  We discuss the production of radiation and dark matter assuming a
time-dependent inflaton decay rate during the reheating period. It is shown
that the time dependence of the inflaton decay rate can substantially modify
the reheating dynamics. As an illustration, a leading interaction between the
inflaton $\phi$ and the Higgs doublet ${\boldsymbol h}$ of the form $\phi
|{\boldsymbol h}|^2$ was adopted. In the presence of such interaction, the
Higgs doublet acquires a $\phi$-dependent mass which generates
vacuum-expectation-value due to inflaton oscillations and breaks the Standard
Model gauge symmetry. This leads to a time-dependent inflaton decay rate during
the reheating period, and consequently, the production of radiation and dark
matter during this period is modified. Regions of the parameter space that
describe the observed value of the dark matter abundance were found and
compared with the standard case when inflaton the decay rate is constant.
