Numerical study of curvature perturbations in a brane-world inflation at high-energies

TL;DR

This paper investigates how scalar curvature perturbations evolve in a brane-world inflation model within a 5D Anti-de Sitter spacetime, revealing strong coupling effects between inflaton and bulk metric perturbations at high energies.

Contribution

It provides a numerical analysis of coupled brane-bulk perturbations during inflation, highlighting the breakdown of the usual 4D perturbation equations at high energies.

Findings

Inflaton perturbations are strongly coupled to bulk metric perturbations at high energies.

Coupling leads to suppression of curvature perturbation amplitude at horizon crossing.

Standard 4D equations are insufficient for high-energy brane-world inflation.

Abstract

We study the evolution of scalar curvature perturbations in a brane-world inflation model in a 5D Anti-de Sitter spacetime. The inflaton perturbations are confined to a 4D brane but they are coupled to the 5D bulk metric perturbations. We numerically solve full coupled equations for the inflaton perturbations and the 5D metric perturbations using Hawkins-Lidsey inflationary model. At an initial time, we assume that the bulk is unperturbed. We find that the inflaton perturbations at high energies are strongly coupled to the bulk metric perturbations even on subhorizon scales, leading to the suppression of the amplitude of the comoving curvature perturbations at a horizon crossing. This indicates that the linear perturbations of the inflaton field does not obey the usual 4D Klein-Gordon equation due to the coupling to 5D gravitational field on small scales and it is required to quantise the coupled brane-bulk system in a consistent way in order to calculate the spectrum of the scalar perturbations in a brane-world inflation.