Constraining the Hubble Constant using Cross-Correlation of Gravitational Wave Events with Flux-Limited Galaxy Catalog

Abstract

Gravitational waves (GWs) from the compact binary coalescence provide direct measurement of the luminosity distance to the event. However, unlike binary neutron stars, redshift information is not available from GW observations of binary black holes. Consequently, independent redshift measurements of such GW events are necessary to measure $H_0$. In this study, we demonstrate a novel Bayesian formalism to infer $H_0$ utilizing the $3$D cross-correlation of GW events with galaxies from flux-limited catalog in configuration space. We demonstrate the efficacy of our method with $300$ 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 $\sim 9 \%$ ($90\%$ 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.