  Coupled, multi-field models of inflation can provide several attractive
features unavailable in the case of a single inflaton field. These models have
a rich dynamical structure resulting from the interaction of the fields and
their associated fluctuations. We present a formalism to study the
nonequilibrium dynamics of coupled scalar fields. This formalism solves the
problem of renormalizing interacting models in a transparent way using
dimensional regularization. The evolution is generated by a renormalized
effective Lagrangian which incorporates the dynamics of the mean fields and
their associated fluctuations at one-loop order. We apply our method to two
problems of physical interest: (i) a simple two-field model which exemplifies
applications to reheating in inflation, and (ii) a supersymmetric hybrid
inflation model. This second case is interesting because inflation terminates
via a smooth phase transition which gives rise to a spinodal instability in one
of the fields. We study the evolution of the zero mode of the fields and the
energy density transfer to the fluctuations from the mean fields. We conclude
that back reaction effects can be significant over a wide parameter range. In
particular for the supersymmetric hybrid model we find that particle production
can be suppressed due to these effects.
