Scalar perturbations from brane-world inflation

TL;DR

This paper studies scalar metric perturbations in a brane-world inflation model, comparing different formalisms and analyzing the effects of various modes, revealing that corrections are small on large scales but can be significant on small scales.

Contribution

It provides a detailed analysis of scalar perturbations in a 5D brane-world inflation model, including mode normalizability and correction effects, using multiple gauge formalisms.

Findings

Normalizable Kaluza-Klein modes exist for vacuum branes.

A light radion mode satisfies boundary conditions but is not normalizable in single-brane cases.

Corrections to scalar perturbations are small on super-Hubble scales but significant on small scales.

Abstract

We investigate the scalar metric perturbations about a de Sitter brane universe in a 5-dimensional anti de Sitter bulk. We compare the master-variable formalism, describing metric perturbations in a 5-dimensional longitudinal gauge, with results in a Gaussian normal gauge. For a vacuum brane (with constant brane tension) there is a continuum of normalizable Kaluza-Klein modes, with m>3H/2, which remain in the vacuum state. A light radion mode, with m=\sqrt{2}H, satisfies the boundary conditions for two branes but is not normalizable in the single-brane case. When matter is introduced (as a test field) on the brane, this mode, together with the zero-mode and an infinite ladder of discrete tachyonic modes, become normalizable. However, the boundary condition requires the self-consistent 4-dimensional evolution of scalar field perturbations on the brane and the dangerous growing modes are not excited. These normalizable discrete modes introduce corrections at first-order to the scalar field perturbations computed in a slow-roll expansion. On super-Hubble scales, the correction is smaller than slow-roll corrections to the de Sitter background. However on small scales the corrections can become significant.