Large-scale cosmological perturbations on the brane

TL;DR

This paper demonstrates that in Randall-Sundrum brane-world cosmologies, large-scale curvature perturbations can be analyzed on the brane without solving bulk equations, revealing how bulk effects influence observable cosmological features.

Contribution

It introduces a method to determine large-scale curvature perturbations on the brane by accounting for bulk gravitational effects via the Weyl tensor, without solving bulk perturbation equations.

Findings

Total curvature perturbation can vary due to Weyl entropy perturbation.

Evolution of curvature perturbations follows from energy conservation of matter and Weyl fluids.

Implications for large-angle CMB anisotropies are discussed.

Abstract

In brane-world cosmologies of Randall-Sundrum type, we show that evolution of large-scale curvature perturbations may be determined on the brane, without solving the bulk perturbation equations. The influence of the bulk gravitational field on the brane is felt through a projected Weyl tensor which behaves effectively like an imperfect radiation fluid with anisotropic stress. We define curvature perturbations on uniform density surfaces for both the matter and Weyl fluids, and show that their evolution on large scales follows directly from the energy conservation equations for each fluid. The total curvature perturbation is not necessarily constant for adiabatic matter perturbations, but can change due to the Weyl entropy perturbation. To relate this curvature perturbation to the longitudinal gauge metric potentials requires knowledge of the Weyl anisotropic stress which is not determined by the equations on the brane. We discuss the implications for large-angle anisotropies on the cosmic microwave background sky.