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Parity-violating (PV) gravity has recently attracted interest in severalaspects. One of them is the axion-graviton coupling to test the axion-darkmatter model. Moreover, by extending Chern-Simons (CS) gravity to includederivatives of a scalar field up to the second order, a more general class ofPV gravity theory, which we call the CNCL model, has been proposed~[M.Crisostomi {\it et al.}, Phys. Rev. D, {\bf 97}, 044034 (2018)]. The model canbe further extended by including even higher derivatives of the scalar fieldand/or higher curvature terms. In this paper, we discuss the effect of parityviolation in the gravitational sector on the propagation of gravitational wavesfrom binary coalescence by introducing a model-independent parametrization ofmodification. Our parametrization includes the CNCL model as well as CSgravity. The effect of parity violation on the gravitational waveform ismaximum when the source binary orientation to our line of sight is edge-on,while the modified waveform reduces to the parity-symmetric one when the sourceis face-on. We perform a search for the signature of such modification by usingthe LIGO/Virgo O1/O2 catalog. We find that the catalog data is consistent withgeneral relativity and obtain constraints on parity violation in gravity forvarious post-Newtonian order modifications for the first time. The obtainedconstraint on CS gravity is consistent with the results in previous works. Onthe other hand, the constraint on the CNCL model that we obtain is tighter thanthe previous results by roughly 7 orders of magnitude.

Parametrized test of parity-violating gravity using GWTC-1 events