Scalar perturbations from brane-world inflation

Abstract

We investigate the scalar metric perturbations about a de Sitter brane universe in afive-dimensional anti-de Sitter bulk. We compare the master variable formalism, describingmetric perturbations in a five-dimensional longitudinal gauge, with results ina Gaussian normal gauge. For a vacuum brane (with constant brane tension)there is a continuum of normalizable Kaluza–Klein modes, with , which remain in the vacuum state. A light radion mode, with , satisfies the boundary conditions for two branes but is not normalizable in thesingle-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, becomesnormalizable. However, the boundary condition requires the self-consistent four-dimensionalevolution of scalar field perturbations on the brane and the dangerous growing modesare not excited. These normalizable discrete modes introduce corrections at firstorder to the scalar field perturbations computed in a slow-roll expansion. Onsuper-Hubble scales, the correction is smaller than slow-roll corrections to the de Sitterbackground. However, on small scales the corrections can become significant.