  We study cosmology in the five-dimensional Randall-Sundrum brane-world with a
stabilizing effective potential for the radion and matter localized on the
branes. The analysis is performed by employing a perturbative expansion in the
ratio rho/V between the matter energy density on the branes and the brane
tensions around the static Randall-Sundrum solution (which has rho=0 and brane
tensions +-V). This approach ensures that the matter evolves adiabatically and
allows us to find approximate solutions to second order in \rho/V. Some
particular cases are then analyzed in details.
