  At the first stage of reheating after inflation, parametric resonance may
rapidly transfer most of the energy of an inflaton field $\phi$ to the energy
of other bosons. We show that quantum fluctuations of scalar and vector fields
produced at this stage are much greater than they would be in a state of
thermal equilibrium. This leads to cosmological phase transitions of a new
type, which may result in a copious production of topological defects and in a
secondary stage of inflation after reheating.
