  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.
