Transition from big crunch to big bang in brane cosmology

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.

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Published 1 January 2004