Radiation damping and the expansion of the universe

An exactly soluble model consisting of a massless scalar field coupled to a harmonic oscillator considered previously in Minkowski space is generalized to spatially open Robertson-Walker cosmologies. It is shown that the dissipative behavior displayed by the system in Minkowski space when the total energy is finite is improved (weakened) by the expansion (contraction) of the universe. Further, we investigate the existence of solutions with purely retarded or purely advanced fields. We show that the system embedded in a universe which originates ("big bang") is similar to the open (external forces acting) system in Minkowski space, thus allowing for retarded but not advanced solutions.