Generalized slow roll approximation for large power spectrum features

We develop a variant of the generalized slow roll approach for calculating the curvature power spectrum that is well suited for order unity deviations in power caused by sharp features in the inflaton potential. As an example, we show that predictions for a step function potential, which has been proposed to explain order unity glitches in the cosmic microwave background temperature power spectrum at multipoles =20--40, are accurate at the percent level. Our analysis shows that to good approximation there is a single source function that is responsible for observable features and that this function is simply related to the local slope and curvature of the inflaton potential. These properties should make the generalized slow roll approximation useful for inflation-model-independent studies of features, both large and small, in the observable power spectra.