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 \left ( H ^ { 2 } , ( \rho + \sigma ) ^ { 2 } \right ) plane , where \sigma is the brane tension and \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 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 .