Primordial perturbations from slow-roll inflation on a brane

Abstract

In this paper we quantize scalar perturbations in a Randall–Sundrum-type model ofinflation where the inflaton field is confined to a single brane embedded in five-dimensionalanti-de Sitter space–time. In the high energy regime, small-scale inflaton fluctuations arestrongly coupled to metric perturbations in the bulk and gravitational back-reaction has adramatic effect on the behaviour of inflaton perturbations on sub-horizon scales. This is incontrast to the standard four-dimensional result where gravitational back-reaction can beneglected on small scales. Nevertheless, this does not give rise to significant particleproduction, and the correction to the power spectrum of the curvature perturbations onsuper-horizon scales is shown to be suppressed by a slow-roll parameter. We calculate thecomplete first-order slow-roll corrections to the spectrum of primordial curvatureperturbations.