Inflationary slow-roll formalism and perturbations in the Randall-Sundrum type II braneworld

We formalize the Hubble slow-roll formalism for inflationary dynamics in Randall-Sundrum type II braneworld cosmologies, defining Hubble slow-roll parameters which can be used along with the Hamilton-Jacobi formalism. Focusing on the high-energy limit, we use these to calculate the exact power spectrum for power-law inflation, and then perturb around this solution to derive the higher-order expression for the density perturbations (sometimes called the Stewart-Lyth correction) of slow-roll braneworld models. Finally we apply our result to specific examples of potentials to calculate the correction to the amplitude of the power spectrum, and compare it with the standard cosmology. We find that the amplitude is not changed significantly by the higher-order correction.