Testing Gravity with Gravitational Waves from Binary Black Hole Mergers: Contributions from Amplitude Corrections

The detection of gravitational waves has offered us the opportunity to explore the dynamical and strong-field regime of gravity. Because matched filtering is more sensitive to variations in the gravitational waveform phase than the amplitude, many tests of gravity with gravitational waves have been carried out using only the former. Such studies cannot probe the non-Einsteinian effects that may enter only in the amplitude. Besides, if not accommodated in the waveform template, a non-Einsteinian effect in the amplitude may induce systematic errors on other parameters such as the luminosity distance. In this paper, we derive constraints on a few modified theories of gravity (Einstein-dilaton-Gauss-Bonnet gravity, scalar-tensor theories, and varying-$G$ theories), incorporating both phase and amplitude corrections. We follow the model-independent approach of the parametrized post-Einsteinian formalism. We perform Fisher analyses with Monte-Carlo simulations using the LIGO/Virgo posterior samples. We find that the contributions from amplitude corrections can be comparable to the ones from the phase corrections in case of massive binaries like GW150914. Also, constraints derived by incorporating both phase and amplitude corrections differ from the ones with phase corrections only by 4% at most, which supports many of the previous studies that only considered corrections in the phase. We further derive reliable constraints on the time-evolution of a scalar field in a scalar-tensor theory for the first time with gravitational waves.