TY - JOUR

T1 - Testing general relativity with compact coalescing binaries

T2 - comparing exact and predictive methods to compute the Bayes factor

AU - Del Pozzo, Walter

AU - Grover, Katherine

AU - Mandel, Ilya

AU - Vecchio, Alberto

PY - 2014/10/3

Y1 - 2014/10/3

N2 - 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 (GR). Computationally expensive data analysis pipelines, including TIGER (test infrastructure for general relativity), have been developed to carry out such tests. As a means to cheaply assess whether a particular deviation from GR can be detected, Cornish et al (2011 Phys. Rev. D 84 062003) and Vallisneri (2012 Phys. Rev. D 86 082001) recently proposed an approximate scheme to compute the Bayes factor between a GR gravitational-wave model and a model representing a class of alternative theories of gravity parametrized by one additional parameter. This approximate scheme is based on only two easy-to-compute quantities: the signal-to-noise ratio (SNR) of the signal and the fitting factor (FF) between the signal and the manifold of possible waveforms within GR. 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 SNR at a FF value of 0.992 and the correct scaling with the FF at a SNR of 20, down to a FF of 0.9. We extend the framework for the approximate calculation of the Bayes factor, which significantly increases its range of validity, at least to FFs of 0.7 or higher.

AB - 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 (GR). Computationally expensive data analysis pipelines, including TIGER (test infrastructure for general relativity), have been developed to carry out such tests. As a means to cheaply assess whether a particular deviation from GR can be detected, Cornish et al (2011 Phys. Rev. D 84 062003) and Vallisneri (2012 Phys. Rev. D 86 082001) recently proposed an approximate scheme to compute the Bayes factor between a GR gravitational-wave model and a model representing a class of alternative theories of gravity parametrized by one additional parameter. This approximate scheme is based on only two easy-to-compute quantities: the signal-to-noise ratio (SNR) of the signal and the fitting factor (FF) between the signal and the manifold of possible waveforms within GR. 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 SNR at a FF value of 0.992 and the correct scaling with the FF at a SNR of 20, down to a FF of 0.9. We extend the framework for the approximate calculation of the Bayes factor, which significantly increases its range of validity, at least to FFs of 0.7 or higher.

KW - compact binaries

KW - tests of general relativity

KW - data analysis

UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000343412700007&KeyUID=WOS:000343412700007

U2 - 10.1088/0264-9381/31/20/205006

DO - 10.1088/0264-9381/31/20/205006

M3 - Article

SN - 0264-9381

VL - 31

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 20

M1 - 205006

ER -