  We derive the renormalized nonequilibrium equations of motion for a scalar
field and its quantum back reaction in a conformally flat
Friedmann-Robertson-Walker universe. We use a fully covariant formalism
proposed by us recently for handling numerically and analytically
nonequilibrium dynamics in one-loop approximation. The system is assumed to be
in a conformal vacuum state initially. We use dimensional regularization; we
find that the counter terms can be chosen independent of the initial conditions
though the divergent leading order graphs do depend on them.
