Advances in Theoretical and Mathematical Physics
Volume 8 (2004)
Transition from big crunch to big bang in brane cosmology
Pages: 319 – 343
We consider branes N = I x S0, where S0 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 ℝ2 x S0, 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 ℝ2 x S0. 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.