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We study the nonlinear dynamics of quantum fields in matter- and radiation-dominated universes, using the nonequilibrium field theory approach combined with the nonperturbative Hartree and the large N approximations. We examine the phenomenon of explosive particle production due to spinodal instabilities and parametric amplification in expanding universes with and without symmetry breaking. For a variety of initial conditions, we compute the evolution of the inflaton, its quantum fluctuations, and the equation of state. We find explosive growth of quantum fluctuations, although particle production is somewhat sensitive to the expansion of the universe. In the large N limit for symmetry-breaking scenarios, we determine generic late time solutions for any flat Friedmann-Robertson-Walker (FRW) cosmology. We also present a complete and numerically implementable renormalization scheme for the equation of motion and the energy momentum tensor in flat FRW cosmologies. In this scheme the renormalization constants are independent of time and of the initial conditions.
Boyanovsky et al. (Fri,) studied this question.