Exactly solvable model for cosmological perturbations in dilatonic brane worlds

TL;DR

This paper presents an exactly solvable model of cosmological perturbations in dilatonic brane worlds, revealing insights into the interplay between bulk geometry and brane perturbations during power-law inflation.

Contribution

It provides an analytical solution for cosmological perturbations in a dilatonic brane world with a bulk scalar field, including back-reaction effects and junction conditions.

Findings

Exact solutions for perturbations satisfying junction conditions

Analysis of anisotropic stress induced by bulk gravitational fields

Connection between bulk geometry and brane perturbation behavior

Abstract

We construct a model where cosmological perturbations are analytically solved based on dilatonic brane worlds. A bulk scalar field has an exponential potential in the bulk and an exponential coupling to the brane tension. The bulk scalar field yields a power-law inflation on the brane. The exact background metric can be found including the back-reaction of the scalar field. Then exact solutions for cosmological perturbations which properly satisfy the junction conditions on the brane are derived. These solutions provide us an interesting model to understand the connection between the behavior of cosmological perturbations on the brane and the geometry of the bulk. Using these solutions, the behavior of an anisotropic stress induced on the inflationary brane by bulk gravitational fields is investigated.