Semiclassical Approximations to Cosmological Perturbations

TL;DR

This paper develops semiclassical WKB-based methods to compute the power spectra of cosmological perturbations during inflation, achieving higher-order accuracy and validating results against other techniques like the Green's function method.

Contribution

It introduces and applies semiclassical WKB approximations to derive inflationary perturbation spectra up to second order in slow-roll parameters, with validation against existing methods.

Findings

WKB methods produce power spectra consistent with Green's function results.

Second-order slow-roll corrections are successfully computed.

Scalar wave propagation on Schwarzschild background is also analyzed.

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.