Brane-world generalizations of the Einstein static universe

TL;DR

This paper explores static Friedmann branes within a 5-dimensional bulk, revealing new relationships between density, pressure, and curvature that differ from classical Einstein static universe models, including cases with zero cosmological constant.

Contribution

It introduces novel static Friedmann brane solutions in a 5D bulk that are not limited to Schwarzschild-anti de Sitter spacetimes, expanding the understanding of brane-world cosmologies.

Findings

Static Friedmann branes with zero cosmological constant and curvature are possible.

New relations between density, pressure, and curvature in brane-world scenarios.

Existence of static branes in non-Schwarzschild bulk solutions.

Abstract

A static Friedmann brane in a 5-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 rho>0 and rho+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.