‘gauge’’ choice where we follow the work of Mead and Berry. The ‘‘Berry phase’’ turns out to be related to the time integral of the energy. The second question is concerned with the justification of the use of the mean matter energy to drive the cosmological expansion. This is shown to be valid in an inflationary universe. At the same time one obtains the Schrödinger equation for matter in conformity with previous work where these particular questions were not addressed. All of this means that cosmology as a theory of the mean is meaningful.