The Hitchhiker's guide to the galaxy catalog approach for gravitational wave cosmology

TL;DR

This paper clarifies the galaxy catalog method for gravitational wave cosmology, emphasizing correct implementation to avoid biases in estimating the Hubble constant, and addresses misconceptions about its accuracy.

Contribution

It demonstrates that the dark siren galaxy catalog approach yields unbiased Hubble constant estimates when properly implemented, correcting recent claims of bias.

Findings

Proper implementation ensures unbiased $H_0$ estimates.

Common errors can introduce spurious biases.

Addressing misconceptions clarifies the method's reliability.

Abstract

We outline the ``dark siren'' galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz (1986), one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Hunterer 2021 recently claimed that this approach results in a biased estimate of the Hubble constant, $H_0$, when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.