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Hierarchical Test of General Relativity with Gravitational Waves

Isi, Maximiliano and Chatziioannou, Katerina and Farr, Will M. (2019) Hierarchical Test of General Relativity with Gravitational Waves. Physical Review Letters, 123 (12). Art. No. 121101. ISSN 0031-9007. doi:10.1103/physrevlett.123.121101.

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We propose a hierarchical approach to testing general relativity with multiple gravitational wave detections. Unlike existing strategies, our method does not assume that parameters quantifying deviations from general relativity are either common or completely unrelated across all sources. We instead assume that these parameters follow some underlying distribution, which we parametrize and constrain. This can be then compared to the distribution expected from general relativity, i.e., no deviation in any of the events. We demonstrate that our method is robust to measurement uncertainties and can be applied to theories of gravity where the parameters beyond general relativity are related to each other, as generally expected. Our method contains the two extremes of common and unrelated parameters as limiting cases. We apply the hierarchical model to the population of 10 binary black hole systems so far detected by LIGO and Virgo. We do this for a parametrized test of gravitational wave generation, by modeling the population distribution of beyond-general-relativity parameters with a Gaussian distribution. We compute the mean and the variance of the population and show that both are consistent with general relativity for all parameters we consider. In the best case, we find that the population properties of the existing binary signals are consistent with general relativity at the ∼1% level. This hierarchical approach subsumes and extends existing methodologies and is more robust at revealing potential subtle deviations from general relativity with increasing number of detections.

Item Type:Article
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URLURL TypeDescription Paper
Isi, Maximiliano0000-0001-8830-8672
Chatziioannou, Katerina0000-0002-5833-413X
Farr, Will M.0000-0003-1540-8562
Additional Information:© 2019 American Physical Society. Received 5 May 2019; published 16 September 2019. We thank Aaron Zimmerman and Carl-Johan Haster for useful discussions. We thank Nathan Johnson-McDaniel for comments on the draft. Samples from the μ_i and σ_i posteriors were drawn with STAN [33], and plots were produced with MATPLOTLIB [34]. M. I. is supported by NASA through the NASA Hubble Fellowship Grant No. #HST-HF2-51410.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under Contract No. NAS5-26555. The Flatiron Institute is supported by the Simons Foundation. This Letter carries LIGO document number LIGO-P1900109.
Funding AgencyGrant Number
NASA Hubble FellowshipHST-HF2-51410.001-A
Simons FoundationUNSPECIFIED
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Other Numbering System NameOther Numbering System ID
LIGO DocumentP1900109
Issue or Number:12
Record Number:CaltechAUTHORS:20200729-103003532
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104637
Deposited By: Tony Diaz
Deposited On:29 Jul 2020 17:44
Last Modified:16 Nov 2021 18:33

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