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 spacelike as well as timelike. The resulting equations of motion have the form of a cubic equation in the $({H}^{2},(\ensuremath{\rho}+\ensuremath{\sigma}{)}^{2})$ plane, where $\ensuremath{\sigma}$ is the brane tension and $\ensuremath{\rho}$ 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 phantomlike so that $wl\ensuremath{-}1$. At late times, this branch approaches de Sitter space ($w=\ensuremath{-}1$) and avoids the big-rip singularities usually present in phantom models. For a timelike extra dimension the Gauss-Bonnet brane can bounce and avoid the initial singularity.