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

TL;DR

The paper investigates how large-scale curvature perturbations evolve during reheating when the inflaton decay rate can vary in space and time. It develops a gauge-invariant multi-fluid formalism that includes energy transfer and a gauge-invariant decay-rate perturbation. A key finding is that the final curvature perturbation can differ from its inflationary value, leading to a violation of the standard single-field consistency relation and the possibility of a larger tensor-to-scalar ratio. The work also discusses nonperturbative decay (preheating) and notes that additional fluctuations in the decay process can further modify the curvature perturbation, motivating future explorations.

Abstract

We present a gauge-invariant formalism to study the evolution of the curvature and entropy perturbations in the case in which spatial and time variations of the inflaton decay rate into ordinary matter are present. During the reheating stage after inflation curvature perturbations can vary with time on super-horizon scales sourced by a a gauge-invariant inflaton decay rate perturbation. We show that the latter is a function not only of the spatial variations of the decay rate generated during inflation, as envisaged in a recently proposed scenario, but also of the time variation of the inflaton decay rate during reheating. If only the second source is present, the final curvature perturbation at the end of the reheating stage is proportional to the curvature perturbation at the beginning of reheating with a coefficient of proportionality which can be either smaller or larger than unity depending upon the underlying physics 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 violated and there is the possibility that the tensor-to-curvature amplitude ratio is larger than in the standard case.