Testing general relativity with compact coalescing binaries: comparing exact and predictive methods to compute the Bayes factor

The second generation of gravitational-wave detectors is scheduled to start operations in 2015. Gravitational-wave signatures of compact binary coalescences could be used to accurately test the strong-field dynamical predictions of general relativity. Computationally expensive data analysis pipelines, including TIGER, have been developed to carry out such tests. As a means to cheaply assess whether a particular deviation from general relativity can be detected, Cornish et al. and Vallisneri recently proposed an approximate scheme to compute the Bayes factor between a general-relativity gravitational-wave model and a model representing a class of alternative theories of gravity parametrised by one additional parameter. This approximate scheme is based on only two easy-to-compute quantities: the signal-to-noise ratio of the signal and the fitting factor between the signal and the manifold of possible waveforms within general relativity. In this work, we compare the prediction from the approximate formula against an exact numerical calculation of the Bayes factor using the lalinference library. We find that, using frequency-domain waveforms, the approximate scheme predicts exact results with good accuracy, providing the correct scaling with the signal-to-noise ratio at a fitting factor value of 0.992 and the correct scaling with the fitting factor at a signal-to-noise ratio of 20, down to a fitting factor of $\sim$ 0.9. We extend the framework for the approximate calculation of the Bayes factor which significantly increases its range of validity, at least to fitting factors of $\sim$ 0.7 or higher.