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April, 2004 Transition from big crunch to big bang in brane cosmology
Claus Gerhardt
Adv. Theor. Math. Phys. 8(2): 319-343 (April, 2004).


We consider branes $N=I \times \mathcal{S}_0$, where $\mathcal{S}_0$ is an $n$-dimensional space form, not necessarily compact, in a Schwarzschild-AdS$_{(n+2)}$ bulk $\mathcal{N}$. 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 $\hat{\mathcal{N}}$. The joint branes $N \cup \hat{N}$ can thus be naturally embedded in $\mathbb{R}^2 \times \mathcal{S}_0$, hence there exists a second possibility of defining a smooth transition from big crunch to big bang by requiring that $N \cup \hat{N}$ forms a $C^\infty$-hypersurface in $\mathbb{R}^2 \times \mathcal{S}_0$. 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.


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Claus Gerhardt. "Transition from big crunch to big bang in brane cosmology." Adv. Theor. Math. Phys. 8 (2) 319 - 343, April, 2004.


Published: April, 2004
First available in Project Euclid: 3 August 2004

zbMATH: 1071.83057
MathSciNet: MR2086924

Rights: Copyright © 2004 International Press of Boston

Vol.8 • No. 2 • April, 2004
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