Improved WKB analysis of Slow-Roll Inflation

TL;DR

This paper advances the WKB method for calculating cosmological perturbations during inflation, achieving second-order accuracy in slow-roll parameters without assuming their constancy, aligning with upcoming observational precision.

Contribution

It introduces an improved WKB approach for inflationary perturbations that extends beyond leading order and does not require constant slow-roll parameters.

Findings

Second-order power spectra for scalar and tensor perturbations derived.

Method aligns with observational accuracy requirements.

Comparison with previous techniques confirms improvements.

Abstract

We extend the WKB method for the computation of cosmological perturbations during inflation beyond leading order and provide the power spectra of scalar and tensor perturbations to second order in the slow-roll parameters. Our method does not require that the slow-roll parameters be constant. Although leading and next-to-leading results in the slow-roll parameters depend on the approximation technique used in the computation, we find that the inflationary theoretical predictions obtained may reach the accuracy required by planned observations. In two technical appendices, we compare our techniques and results with previous findings.