  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 $\rho ^2$ 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.
