Brane World Solutions of Perfect Fluid in the Background of a Bulk Containing Dust or a Cosmological Constant

The paper presents some solutions to the five-dimensional Einstein equations with 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 another 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 a Chaplygin gas. Cosmological solutions are found both for the brane and the bulk scenarios, and some interesting features are obtained for the Chaplygin gas on the brane which are distinctly different from standard cosmology in four dimensions.