Parity-violating gravity and GW170817

We consider gravitational waves (GWs) in generic parity-violating gravity, including recently proposed ghost-free theories with parity violation as well as Chern-Simons (CS) modified gravity, and study the implications of observational constraints from GW170817/GRB 170817A. Whereas GWs propagate at the speed of light, c, in CS gravity, we point out that this is specific to CS gravity and the GW propagation speed deviates from c, in general, in parity-violating gravity. Therefore, contrary to the previous literature in which only CS gravity is studied as a concrete example, we show that GW170817/GRB 170817A can, in fact, be used to limit gravitational parity violation. Our argument implies that the constraint on the propagation speed of GWs can pin down the parity-violating sector, if any, to CS gravity.