Time in Cosmology

Abstract

The notion of time in cosmology is revealed through an examination of transition matrix elements of radiative processes occurring in the cosmos. To begin with, the very concept of time is delineated in classical physics in terms of correlations between the succession of configurations which describe a process and a standard trajectory called the clock. The total is an isolated system of fixed energy. This is relevant for cosmology in that the universe is an isolated system which we take to be homogeneous and isotropic. Furthermore, in virtue of the constraint which arises from reparametrization invariance of time, it has total energy zero. Therefore the momentum of the scale factor is determined from the energy of matter. In the quantum theory this is exploited through use of the WKB approximation for the wave function of the scale factor, justified for a large universe. The formalism then gives rise to matrix elements describing matter processes. These are shown to take on the form of usual time dependent quantum amplitudes wherein the temporal dependence is given by a background which is once more fixed by the total energy of matter.