Reheating with Axion-SU(2) and Gravitational Chern-Simons Couplings

We study the early stages of an oscillatory reheating phase in an inflaton plus spectator axion-SU(2) system, including both an axion-gauge Chern-Simons coupling $\chi F\tilde{F}$ and a gravitational Chern-Simons coupling $\chi R\tilde{R}$. Assuming an isotropic SU(2) background configuration of chromo-natural type and quadratic potentials, we numerically solve the coupled background and tensor perturbation equations during the first e-fold of reheating. The gravitational Chern-Simons term induces a helicity-dependent modification of the tensor kinetic coefficient, yielding a chiral enhancement of the tensor power spectrum on the order of tens of percent for a representative benchmark. We illustrate how such an early-time enhancement can map to a narrow feature in the present-day stochastic gravitational wave spectrum, potentially relevant for upcoming and proposed space-based detectors, while a fully self-consistent determination of the peak scale requires scanning comoving wavenumbers and specifying the reheating history.