Higher derivatives and power spectrum in effective single field inflation

TL;DR

This paper investigates how integrating out heavy fields in single-field inflation introduces higher derivative corrections to the effective action, affecting the curvature perturbation's power spectrum.

Contribution

It provides a detailed analysis of next-to-leading order corrections from heavy isocurvature modes, highlighting the suppression by the heavy mass scale.

Findings

Corrections are suppressed by the ratio H/M.

Explicit form of corrections to the power spectrum.

Illustrative example demonstrating the impact.

Abstract

We study next-to-leading corrections to the effective action of the curvature perturbation obtained by integrating out the coupled heavy isocurvature perturbation. These corrections result from including higher order derivative operators, weighted by the mass scale of the heavy physics, in the effective theory expansion. We find that the correction terms are suppressed by the ratio of the Hubble parameter to the heavy mass scale. The corresponding corrections to the power spectrum of the curvature perturbation are presented for a simple illustrative example.