On Brane-World Cosmology

TL;DR

This paper investigates the effects of curvature-dependent terms in the brane action on cosmological expansion laws, deriving new field equations and exploring their solutions in five-dimensional brane-world models.

Contribution

It derives modified field equations for brane-world cosmology including curvature terms, extending previous models and analyzing their cosmological implications.

Findings

Derived new field equations with curvature-dependent terms.

Identified differences in expansion laws compared to standard models.

Explored cosmological solutions of the modified equations.

Abstract

In the study of three-brane cosmological models, an unusual law of cosmological expansion on the brane has been reported. According to this law, the energy density of matter on the brane quadratically enters the right-hand side of the new equations for the brane world, in contrast with the standard cosmology, where it enters the similar equations linearly. However, this result is obtained in the absence of curvature-dependent terms in the action for the brane. In this paper, we derive the field equations for a brane world embedded into a five-dimensional spacetime in the case where such terms are present. We also discuss some cosmological solutions of the resulting equations.