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

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