Observational Constraints on Gauge Field Production in Axion Inflation
  Models of axion inflation are particularly interesting since they provide a
natural justification for the flatness of the potential over a super-Planckian
distance, namely the approximate shift-symmetry of the inflaton. In addition,
most of the observational consequences are directly related to this symmetry
and hence are correlated. Large tensor modes can be accompanied by the
observable effects of a the shift-symmetric coupling $\phi F\tilde F$ to a
gauge field. During inflation this coupling leads to a copious production of
gauge quanta and consequently a very distinct modification of the primordial
curvature perturbations. In this work we compare these predictions with
observations. We find that the leading constraint on the model comes from the
CMB power spectrum when considering both WMAP 7-year and ACT data. The
bispectrum generated by the non-Gaussian inverse-decay of the gauge field leads
to a comparable but slightly weaker constraint. There is also a constraint from
mu-distortion using TRIS plus COBE/FIRAS data, but it is much weaker. Finally
we comment on a generalization of the model to massive gauge fields. When the
mass is generated by some light Higgs field, observably large local
non-Gaussianity can be produced.
