The method of comparison equations for cosmological perturbations

We apply the method of comparison equations to study cosmological perturbations during inflation, obtaining the full power spectra of scalar and tensor perturbations to first and to second order in the slow-roll parameters. We compare our results with those derived by means of other methods, in particular the Green's function method and the improved Wentzel-Kramers-Brillouin(WKB) approximation, and find agreement for the slow-roll structure. The method of comparison equations, just like the improved WKB approximation, can however be applied to more general situations where the slow-roll approximation fails.