Braneworld cosmological perturbation theory at low energy

Homogeneous cosmology in the braneworld can be studied without solving bulk equations of motion explicitly. The reason is simply because the symmetry of the spacetime restricts possible corrections in the 4-dimensional effective equations of motion. It would be great if we could analyze cosmological perturbations without solving the bulk. For this purpose, we combine the geometrical approach and the low energy gradient expansion method to derive the 4-dimensional effective action. Given our effective action, the standard procedure to obtain the cosmological perturbation theory can be utilized and the temperature anisotropy of the cosmic background radiation can be computed without solving the bulk equations of motion explicitly.