Inhomogeneous Dark Radiation Dynamics on a de Sitter Brane

TL;DR

This paper investigates the complex behavior of inhomogeneous dark radiation on a de Sitter brane within a Randall-Sundrum model, deriving exact solutions and conditions for singularity formation or bouncing scenarios.

Contribution

It provides the first exact dynamical solutions for inhomogeneous dark radiation on a de Sitter brane, linking brane parameters to the evolution and singularity conditions.

Findings

Exact solutions depend on cosmological constant, tidal charge, and initial conditions.

Conditions for singularity formation or regular bounces are identified.

Analysis is restricted to negative dark energy density scenarios.

Abstract

Assuming spherical symmetry we analyse the dynamics of an inhomogeneous dark radiation vaccum on a Randall and Sundrum 3-brane world. Under certain natural conditions we show that the effective Einstein equations on the brane form a closed system. On a de Sitter brane and for negative dark energy density we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We also identify the conditions leading to the formation of a singularity or of regular bounces inside the dark radiation vaccum.