Kaluza-Klein brane cosmology with a bulk scalar field

TL;DR

This paper explores a higher-dimensional brane-world cosmology model incorporating a bulk scalar field, deriving gravitational equations, formulating the Friedmann equation, and presenting exact solutions for vacuum and matter scenarios.

Contribution

It introduces a formalism for Kaluza-Klein brane cosmology with a bulk scalar field, deriving gravitational equations and solutions in higher-dimensional spacetime.

Findings

Derived the $(4+n)$-dimensional gravitational field equations.

Formulated the Friedmann equation with energy leakage.

Presented exact solutions for vacuum and matter branes.

Abstract

The brane-world cosmological model in higher-dimensional spacetime with a bulk scalar field is investigated. We derive the $(4+n)$-dimensional gravitational field equations for the scalar field on the $(3+n)$-brane in a $(5+n)$-dimensional bulk with Einstein gravity plus a self-interacting scalar field. The $(4+n)$-dimensional gravitational field equations can be formulated to standard form with the extra component. Using this formalism we study the Kaluza-Klein brane cosmology. We derive the Friedmann equation and a possible energy leak out of the brane into the bulk. We present some exact solutions corresponding to vacuum brane and matter on the brane.