Exploring String Axions with Gravitational Waves

We explore the string axion dark matter with gravitational waves in Chern–Simons gravity. We show that the parametric resonance of gravitational waves occurs due to the axion coherent oscillation. Remarkably, the circular polarization of gravitational waves is induced by the parity violating Chern–Simons coupling. In fact, the gravitational waves should be enhanced ten times every 10−8 pc propagation in the presence of the axion dark matter with mass 10−10 eV provided the coupling constant ` = 108 km. Hence, after 10 kpc propagation, the amplitude of gravitational waves is enhanced significantly and the polarization of gravitational waves becomes circular. However, we have never observed these signatures. This implies that the Chern–Simons coupling constant and/or the abundance of string axions should be constrained much stronger than the current limits.