On brane world cosmological perturbations

We discuss the scalar cosmological perturbations in a 3-brane world with a 5D bulk. We first show explicitly how the effective perturbed Einstein equations on the brane (involving the Weyl fluid) are encoded into Mukohyama’s master equation. We give the relation between Mukohyama’s master variable and the perturbations of the Weyl fluid; we also discuss the relation between the former and the perturbations of matter and induced metric. The boundary condition for the master variable on the brane is then given in the case of a perfect fluid with adiabatic perturbations on a Randall-Sundrum or Dvali-Gabadadze-Porrati brane. This provides an easy way to solve numerically for the evolution of the perturbations and also should shed light on the various approximations done in the literature to deal with the Weyl degrees of freedom.