Exploring the string axiverse and parity violation in gravity with gravitational waves

We show that the parametric resonance of gravitational waves occurs due to the axion coherent oscillation and the circular polarization of gravitational waves is induced by the Chern-Simons coupling. However, we have never observed these signatures in the data of gravitational waves. Using this fact, we give stringent constraints on the Chern-Simons coupling constant $\ell$ and the abundance of the light string axion. In particular, we improved the current bound $\ell\leq10^{8}\,\,{\rm km}$ by many orders of magnitude.