Brane world solutions of perfect fluid in the background of a bulk containing dust or cosmological constant

TL;DR

This paper derives solutions to five-dimensional Einstein equations involving a perfect fluid on the brane, exploring cases with dust and cosmological constant in the bulk, revealing unique cosmological features especially with chaplygin gas.

Contribution

It provides new five-dimensional brane world solutions with perfect fluids, including chaplygin gas, highlighting differences from standard four-dimensional cosmology.

Findings

Linear relation between pressure, density, and brane tension in dust case

Distinct cosmological features with chaplygin gas on the brane

Solutions applicable to both brane and bulk scenarios

Abstract

The paper presents some solutions to the five dimensional Einstein equations due to a perfect fluid on the brane with pure dust filling the entire bulk in one case and a cosmological constant (or vacuum) in the bulk for the second case. In the first case, there is a linear relationship between isotropic pressure, energy density and the brane tension, while in the second case, the perfect fluid is assumed to be in the form of chaplygin gas. Cosmological solutions are found both for brane and bulk scenarios and some interesting features are obtained for the chaplygin gas on the brane which are distinctly different from the standard cosmology in four dimensions.