Spherically Symmetric Thick Branes Cosmological Evolution

TL;DR

This paper derives spherically symmetric, time-dependent solutions for a 5D scalar field coupled to gravity, exploring their implications for thick brane cosmology and demonstrating how anisotropic warp factors influence the universe's evolution.

Contribution

It extends previous 5D scalar field models by analyzing spherically symmetric, time-dependent solutions and their role in emergent thick brane-world cosmology.

Findings

Warp factor and Hubble parameter driven by radial coordinate

Separable equations allow recovery of known extra dimensional profiles

Potential for stable asymmetric brane-world scenarios

Abstract

Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed, Grzadkowskia and Wudkab. The corresponding cosmology of models with regularized branes generated by such a 5D scalar field scenario is also investigated. It has been shown that the anisotropic evolution of the warp factor and consequently the Hubble like parameter are both driven by the radial coordinate on the brane, which leads to an emergent thick brane-world scenario with spherically symmetric time dependent warp factor. Meanwhile, the separability of variables depending on fifth dimension, y, which is exhibited by the equations of motion, allows one to recover the extra dimensional profiles obtained in the literature, namely the extra dimensional part of the scale (warp) factor and the scalar field dependence on y. Therefore, our results are mainly concerned with the time dependence of a spherically symmetric warp factor. Besides evincing possibilities for obtaining asymmetric stable brane-world scenarios, the extra dimensional profiles here obtained can also be reduced to those ones investigated in the literature.