The Cosmological Perturbation of Braneworld with An Anisotropic Bulk

TL;DR

This paper develops a formalism for cosmological perturbations in an anisotropic braneworld model, revealing how anisotropy affects tensor modes and gravitational waves, differing significantly from isotropic models.

Contribution

It introduces a new perturbation formalism for anisotropic braneworlds, extending previous isotropic models and analyzing the impact on gravitational wave modes.

Findings

Anisotropic bulk supports perfect fluid matter on the brane.

Perturbation formalism differs from isotropic case, especially in tensor modes.

Anisotropy influences gravitational wave behavior.

Abstract

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.