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.
14 pages, 2 figures, discussion added, version to be published in Phys. Lett. B