Tarnished by Tools: Cost of Systematics in Golden Dark Siren Cosmology

TL;DR

This paper assesses how waveform modeling and calibration systematics impact the precision of Hubble constant measurements using golden dark sirens with next-generation gravitational-wave detectors, highlighting the need for improved accuracy.

Contribution

It quantifies the effects of waveform and calibration systematics on dark siren cosmology and establishes accuracy requirements for future detectors to achieve sub-percent H_0 precision.

Findings

Waveform inaccuracies can bias luminosity distance and host galaxy identification.

Current models generally recover consistent H_0 posteriors but can mislocalize sources.

Calibration errors must be minimized to prevent systematic biases in H_0 measurements.

Abstract

Golden dark sirens - exceptionally well-localized gravitational-wave (GW) sources without electromagnetic counterparts - offer a powerful route to precision measurements of the Hubble constant, $H_0$, with next-generation (XG) detectors. The statistical promise of this method, however, places stringent demands on waveform accuracy and detector calibration, as even small systematic errors can dominate over statistical uncertainties at high signal-to-noise ratios. We investigate the impact of waveform-modeling systematics on golden dark siren cosmology using a synthetic population of binary black holes consistent with current GW observations and analyzed in the XG-detector era. By comparing state-of-the-art waveform models against numerical-relativity-based reference signals, we quantify modeling inaccuracies from both modeling and data-analysis perspectives and assess how they propagate into biases in luminosity distance, host-galaxy association, and single-event $H_0$ inference. We find that while current waveform models often allow recovery of statistically consistent $H_0$ posteriors, small waveform-induced biases can significantly affect three-dimensional localization and host galaxy ranking, occasionally leading to incorrect redshift assignments. We further derive order-of-magnitude requirements on detector calibration accuracy needed to ensure that calibration systematics remain subdominant for golden dark sirens observed with XG networks. To realize sub-percent $H_0$ measurements with golden dark sirens will require waveform and calibration accuracies that scale as $\mathcal{O}(\rho^{-2})$ with signal-to-noise ratio, motivating sustained advances in waveform modeling, numerical relativity, and detector calibration for the XG era.