We show that an inflation model in which a spectator axion field is coupled to an $SU(2)$ gauge field produces a large three-point function (bispectrum) of primordial gravitational waves, $B_h$, on the scales relevant to the cosmic microwave background experiments. The amplitude of the bispectrum at the equilateral configuration is characterized by $B_h/P_h^2=\mathcal{O}(10)\times {\mathrm{\Omega }}_A^{-1}$, where ${\mathrm{\Omega }}_A$ is a fraction of the energy density in the gauge field and $P_h$ is the power spectrum of gravitational waves produced by the gauge field.

• Received 10 July 2017
• Revised 19 February 2018

DOI:https://doi.org/10.1103/PhysRevD.97.103526