Investigating the impact of galaxies' compact binary hosting probability for gravitational-wave cosmology

TL;DR

This paper examines how incorrect assumptions about galaxy host probabilities for gravitational wave sources can bias measurements of the Hubble constant, emphasizing the importance of accurate modeling in future GW cosmology.

Contribution

It analyzes the impact of mismodeling galaxy host probabilities on $H_0$ estimation, highlighting conditions under which biases occur in future GW observations.

Findings

Bias in $H_0$ depends on galaxy catalog completeness and size.

Luminosity-based host probability mismodeling biases in small fields.

Redshift dependence mismodeling affects wide-field, distant GW events.

Abstract

With the advent of future-generation interferometers a huge number of Gravitational Wave (GW) signals is expected to be measured without an electromagnetic counterpart. Although these signals do not allow a simultaneous measurement of the redshift and the luminosity distance, it is still possible to infer cosmological parameters. In this paper, we focus on the systematic biases that could arise from mismodeling the GW host probability when inferring the Hubble constant ($H_0$) with GW dark sirens jointly with galaxy catalogues. We discuss the case in which the GW host probability is a function of galaxies' luminosity and redshift as it has been predicted by state-of-the-art compact binary coalescences (CBCs) synthetic catalogues. We show that, in the limiting case in which the analysis is done with a complete galaxy catalog covering a footprint of $\sim 10~\rm {deg}^2$, mismatching the host probability in terms of galaxy's luminosity will introduce a bias on $H_0$. In this case, the magnitude of the bias will depend on the distribution of the Large-Scale Structure over the line-of-sight. Instead, in the limit of a complete wide-field of view galaxy catalog and GW events localized at O$({\rm Gpc})$ distance, mismatching the redshift dependence of the GW hosting probability is more likely to introduce a systematic bias.