The statistical state of the universe

The idea that the cosmological state of the universe can be described in terms of a statistical state is discussed. A dynamical model with infinite degrees of freedom that describes a Robertson-Walker universe with nonhomogeneous electromagnetic radiation is defined. Its statistical mechanics is studied by using the covariant statistical theory. A simple statistical state that represents the cosmic background radiation is constructed. The properties of this state support the general theory; in particular, the idea that a preferred time variable, denoted thermodynamical time, is singled out by the statistical state can be tested within this model. The thermodynamical time is computed and shown to agree with the standard Robertson-Walker time. In addition, an application of the general theory to a simple special relativistic system, and a proposal for an application to full general relativity are also presented. The relevance of this application for the physics of the very early universe is discussed.