Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence

Coalescences of binary neutron stars and/or black holes are amongst the most likely gravitational-wave signals to be observed in ground-based interferometric detectors. Apart from the astrophysical importance of their detection, they will also provide us with our very first empirical access to the genuine strong-field dynamics of general relativity (GR). We present a new framework based on Bayesian model selection aimed at detecting deviations from GR, subject to the constraints of the Advanced Virgo and LIGO detectors. The method tests the consistency of coefficients appearing in the waveform with the predictions made by GR, without relying on any specific alternative theory of gravity. The framework is suitable for low signal-to-noise ratio events through the construction of multiple subtests, most of which involve only a limited number of coefficients. It also naturally allows for the combination of information from multiple sources to increase one's confidence in GR or a violation thereof. We expect it to be capable of finding a wide range of possible deviations from GR, including ones which, in principle, cannot be accommodated by the model waveforms, on the condition that the induced change in phase at frequencies where the detectors are the most sensitive is comparable to the effect of a few percent change in one or more of the low-order post-Newtonian phase coefficients. In principle, the framework can be used with any GR waveform approximant, with arbitrary parametrized deformations, to serve as model waveforms. In order to illustrate the workings of the method, we perform a range of numerical experiments in which simulated gravitational waves modeled in the restricted post-Newtonian, stationary phase approximation are added to Gaussian and stationary noise that follows the expected Advanced LIGO/Virgo noise curves.