Transition from big crunch to big bang in brane cosmology

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 (N) over cap, which has a big bang singularity and which can be viewed as a brane in a reflected Schwarzschild-AdS((n+2)) bulk (N) over cap. The joint branes N boolean OR (N) over cap 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 boolean OR (N) over cap forms a C-infinity-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.