A note on the wellposedness of scalar brane world cosmological perturbations

TL;DR

This paper analyzes the well-posedness of scalar perturbations in brane world cosmology, demonstrating that the master equations yield a well-posed problem even with non-local boundary conditions, and discusses initial data specification.

Contribution

It shows that Mukoyama's master equations lead to a well-posed problem for scalar perturbations in brane cosmology with specific matter types, clarifying initial data setup.

Findings

Master equations are well-posed for adiabatic perfect fluid perturbations.

The problem remains well-posed with scalar field matter on the brane.

Guidance on specifying initial data in the bulk for these perturbations.

Abstract

We discuss scalar brane world cosmological perturbations for a 3-brane world in a maximally symmetric 5D bulk. We show that Mukoyama's master equations leads, for adiabatic perturbations of a perfect fluid on the brane and for scalar field matter on the brane, to a well posed problem despite the "non local" aspect of the boundary condition on the brane. We discuss in relation to the wellposedness the way to specify initial data in the bulk.