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

TL;DR

This paper evaluates an approximate method for computing the Bayes factor in gravitational wave tests of general relativity, comparing it to exact calculations and extending its validity range.

Contribution

It demonstrates that the approximate scheme accurately predicts the Bayes factor and extends its applicability to lower fitting factors, improving computational efficiency in gravitational wave analysis.

Findings

Approximate scheme predicts exact Bayes factors with good accuracy.

The method remains valid down to a fitting factor of about 0.7.

The approach correctly scales with signal-to-noise ratio and fitting factor.

Abstract

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.