Second order brane cosmology with radion stabilization

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 $\ensuremath{\rho}/V$ between the matter energy density on the branes and the brane tensions around the static Randall-Sundrum solution (which has $\ensuremath{\rho}=0$ and brane tensions $\ifmmode\pm\else\textpm\fi{}V$). This approach ensures that the matter evolves adiabatically and allows us to find approximate solutions to second order in $\ensuremath{\rho}/V$. Some particular cases are then analyzed in detail.