Semiclassical Approximations to Cosmological Perturbations

Abstract

We apply several methods related to the WKB approximation 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 find agreement for the slow-roll structure. Scalar wave propagation on the Schwarzschild background is also considered.