Cosmological Equations for a Thick Brane

TL;DR

This paper derives generalized cosmological equations for a thick brane in a five-dimensional Anti-de Sitter space, bridging thin brane and Kaluza-Klein limits, and discusses the conditions for effective four-dimensional reduction.

Contribution

It introduces a framework for deriving effective Friedmann equations for thick branes, extending previous thin brane models to include finite thickness effects.

Findings

Effective equations interpolate between thin brane and infinite thickness limits.

No four-dimensional reduction is possible for thick branes in Minkowski bulk.

Different regimes of brane thickness influence cosmological behavior.

Abstract

Generalized Friedmann equations governing the cosmological evolution inside a thick brane embedded in a five-dimensional Anti-de Sitter spacetime are derived. These equations are written in terms of four-dimensional effective brane quantities obtained by integrating, along the fifth dimension, over the brane thickness. In the case of a Randall-Sundrum type cosmology, different limits of these effective quantities are considered yielding cosmological equations which interpolate between the thin brane limit (governed by unconventional brane cosmology), and the opposite limit of an ``infinite'' brane thickness corresponding to the familiar Kaluza-Klein approach. In the more restrictive case of a Minkowski bulk, it is shown that no effective four-dimensional reduction is possible in the regimes where the brane thickness is not small enough.