Echoes from the dark: Galaxy catalog incompleteness in standard siren cosmology

¹ Dipartimento di Fisica e Astronomia “Augusto Righi”–Università di Bologna Via Gobetti 93/2 I-40129 Bologna, Italy
² INAF-OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna Via Gobetti 93/3 I-40129 Bologna, Italy
³ INFN-Sezione di Bologna Viale Berti Pichat 6/2 40127 Bologna, Italy
⁴ Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca Piazza della Scienza 3 20126 Milano, Italy
⁵ INFN, Sezione di Milano-Bicocca Piazza della Scienza 3 20126 Milano, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 22 September 2025
Accepted: 14 December 2025

Abstract

Gravitational wave observations can be combined with galaxy catalogs to constrain cosmology and test modified gravity theories using the standard siren method. However, galaxy catalogs are intrinsically incomplete due to observational limitations, potentially leaving host galaxies undetected, thereby weakening constraints and potentially introducing systematic errors. In this work, we present a self-consistent framework to study catalog incompleteness and host weighting effects, implemented in the publicly available CHIMERA pipeline. We obtained joint cosmological and astrophysical population constraints from 100 binary black hole (BBH) events in a LIGO-Virgo-KAGRA O5-like configuration using spectroscopic galaxy catalogs with varying completeness levels and stellar-mass host weighting schemes. We find percent-level constraints on H₀ with complete catalogs, reaching precisions of 1.6%, 1.3%, and 0.9% for constant, linear, and quadratic mass weighting, respectively. As completeness decreases, the precision degrades following a sigmoid trend, with a threshold and steepness that increase for stronger weightings. Simultaneously, the correlation between H₀ and the BBH population mass scale increases, making results more sensitive to assumptions about the astrophysical population. Remarkably, 2% precision remains achievable even when catalogs contain only 50% of the potential host galaxies within the gravitational wave detection horizon, while 1% precision requires host probabilities scaling with stellar mass squared. The results are robust against host weighting mismodeling, even at moderate completeness levels. This work further highlights the importance of spectroscopic galaxy surveys in standard siren cosmology and provides a pathway for developing the science case of future facilities.