Quantum evolution of an unstable field in a de Sitter-space thermal bath

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Abstract
We discuss the evolution in time, from an arbitrary initial state, of the low-momentum modes of an unstable field (i.e., the inflation field) which is coupled to a thermal bath in de Sitter space. For convenience, the thermal bath is modeled as a massless scalar field conformally coupled to a background de Sitter space. We give the exact solution for the Feynman-Vernon influence functional which describes the coupling of the thermal bath to the inflation field, as well as an exact solution to a simple evolution problem in which instability of the inflation field is modeled with a negative mass term, in the manner of Guth and Pi. Coupling to a thermal bath leads, in principle, to viscosity and momentum-space diffusion; these effects are not describable with a conventional Hamiltonian. Viscosity and diffusion govern the approach to thermal equilibrium, and compete with de Sitter-space gravitational expansion.