Power-counting during single-field slow-roll inflation

TL;DR

This paper clarifies the parameter counting in single-field slow-roll inflation, establishing the validity limits of semi-classical gravity and deriving how inflationary correlation functions depend on key parameters like psilon and H/Mp.

Contribution

It provides a systematic approach to determine the domain of validity for inflationary perturbation theory in single-field models with varying parameters.

Findings

Derived an explicit expression for correlation functions dependence on psilon and H/Mp.

Identified the boundaries of validity for models with small sound speed.

Analyzed the applicability of perturbation theory in eternal inflation regimes.

Abstract

We elucidate the counting of the relevant small parameters in inflationary perturbation theory. Doing this allows for an explicit delineation of the domain of validity of the semi-classical approximation to gravity used in the calculation of inflationary correlation functions. We derive an expression for the dependence of correlation functions of inflationary perturbations on the slow-roll parameter $\epsilon = -\dot{H}/H^2$, as well as on $H/M_p$, where $H$ is the Hubble parameter during inflation. Our analysis is valid for single-field models in which the inflaton can traverse a Planck-sized range in field values and where all slow-roll parameters have approximately the same magnitude. As an application, we use our expression to seek the boundaries of the domain of validity of inflationary perturbation theory for regimes where this is potentially problematic: models with small speed of sound and models allowing eternal inflation.