Thick Brane Isotropization in a Generalized 5D Anisotropic Standing Wave Braneworld Model

TL;DR

This paper presents a cosmological model of a 5D anisotropic braneworld that naturally evolves towards isotropy through energy dissipation into the bulk, leading to a de Sitter symmetric brane in a 5D de Sitter space.

Contribution

It introduces a novel time-dependent scale factor in a 5D standing wave braneworld model and demonstrates a natural isotropization mechanism for the anisotropic brane.

Findings

The braneworld isotropizes rapidly via energy leakage into the bulk.

The model results in a de Sitter symmetric brane with vanishing phantom scalar.

The bulk becomes less anisotropic over time due to energy dissipation.

Abstract

We study a smooth cosmological solution within a generalized 5D standing wave braneworld modeled by gravity and a phantom scalar field. In this model the 3-brane is anisotropically warped along its spatial dimensions and contains a novel time-dependent scale factor that multiplies the anisotropic spatial interval of the 5D metric, a fact that allows us to study cosmological effects. By explicitly solving the bulk field equations we found a natural mechanism which isotropizes the braneworld for a wide class of natural initial conditions. We are able to give a physical interpretation of the anisotropic dissipation: as the anisotropic energy of the 3-brane rapidly leaks into the bulk through the nontrivial components of the projected to the brane non-local Weyl tensor, the bulk becomes less isotropic. At the same time, under the action of the 4D cosmological constant, the anisotropic braneworld super-exponentially isotropizes by itself, rendering a 3-brane with de Sitter symmetry embedded in a 5D de Sitter space-time, while the phantom scalar field exponentially vanishes.