Codimension Two Branes: Examples

We study a six dimensional cosmological model with co-dimension two. The starting point is a general 6d metric ansatz in normal coordinates: $\,ds^2\,=\, d\rho^2 + e^{2B(\rho)} d\sigma^2 + e^{2W(\rho)} g_{\mu\nu}(x) dx^{\mu} dx^{\nu}$, where the submanifold defined by the 4d metric $g_{\mu\,\nu}$ represents our observable universe. One of the solutions display a conical singularity at $\rho\,=\,0$, opening the possibility that a four dimensional brane may be embedded there, following the the work of Bostok et al. [1]. Here we concentrate in the solution where $B(\rho)\,= \ln\left[\,A\,\sin\left(\sqrt{\Lambda/\,10}\,\rho\,\right)\,\right]$\,$\approx\,\ln\left(\sqrt{\Lambda/\,10}\,\rho\,\right)$, which generates a conical singularity at $\rho\,=\,0$. The presence of this $\delta(\rho)$ in the Einstein equations induces a cosmological constant on the brane. It is also possible to introduce a Gauss-Bonnet term in this solution. A future work considers a scalar field in the bulk and perturbations on the brane to generate other cosmological models.\\[4pt] [1] P. Bostock, R. Gregory, I. Navarro and J. Santiago, Phys. Rev. Letter,Vol 92,\,22,\,22160-1.