Energy-momentum tensor and helicity for gauge fields coupled to a pseudo-scalar inflaton

TL;DR

This paper analytically computes the energy-momentum tensor and helicity of gauge fields coupled to a pseudo-scalar inflaton, clarifying the validity of previous approximations and implications for inflation dynamics.

Contribution

It introduces a method to accurately calculate gauge field energy density and helicity during inflation, including divergences and counterterms, for any coupling strength.

Findings

Analytic expressions for gauge field energy density and helicity.

Validation of approximations in strong coupling regime.

Insights into backreaction effects on inflaton evolution.

Abstract

We study the energy-momentum tensor and helicity of gauge fields coupled through $g \phi F \tilde{F}/4$ to a pseudo-scalar field $\phi$ driving inflation. Under the assumption of a constant time derivative of the background inflaton, we compute analitically divergent and finite terms of the energy density and helicity of gauge fields for any value of the coupling $g$. We introduce a suitable adiabatic expansion for mode functions of physical states of the gauge fields which correctly reproduces ultraviolet divergences in average quantities and identify corresponding counterterms. Our calculations shed light on the accuracy and the range of validity of approximated analytic estimates of the energy density and helicity terms previously existed in the literature in the strongly coupled regime only, i.e. for $g \dot \phi/(2H) \gg 1$. We discuss the implications of our analytic calculations for the backreaction of quantum fluctuations onto the inflaton evolution.