Large-scale curvature perturbations with spatial and time variations of the inflaton decay rate

Abstract

We present a gauge-invariant formalism to study the evolution of the curvature and entropy perturbations in the case in which spatialand time variations of the inflaton decay rate into ordinarymatter are present. During the reheating stage after inflation, curvature perturbations can vary with time on super-horizon scales sourced by a gauge-invariant inflaton decay rate perturbation. We showthat the latter is a function not only of the spatial variationsof the decay rate generated during inflation, as envisagedin a recently proposed scenario, but also ofthe time variation of the inflaton decay rate during reheating. If only the second source is present, the final curvatureperturbation at the end of the reheating stage is proportionalto the curvature perturbation at the beginning of reheating, with a coefficient of proportionality which can be either smalleror larger than unity depending upon the underlyingphysics governing the time variation of the inflaton decay rate.As a consequence, we show that the standard consistency relation between the amplitude of curvature perturbations, the amplitude of tensor perturbations and the tensor spectral index of one-single-field models of inflation is violatedand there is the possibility that the tensor-to-curvature amplitude ratio is larger than in the standard case.