Generalized approach for the perturbative dynamical braneworld in $D$ dimensions

TL;DR

This paper develops a generalized perturbative method to derive cosmological equations in D-dimensional braneworld models, including nonlinear effects, and demonstrates the recovery of Friedmann and de Sitter solutions.

Contribution

It introduces a novel perturbative approach for dynamical braneworlds in arbitrary dimensions, extending previous static models to include nonlinear and time-dependent effects.

Findings

Recovered Friedmann equations with and without cosmological constant

Demonstrated de Sitter expansion in the model

Analyzed stability of the dynamical brane

Abstract

In this paper, we propose an approach to derive the brane cosmology in the $D$-dimensional braneworld model. We generalize the "bulk-based" approach by treating the 4-brane as a small perturbation to the $D$-dimensional spherically symmetric spacetime. The linear corrections from a static 4-brane to the metric are derived from the linearized perturbation equations, while the nonlinear corrections are found by a parameterization of the perturbed metric solution. We use a time-dependent generalization to give the nonlinearly perturbed metric solution for the dynamical braneworld model, and analyse the stability of the model under the motion of the 4-brane. Through the fine tuning, we can recover the Friedmann equations for the universe with and without an effective cosmological constant. More importantly, the de Sitter expansion of the universe can be reproduced.