Large-scale cosmological perturbations on tbe brane - art. no. 084009

In brane-world cosmologies of Randall-Sundrum type, we show that the evolut ion 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 wh ich behaves effectively like an imperfect radiation fluid with anisotropic stress. We define curvature perturbations on uniform density surfaces far b oth the matter and Weyl fluids, and show that their evolution on large scal es 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 pote ntials requires knowledge of the Weyl anisotropic stress which is not deter mined by the equations on the brane. We discuss the implications for large- angle anisotropies on the cosmic microwave background sky.