Large-scale perturbations on the brane and the isotropy of the cosmological singularity

TL;DR

This paper derives and analyzes the equations governing linear perturbations in a flat braneworld cosmology, revealing conditions under which the universe isotropizes, with results matching previous spatially inhomogeneous models.

Contribution

It provides a comprehensive set of equations and a detailed dynamical analysis for perturbations in flat FRW braneworlds, including scalar, vector, and tensor modes, across different energy regimes.

Findings

Isotropization occurs for b3 > 4/3.

Perturbation evolution matches previous G2 braneworld results.

Tables facilitate comparison of asymptotic behaviors.

Abstract

We present the complete set of propagation and constraint equations for the kinematic and non-local first order quantities which describe general linear inhomogeneous and anisotropic perturbations of a flat FRW braneworld with vanishing cosmological constant and decompose them in the standard way into their scalar, vector and tensor contributions. A detailed analysis of the perturbation dynamics is performed using dimensionless variables that are specially tailored for the different regimes of interest; namely, the low energy GR regime, the high energy regime and the dark energy regime. Tables are presented for the evolution of all the physical quantities, making it easy to do a detailed comparison of the past asymptotic behaviour of the perturbations of these models. We find results that exactly match those obtained in the analysis of the spatially inhomogeneous $G_{2}$ braneworld cosmologies presented recently; i.e., that isotropization towards the ${\cal F}_b$ model occurs for $\gamma > 4/3$.