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We develop a four-dimensional effective theory for Randall-Sundrum modelswhich allows us to calculate long wavelength adiabatic perturbations in aregime where the $\rho ^2$ terms characteristic of braneworld cosmology aresignificant. This extends previous work employing the moduli spaceapproximation. We extend the treatment of the system to include higherderivative corrections present in the context of braneworld cosmology. Thedeveloped formalism allows us to study perturbations beyond the general longwavelength, slow-velocity regime to which the usual moduli approximation isrestricted. It enables us to extend the study to a wide range of braneworldcosmology models for which the extra terms play a significant role. As anexample we discuss high energy inflation on the brane and analyze the keyobservational features that distinguish braneworlds from ordinary inflation byconsidering scalar and tensor perturbations as well as non-gaussianities. Wealso compare inflation and Cyclic models and study how they can bedistinguished in terms of these corrections.Comment: 48 pages, no figure. Version published in the Physical Review

Beyond the low energy approximation in braneworld cosmology