Incompleteness Matters Not: Inference of $H_0$ from BBH-galaxy cross-correlations

TL;DR

This paper demonstrates that cross-correlating gravitational-wave sources with galaxy catalogs enables accurate measurement of the Hubble constant even with incomplete data, bypassing the need for host galaxy identification.

Contribution

It introduces a novel cross-correlation method for inferring H0 that remains effective despite 100% catalog incompleteness, validated with realistic simulations.

Findings

H0 can be inferred with less than 10% precision using 50 sources.

The method remains robust with 100% incomplete galaxy catalogs.

Cross-correlation outperforms traditional host galaxy identification techniques.

Abstract

We show how the angular clustering between gravitational-wave standard sirens and galaxies with known redshifts allows an inference of the Hubble constant, regardless of whether the host galaxies of any of these sirens are present in the galaxy catalog. We demonstrate this for the first time with realistic simulations of gravitational-wave signals from binary black holes in a three-detector network with Advanced LIGO and Advanced Virgo sensitivities. We show that with such a network, the cross-correlation technique can be used to infer the Hubble parameter with a precision of less than 10% (2%) at 90% confidence with 50 (500) sources, even with a 100% incomplete catalog, which does not contain the hosts of any of the gravitational-wave events. We compare our method with the current state-of-the-art techniques used for the inference of the Hubble parameter from real data. We argue that, if the clustering information is not used explicitly, the inference of $H_0$ from real data is expected to be prior-dominated.