Quantization of scalar perturbations in brane-world inflation

TL;DR

This paper develops a framework for quantizing scalar perturbations in brane-world inflation models, analyzing mode spectra, and calculating their effects on inflationary perturbations.

Contribution

It derives the second order action for bulk perturbations and quantizes scalar modes, including the continuum KK modes and discrete tachyonic modes, in a brane-world inflation context.

Findings

Identifies the spectrum of normalizable modes including KK and radion modes.

Calculates corrections to scalar perturbations from bulk modes during inflation.

Provides a second order action for the coupled Mukhanov-Sasaki and bulk perturbations.

Abstract

We consider a quantization of scalar perturbations about a de Sitter brane in a 5-dimensional anti-de Sitter (AdS) bulk spacetime. We first derive the second order action for a master variable $\Omega$ for 5-dimensional gravitational perturbations. For a vacuum brane, there is a continuum of normalizable Kaluza-Klein (KK) modes with $m>3H/2$. There is also a light radion mode with $m=\sqrt{2}H$ which satisfies the junction conditions for two branes, but is non-normalizable for a single brane model. We perform the quantization of these bulk perturbations and calculate the effective energy density of the projected Weyl tensor on the barne. If there is a test scalar field perturbation on the brane, the $m^2 = 2H^2$ mode together with the zero-mode and an infinite ladder of discrete tachyonic modes become normalizable in a single brane model. This infinite ladder of discrete modes as well as the continuum of KK modes with $m>3H/2$ introduce corrections to the scalar field perturbations at first-order in a slow-roll expansion. We derive the second order action for the Mukhanov-Sasaki variable coupled to the bulk perturbations which is needed to perform the quantization and determine the amplitude of scalar perturbations generated during inflation on the brane.