We develop a four-dimensional effective theory for Randall-Sundrum models which allows us to calculate long-wavelength adiabatic perturbations in a regime where the
ρ
2
terms characteristic of braneworld cosmology are significant. This extends previous work employing the moduli space approximation. We extend the treatment of the system to include higher derivative corrections present in the context of braneworld cosmology. The developed formalism allows us to study perturbations beyond the general long-wavelength, slow-velocity regime to which the usual moduli approximation is restricted. It enables us to extend the study to a wide range of braneworld cosmology models for which the extra terms play a significant role. As an example we discuss high-energy inflation on the brane and analyze the key observational features that distinguish braneworlds from ordinary inflation by considering scalar and tensor perturbations as well as non-Gaussianities. We also compare inflation and cyclic models and study how they can be distinguished in terms of these corrections.