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# Advances in Theoretical and Mathematical Physics

## Volume 8 (2004)

### Number 2

### Transition from big crunch to big bang in brane cosmology

Pages: 319 – 343

DOI: http://dx.doi.org/10.4310/ATMP.2004.v8.n2.a2

#### Author

#### Abstract

We consider branes *N = I *x *S*_{0}, where *S*_{0} is an *n*-dimensional space form, not necessarily compact, in a Schwarzschild-AdS(*n+2*) bulk *N*. The branes have a big crunch singularity. If a brane is an ARW space, then, under certain conditions, there exists a smooth natural transition flow through the singularity to a reflected brane \hat *N*, which has a big bang singularity and which can be viewed as a brane in a reflected Schwarzschild-AdS(*n+2*) bulk \hat *N* . The joint branes *N* ⋃ \hat *N* can thus be naturally embedded in ℝ^{2} x *S*_{0}, hence there exists a second possibility of defining a smooth transition from big crunch to big bang by requiring that *N* ⋃ \hat *N* forms a C^{∞}-hypersurface in ℝ^{2} x *S*_{0}. This last notion of a smooth transition also applies to branes that are not ARW spaces, allowing a wide range of possible equations of state.