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.
