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Uncertainty and Bias of Cosmology and Astrophysical Population Model from Statistical Dark Sirens

Yu, Hang and Seymour, Brian and Wang, Yijun and Chen, Yanbei (2022) Uncertainty and Bias of Cosmology and Astrophysical Population Model from Statistical Dark Sirens. Astrophysical Journal, 941 (2). Art. No. 174. ISSN 0004-637X. doi:10.3847/1538-4357/ac9da0.

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Gravitational-wave (GW) radiation from a coalescing compact binary is a standard siren, as the luminosity distance of each event can be directly measured from the amplitude of the signal. One possibility to constrain cosmology using the GW siren is to perform statistical inference on a population of binary black hole (BBH) events. In essence, this statistical method can be viewed as follows. We can modify the shape of the distribution of observed BBH events by changing the cosmological parameters until it eventually matches the distribution constructed from an astrophysical population model, thereby allowing us to determine the cosmological parameters. In this work, we derive the Cramér–Rao bound for both cosmological parameters and those governing the astrophysical population model from this statistical dark siren method by examining the Fisher information contained in the event distribution. Our study provides analytical insights and enables fast yet accurate estimations of the statistical accuracy of dark siren cosmology. Furthermore, we consider the bias in cosmology due to unmodeled substructures in the merger rate and mass distribution. We find that a 1% deviation in the astrophysical model can lead to a more than 1% error in the Hubble constant. This could limit the accuracy of dark siren cosmology when there are more than 104 BBH events detected.

Item Type:Article
Related URLs:
URLURL TypeDescription
Yu, Hang0000-0002-6011-6190
Seymour, Brian0000-0002-7865-1052
Wang, Yijun0000-0002-5581-2001
Chen, Yanbei0000-0002-9730-9463
Additional Information:We thank Katerina Chatzioannou, Hsin-Yu Chen, and the LVC colleagues for helpful discussions and comments during the preparation of the manuscript. This material is based upon work supported by NSF's LIGO Laboratory, which is a major facility fully funded by the National Science Foundation. H.Y. acknowledges the support of the Sherman Fairchild Foundation. Y.C., B.S., and Y.W. acknowledge support from the Brinson Foundation, the Simons Foundation (award No. 568762), and NSF grants PHY-2011961, PHY-2011968, and PHY-1836809. Software: Python3 (Van Rossum & Drake 2009), NumPy (Harris et al. 2020), SciPy (Virtanen et al. 2020), Matplotlib (Hunter 2007), PYCBC (Nitz et al. 2022).
Group:Astronomy Department, LIGO, TAPIR, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
Simons Foundation568762
Issue or Number:2
Record Number:CaltechAUTHORS:20230113-705133800.2
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118791
Deposited By: Research Services Depository
Deposited On:10 Feb 2023 17:28
Last Modified:10 Feb 2023 17:28

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