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 LIGO-Virgo observations to provide stringent constraints on post-Newtonian predictions of the inspiral and to assess systematic biases that may arise in such parameterized 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 find that to optimize the GR test of high-mass binaries, comprehensive studies must 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. They provide slightly different bounds, namely, $alpha_0 lesssim 2 imes 10^{-1}$ and $alpha_0 lesssim 4 imes 10^{-1}$, respectively, at $68\%$ credible level. These differences arise mainly because the tidal parameters have to be treated differently in the theory-indepdendent and theory-specific approaches. This poses a conceptual problem in tests of GR. We discuss this in greater detail in the main texts (here poster!).