Non-Equilibrium Quantum Field Evolution in FRW Cosmologies
  We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies. After setting the problem in general we propose a non-perturbative, self-consistent Hartree approximation. The method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. The renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. We investigate the high temperature expansion and show that it breaks down at long times. The infinite time limit is computed for de Sitter spacetime. We obtain the time evolution of the initial Boltzmann distribution functions, and argue that in the Hartree approximation, the time evolved state is a ``squeezed'' state. We illustrate the departure from thermal equilibrium by studying the case of a free field in de Sitter and radiation dominated cosmologies. It is found that a suitably defined non-equilibrium entropy per mode increases linearly with comoving time in a de Sitter cosmology, whereas it is {\it not} a monotonically increasing function in the radiation dominated case. This work has been done in collaboration with D. Boyanovsky and R. Holman. 
H.J. de Vega