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

We study the energy-momentum tensor and helicity of gauge fields coupled through gφFF/4 to a pseudoscalar field φ driving inflation. Under the assumption of a constant time derivative of the background inflaton, we compute analytically 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 identifies 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 gφ/(2H)≫1. We discuss the implications of our analytic calculations for the backreaction of quantum fluctuations onto the inflaton evolution.