Effects of Gravitational Chern-Simons during Axion-SU(2) Inflation

Abstract: In this paper, we examine the viability of inflation models with a spectator axion field coupled to both gravitational and SU(2) gauge fields via Chern-Simons couplings. Requiring phenomenological success of the axion-SU(2) sector constrains the coupling strength of the gravitational Chern-Simons term. We find that the impact of this term on the production and propagation of gravitational waves can be as large as fifty percent enhancement for the helicity that is not sourced by the gauge field, if the cut-off scale is as low as $\Lambda$ = 20H. The effect becomes smaller for a larger value of $\Lambda$, while the impact on the helicity sourced by the gauge field is negligible regardless of $\Lambda$.