Constraining axion inflation with gravitational waves across 29 decades
  in frequency
  We demonstrate that gravitational waves generated by efficient gauge
preheating after axion inflation generically contribute significantly to the
effective number of relativistic degrees of freedom $N_\mathrm{eff}$. We show
that, with existing Planck limits, gravitational waves from preheating already
place the strongest constraints on the inflaton's possible axial coupling to
Abelian gauge fields. We demonstrate that gauge preheating can completely
reheat the Universe regardless of the inflationary potential. Further, we
quantify the variation of the efficiency of gravitational wave production from
model to model and show that it is correlated with the tensor-to-scalar ratio.
In particular, when combined with constraints on models whose tensor-to-scalar
ratios would be detected by next-generation cosmic microwave background
experiments, $r\gtrsim 10^{-3}$, constraints from $N_\mathrm{eff}$ will probe
or rule out the entire coupling regime for which gauge preheating is efficient.
