The Cosmological Perturbation of Braneworld with An Anisotropic Bulk

The braneworld cosmological model was constructed by embedding a 3-brane into a higher dimensional bulk background geometry and the usual matter of our universe was assumed to be confined in the brane while the gravity can propagate in the bulk. By considering that the bulk geometry is anisotropic, after reviewed the separable solution for the bulk metric and the result that the anisotropic property of the bulk can support the perfect fluid kind of the matter in the brane, we develop a formalism of the cosmological perturbation for this kind of anisotropic braneworld model. As in isotropic case, we can also decompose the perturbation into scalar, vector and tensor modes, we find that the formalism for the anisotropic braneworld cosmological perturbation are very different from the isotropic case. The anisotropic effect can be reflected in the tensor modes which dominated the cosmological gravitation waves. Finally, we also discussed the perturbed Einstein equations governed the dynamics of the bulk geometry and the brane with the junction conditions.