Bulk gravitational field and dark radiation on the brane in dilatonic brane world

TL;DR

This paper explores how dark radiation on the brane relates to bulk gravitational fields in a dilatonic brane world, providing exact solutions for cosmological perturbations and linking KK modes to black hole excitations affecting CMB anisotropies.

Contribution

It presents exact analytical solutions for five-dimensional cosmological perturbations in a dilatonic brane world, connecting dark radiation to non-normalizable KK modes and black hole excitations.

Findings

Dark radiation perturbation linked to non-normalizable KK mode.

KK mode mass squared is 2H^2 for de Sitter brane.

KK mode excitation related to small black holes in the bulk.

Abstract

We discuss the connection between the dark radiation on the brane and the bulk gravitational field in a dilatonic brane world model proposed by Koyama and Takahashi where the exact solutions for the five dimensional cosmological perturbations can be obtained analytically. It is shown that the dark radiation perturbation is related to the non-normalizable Kaluza-Klein (KK) mode of the bulk perturbations. For the de Sitter brane in the anti-de Sitter bulk, the squared mass of this KK mode is $2 H^2$ where $H$ is the Hubble parameter on the brane. This mode is shown to be connected to the excitation of small black hole in the bulk in the long wavelength limit. The exact solution for an anisotropic stress on the brane induced by this KK mode is found, which plays an important role in the calculation of cosmic microwave background radiation anisotropies in the brane world.