Brane-world generalizations of the Einstein static universe

Abstract

A static Friedmann brane in a five-dimensional bulk (Randall–Sundrum-type scenario) can have a very different relation between the density, pressure, curvature and cosmological constant than in the case of the general relativistic Einstein static universe. In particular, static Friedmann branes with zero cosmological constant and 3-curvature, but satisfying ρ > 0 and ρ + 3p > 0, are possible. Furthermore, we find static Friedmann branes in a bulk that satisfies the Einstein equations but is not Schwarzschild–anti-de Sitter or its specializations. In the models with negative bulk cosmological constant, a positive brane tension leads to negative density and 3-curvature.