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Parity Violating Non-Gaussianity from Axion-Gauge Field Dynamics

We study scalar-tensor-tensor and tensor-scalar-scalar three point cross correlations generated by the dynamics of a transiently rolling spectator axion-$\mathrm U(1)$ gauge field model during inflation. In this framework, tensor and scalar fluctuations are sourced by gauge fields at the non-linear level due to gravitational interactions, providing a chiral background of gravitational waves while keeping the level of scalar fluctuations at the observationally viable levels at CMB scales. We show that the gravitational couplings between the observable sector and gauge fields can also mediate strong correlations between scalar and tensor fluctuations, generating an amplitude for the mixed type three-point functions that is parametrically larger -- $f_{\rm NL} \simeq \mathcal{O}(1-10) (r/0.01)^{3/2}$-- compared to the single-field realizations of inflation. As the amplification of the gauge field sources are localized around the time of horizon exit, the resulting mixed bispectra are peaked {\it close} to the equilateral configurations. The shape dependence, along with the scale dependence and the parity violating nature of the mixed bispectra can serve as a distinguishing feature of the underlying axion-gauge field dynamics and suggest a careful investigation of their signatures on the CMB observables including cross correlations between temperature T and E,B polarization modes.