  We present a gauge invariant formalism to study the evolution of curvature
perturbations during decay of the inflaton or some other field that dominates
the energy density. We specialize to the case where the total curvature
perturbation arises predominantly from a spatially fluctuating decay rate.
Gaussian fluctuations in the decay rate are present if the inflaton coupling or
mass depends on some light field, which freely fluctuates during inflation. The
isocurvature fluctuations of the light field seeds the total curvature
perturbations, whose amplitude freezes after inflaton decay. We also analyze
the resulting curvature perturbation starting with non-negligible values of the
initial inflaton curvature. Lastly, we study the effects of the energy density
stored in the light field.
