Bayesian framework to infer the Hubble constant from the cross-correlation of individual gravitational wave events with galaxies

TL;DR

This paper introduces a Bayesian method to estimate the Hubble constant by analyzing the galaxy overdensity around individual binary black hole gravitational wave events, accounting for localization uncertainties.

Contribution

The study presents a novel Bayesian framework using 3D cross-correlation to infer $H_0$ from GW events without electromagnetic counterparts, demonstrated with simulated data.

Findings

Can constrain $H_0$ with less than 8% uncertainty using 250 simulated events.

Method effectively accounts for GW localization uncertainties.

Potential for application to real GW data in future observations.

Abstract

Gravitational waves (GWs) from the inspiral of binary compact objects offer a one-step measurement of the luminosity distance to the event, which is essential for the measurement of the Hubble constant, $H_0$, which characterizes the expansion rate of the Universe. However, unlike binary neutron stars, the inspiral of binary black holes is not expected to be accompanied by electromagnetic radiation and a subsequent determination of its redshift. Consequently, independent redshift measurements of such GW events are necessary to measure $H_0$. In this study, we present a novel Bayesian approach to infer $H_0$ by measuring the overdensity of galaxies around individual binary black hole merger events in configuration space. We model the measured overdensity using the $3$D cross-correlation between galaxies and GW events, explicitly accounting for the GW event localization uncertainty. We demonstrate the efficacy of our method with $250$ simulated GW events distributed within $1$ Gpc in colored Gaussian noise of Advanced LIGO and Advanced Virgo detectors operating at O4 sensitivity. We show that such measurements can constrain the Hubble constant with a precision of $\lesssim 8 \%$ ($90\%$ highest density interval). We highlight the potential improvements that need to be accounted for in further studies before the method can be applied to real data.