Cosmological 3-Brane Solutions

TL;DR

This paper investigates cosmological equations in brane world models with an extra space-like dimension, showing conditions under which they reduce to standard 4D cosmology and exploring the effects of finite brane thickness and bulk energy-momentum.

Contribution

It extends brane cosmology models by analyzing finite thickness branes and the role of bulk energy-momentum in compactification and standard cosmology realization.

Findings

Cosmological equations reduce to 4D Friedmann form with non-zero bulk energy-momentum.

Finite thickness branes relate the 4D Planck scale to the brane's thickness.

Extra dimension can be compactified with a single brane under certain conditions.

Abstract

We analyze cosmological equations in the brane world scenario with one extra space-like dimension. We demonstrate that the cosmological equations can be reduced to the usual 4D Friedmann type if the bulk energy-momentum tensor is different from zero. We then generalize these equations to the case of a brane of finite thickness. We also demonstrate that when the bulk energy-momentum tensor is different from zero, the extra space-like dimension can be compactified with a single brane and show that the stability of the radius of compactification implies standard cosmology and vice versa. For a brane of finite thickness, we provide a solution such that the 4D Planck scale is related to the fundamental scale by the thickness of the brane. In this case, compactification of the extra dimension is unnecessary.