  The hybrid model with a scalar "inflaton" field coupled to a "Higgs" field
with a broken symmetry potential is one of the promising models for inflation
and (p)reheating after inflation. We consider the nonequilibrium evolution of
the quantum fields of this model with quantum back reaction in the Hartree
approximation, in particular the transition of the Higgs field from the
metastable "false vacuum" to the broken symmetry phase. We have performed the
renormalization of the equations of motion, of the gap equations and of the
energy density, using dimensional regularization. We study the influence of the
back reaction on the evolution of the classical fields and of the quantum
fluctuations. We observe that back reaction plays an important role over a wide
range of parameters. Some implications of our investigation for the preheating
stage after cosmic inflation are presented.
