Testing General Relativity using Bayesian model selection: Applications to observations of gravitational waves from compact binary systems

Second generation interferometric gravitational wave detectors, such as Advanced LIGO and Advanced Virgo, are expected to begin operation by 2015. Such instruments plan to reach sensitivities that will offer the unique possibility to test General Relativity in the dynamical, strong field regime and investigate departures from its predictions, in particular using the signal from coalescing binary systems. We introduce a statistical framework based on Bayesian model selection in which the Bayes factor between two competing hypotheses measures which theory is favored by the data. Probability density functions of the model parameters are then used to quantify the inference on individual parameters. We also develop a method to combine the information coming from multiple independent observations of gravitational waves, and show how much stronger inference could be. As an introduction and illustration of this framework - and a practical numerical implementation through the Monte Carlo integration technique of nested sampling - we apply it to gravitational waves from the inspiral phase of coalescing binary systems as predicted by General Relativity and a very simple alternative theory in which the graviton has a non-zero mass. This method can trivially (and should) be extended to more realistic and physically motivated theories.