Slow-roll corrections to inflaton fluctuations on a brane

TL;DR

This paper investigates how slow-roll corrections and bulk metric couplings affect inflaton fluctuations on a brane, revealing significant deviations from standard four-dimensional predictions at high energies and small scales.

Contribution

It extends the analysis of inflaton fluctuations to five-dimensional brane-world scenarios, highlighting the importance of bulk metric couplings at high energies.

Findings

Bulk metric perturbations significantly affect small-scale inflaton fluctuations.

Standard calculations neglecting bulk couplings may be unreliable at high energies.

Couplings lead to modified vacuum oscillation amplitudes on small scales.

Abstract

Quantum fluctuations of an inflaton field, slow-rolling during inflation are coupled to metric fluctuations. In conventional four dimensional cosmology one can calculate the effect of scalar metric perturbations as slow-roll corrections to the evolution of a massless free field in de Sitter spacetime. This gives the well-known first-order corrections to the field perturbations after horizon-exit. If inflaton fluctuations on a four dimensional brane embedded in a five dimensional bulk spacetime are studied to first-order in slow-roll then we recover the usual conserved curvature perturbation on super-horizon scales. But on small scales, at high energies, we find that the coupling to the bulk metric perturbations cannot be neglected, leading to a modified amplitude of vacuum oscillations on small scales. This is a large effect which casts doubt on the reliability of the usual calculation of inflaton fluctuations on the brane neglecting their gravitational coupling.