Braneworld dynamics in Einstein Gauss Bonnet gravity

Abstract

We discuss the cosmological evolution of a braneworld in five dimensional Gauss– Bonnet gravity. Our discussion allows the fifth (bulk) dimension to be space-like as well as time-like. The resulting equations of motion have the form of a cubic equation in the H2, (ρ + σ)2 plane, where σ is the brane tension and ρ is the matter density. This allows us to conduct a comprehensive pictorial analysis of cosmological evolution for the Gauss–Bonnet brane. The many interesting properties of this braneworld include the possibility of accelerated expansion at late times. For a finite region in parameter space the accelerated expansion can be phantom-like so that w < −1. At late times, this branch approaches de Sitter space (w = −1) and avoids the big-rip singularities usually present in phantom models. For a time-like extra dimension the Gauss–Bonnet brane can bounce and avoid the initial singularity.