Branes, moduli spaces and smooth transition from big crunch to big bang

Abstract

We consider branes $N$ in a Schwarzschild-$\text{AdS}_{(n+2)}$ bulk, where the stress-energy tensor is dominated by the energy density of a scalar fields map $\varphi{:}\ N\to \mathcal{S}$ with potential $V$, where $\mathcal{S}$ is a semi-Riemannian moduli space. By transforming the field equation appropriately, we get an equivalent field equation that is smooth across the singularity $r=0$, and which has smooth and uniquely determined solutions which exist across the singularity in an interval $(-\epsilon,\epsilon)$. Restricting a solution to $(-\epsilon,0)$ \resp $(0,\epsilon)$, and assuming $n$ odd, we obtain branes $N$ resp. $\hat{N}$ which together form a smooth hypersurface. Thus a smooth transition from big crunch to big bang is possible both geometrically as well as physically.