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Quantization of scalar perturbations in brane-world inflation

Hiroyuki Yoshiguchi¹ and Kazuya Koyama^1,2

¹Department of Physics, University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
²Institute of Cosmology and Gravitation, Portsmouth University, Portsmouth, PO1 2EG, UK

Phys. Rev. D 71, 043519 – Published 28 February, 2005

DOI: https://doi.org/10.1103/PhysRevD.71.043519

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 $Ω$ for 5-dimensional gravitational perturbations. For a vacuum brane, there is a continuum of normalizable Kaluza-Klein (KK) modes with $m > 3 H / 2$ . 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 $m^{2} = 2 H^{2}$ 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 $m > 3 H / 2$ 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.

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References (31)

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