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