Constraining axion inflation with gravitational waves from preheating

We study gravitational wave production from gauge preheating in a variety of inflationary models, detailing its dependence on both the energy scale and the shape of the potential. We show that preheating into Abelian gauge fields generically leads to a large gravitational wave background that contributes significantly to the effective number of relativistic degrees of freedom in the early universe, Neff. We demonstrate that the efficiency of gravitational wave production is correlated with the tensor-to-scalar ratio, r. In particular, we show that efficient gauge preheating in models whose tensor-to-scalar ratio would be detected by next-generation cosmic microwave background experiments (r≳10−3) will be either detected through its contribution to Neff or ruled out. Furthermore, we show that bounds on Neff provide the most sensitive probe of the possible axial coupling of the inflaton to gauge fields regardless of the potential.