Dark siren cross-correlations and the sensitivity of $H_0$ to methodological choices

TL;DR

This paper examines how methodological choices impact the measurement of the Hubble constant using gravitational wave and galaxy catalog cross-correlations, emphasizing strategies to mitigate biases for future precision cosmology.

Contribution

It analyzes the effects of covariance, bias parametrization, and binning choices on $H_0$ estimates, proposing methods to incorporate selection effects without explicit population modeling.

Findings

Methodological choices significantly influence $H_0$ inference.

Selection effects can be incorporated without explicit missing population modeling.

Proper modeling and large samples can mitigate systematic biases.

Abstract

Gravitational wave sources act as absolute distance indicators, making them powerful probes of the present-day expansion rate of the Universe, $H_0$. The cross-correlation method combines gravitational wave events with galaxy catalogues to constrain cosmological parameters through their shared large-scale structure. In this work, we investigate how key methodological choices -- including covariance treatment, bias parametrisation for galaxies and gravitational wave events, and distance and redshift binning width -- affect the inferred value of $H_0$. We also study catalogue incompleteness, showing that selection effects can be incorporated directly into the theoretical prediction, without the need to model the missing population explicitly, a key advantage over the standard galaxy catalogue approach. Our results indicate that, with appropriate modelling choices and a sufficiently large sample of precise gravitational wave events, the systematic biases considered here can be effectively mitigated, highlighting the potential of the cross-correlation method for future dark siren precision cosmology.