# Testing general relativity using Bayesian model selection: Applications to observations of gravitational waves from compact binary systems

## Abstract

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 nonzero mass. This method can (and should) be extended to more realistic and physically motivated theories.

- Authors:

- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom)
- (Netherlands)
- (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 21541434

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 83; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.83.082002; (c) 2011 American Institute of Physics

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FORECASTING; GENERAL RELATIVITY THEORY; GRAVITATIONAL WAVE DETECTORS; GRAVITATIONAL WAVES; HYPOTHESIS; MASS; MONTE CARLO METHOD; OPERATION; SENSITIVITY; CALCULATION METHODS; FIELD THEORIES; MEASURING INSTRUMENTS; RADIATION DETECTORS; RELATIVITY THEORY

### Citation Formats

```
Del Pozzo, Walter, Nikhef National Institute for Subatomic Physics, Science Park 105, 1098 XG Amsterdam, Veitch, John, Physics and Astronomy, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, and Vecchio, Alberto.
```*Testing general relativity using Bayesian model selection: Applications to observations of gravitational waves from compact binary systems*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVD.83.082002.

```
Del Pozzo, Walter, Nikhef National Institute for Subatomic Physics, Science Park 105, 1098 XG Amsterdam, Veitch, John, Physics and Astronomy, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, & Vecchio, Alberto.
```*Testing general relativity using Bayesian model selection: Applications to observations of gravitational waves from compact binary systems*. United States. doi:10.1103/PHYSREVD.83.082002.

```
Del Pozzo, Walter, Nikhef National Institute for Subatomic Physics, Science Park 105, 1098 XG Amsterdam, Veitch, John, Physics and Astronomy, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, and Vecchio, Alberto. Fri .
"Testing general relativity using Bayesian model selection: Applications to observations of gravitational waves from compact binary systems". United States. doi:10.1103/PHYSREVD.83.082002.
```

```
@article{osti_21541434,
```

title = {Testing general relativity using Bayesian model selection: Applications to observations of gravitational waves from compact binary systems},

author = {Del Pozzo, Walter and Nikhef National Institute for Subatomic Physics, Science Park 105, 1098 XG Amsterdam and Veitch, John and Physics and Astronomy, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA and Vecchio, Alberto},

abstractNote = {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 nonzero mass. This method can (and should) be extended to more realistic and physically motivated theories.},

doi = {10.1103/PHYSREVD.83.082002},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 83,

place = {United States},

year = {Fri Apr 15 00:00:00 EDT 2011},

month = {Fri Apr 15 00:00:00 EDT 2011}

}