Slow-roll corrections to inflaton fluctuations on a brane

Abstract

Quantum fluctuations of an inflaton field, slow rolling during inflation are coupled to metricfluctuations. In conventional four-dimensional cosmology one can calculate the effect ofscalar metric perturbations as slow-roll corrections to the evolution of a massless free fieldin de Sitter spacetime. This gives the well-known first-order corrections to the fieldperturbations after horizon exit. If inflaton fluctuations on a four-dimensional braneembedded in a five-dimensional bulk spacetime are studied to first order in slow roll, thenwe recover the usual conserved curvature perturbation on superhorizon scales. But on smallscales, at high energies, we find that the coupling to the bulk metric perturbationscannot be neglected, leading to a modified amplitude of vacuum oscillations onsmall scales. This is a large effect which casts doubt on the reliability of the usualcalculation of inflaton fluctuations on the brane neglecting their gravitational coupling.