Tests of general relativity with gravitational-wave observations using a flexible theory-independent method

We perform tests of general relativity (GR) with gravitational waves (GWs) from the inspiral stage of compact binaries using a theory-independent framework, which adds generic phase corrections to each multipole of a GR waveform model in frequency domain. This method has been demonstrated on Laser Interferometer Gravitational Wave Observatory-Virgo observations to provide stringent constraints on postNewtonian predictions of the inspiral and to assess systematic biases that may arise in such parametrized tests. Here, we detail the anatomy of our framework for aligned-spin waveform models. We explore the effects of higher modes in the underlying signal on tests of GR through analyses of two unequal-mass simulated binary signals similar to GW190412 and GW190814. We show that the inclusion of higher modes improves both the precision and the accuracy of the measurement of the deviation parameters. Our testing framework also allows us to vary the underlying baseline GR waveform model and the frequency at which the non-GR inspiral corrections are tapered off. We find that to optimize the GR test of high-mass binaries, comprehensive studies would need to be done to determine the best choice of the tapering frequency as a function of the binary's properties. We also carry out an analysis on the binary neutron-star event GW170817 to set bounds on the coupling constant alpha 0 of Jordan-Fierz-Brans-Dicke gravity. We take two plausible approaches; the first approach involves translating directly the "theory-agnostic" bound on dipole-radiation into a bound on alpha 0 for different neutron-star equations of state (EOS). The second "theoryspecific" approach involves reparametrizing the test such that the deviation parameter is alpha 0 itself. The two approaches provide slightly different bounds, namely, alpha 0 < 2 x 10-1 and alpha 0 < 4 x 10-1, respectively, at 68% credible level. These differences arise mainly since in the theory-specific approach the tidal and scalarcharge parameters are fixed coherently for each neutron-star EOS and mass.