In this talk, a tale of two separate studies on gravitational waves (GWs) will be briefly presented.

The first story is about GWs produced by chiral magnetic effect (CME). When a system has chiral asymmetry, CME can produce maximally helical magnetic field at the expense of the amount of chiral asymmetry initially available in the system. We treated CME as a generic sourcing mechanism for primordial GWs, and identified two regimes of interest distinguished by the relative magnitude of two velocities characterising the depletion of chiral asymmetry, $v_\lambda$, and the generation of magnetic field, $v_\mu$. We performed a series of numerical simulations, and found that the overall CME-sourced GW energy scales as $\Omega_{\rm GW}^{\rm sat}\propto v_\lambda^5v_\mu$.

The second story is about using GWs as a constraint on graviton mass. We took a generic massive gravity theory and numerically studied its resulting spectra of GWs sourced by turbulence. Due to the nonlinear dispersion relation caused by massive graviton, the equivalence between spatial and temporal spectra of linear dispersion is no longer valid. We find that, in the spatial domain, the modification of GW spectra appears to be independent of the turbulent eddy size; and, in the temporal domain, there is a characteristic cutoff at the graviton mass scale that can be potentially constrained by pulsar timing arrays.