Higher Order Slow-Roll Predictions for Inflation

TL;DR

This paper improves the analytical predictions for inflationary perturbations by extending the WKB approximation beyond leading order, achieving high accuracy and qualitative agreement with established methods.

Contribution

It introduces an advanced WKB approximation method for inflationary perturbations that enhances accuracy and aligns with traditional approaches.

Findings

First-order WKB matches slow-roll results within 0.1%.

Second-order WKB agrees qualitatively with Green's function method.

Provides analytical predictions with improved precision.

Abstract

We study the WKB approximation beyond leading order for cosmological perturbations during inflation. To first order in the slow-roll parameters, we show that an improved WKB approximation leads to analytical results agreeing to within 0.1% with the standard slow-roll results. Moreover, the leading WKB approximation to second order in the slow-roll parameters leads to analytical predictions in qualitative agreement with those obtained by the Green's function method.