Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model

We investigate a 6D generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. Each stress-energy tensor \begin{document}$ T_{ab}^{i} $\end{document} on the brane is shown to be similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model, in which each 3-brane Lagrangian yielded a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5D Friedmann-Robertson-Walker field equations. In a slightly later period, the expansion of the universe is proportional to the square root of time, \begin{document}$ t^{\frac{1}{2}} $\end{document}, which is similar to the period of the radiation-dominated regime. Moreover, we investigate the case with two \begin{document}$ a(t) $\end{document} and two \begin{document}$ b(t) $\end{document}. In a large range of \begin{document}$ t $\end{document}, we obtain the 3D effective cosmological constant \begin{document}$ \Lambda_{\rm eff} = -2\Omega/3>0 $\end{document}, which is independent of the integral constant. Here, the scale factor is an exponential expansion, which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model that solves the dark energy problem, while guaranteeing a positive brane tension.