Method of comparison equations for cosmological perturbations

TL;DR

This paper introduces the method of comparison equations to compute cosmological perturbation spectra during inflation, providing a versatile approach that aligns with existing methods and extends to scenarios beyond slow-roll conditions.

Contribution

It demonstrates the application of comparison equations to derive scalar and tensor spectra, offering an alternative to traditional methods and applicable when slow-roll approximation breaks down.

Findings

Agreement with existing methods in slow-roll scenarios

Extension to non-slow-roll situations

Potential for broader application in cosmology

Abstract

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 WKB approximation, and find agreement for the slow-roll structure. The method of comparison equations, just as the improved WKB approximation, can however be applied to more general situations where the slow-roll approximation fails.