A robust cosmic standard ruler from the cross-correlations of galaxies and dark sirens

Abstract

Observations of gravitational waves (GWs) from dark sirens allow us to infer their locations and distances. Galaxies, on the other hand, have precise angular positions but no direct measurement of their distances -- only redshifts. The cross-correlation of GWs, which we limit here to binary black hole mergers (BBH), in spherical shells of luminosity distance $D_L$, with galaxies in shells of redshift $z$, leads to a direct measurement of the Hubble diagram $D_L(z)$. Since this standard ruler relies only on the statistical proximity of the dark sirens and galaxies (a general property of large-scale structures), it is essentially model-independent: the correlation is maximal when both redshift and $D_L$ shells coincide. We forecast the constraining power of this technique, which we call {\it{Peak Sirens}}, for run 5 (O5) of LIGO-Virgo-KAGRA (LVK), as well as for the third-generation observatories Einstein Telescope and Cosmic Explorer. We employ thousands of full-sky light cone simulations with realistic numbers for the tracers, and include masking by the Milky Way, lensing and inhomogeneous GW sky coverage. We find that the method is not expected to suffer from some of the issues present in other dark siren methods, such as biased constraints due to incompleteness of galaxy catalogs or dependence on priors for the merger rates of BBH. We show that with Peak Sirens, given the projected O5 sensitivity, LVK can measure $H_0$ with $7\%$ precision by itself, assuming $\Lambda$CDM, and $4\%$ precision using external datasets to constrain ${\Omega }_m$. We also show that future third-generation GW detectors can achieve, without external data, sub-percent uncertainties in $H_0$ assuming $\Lambda$CDM, and 3\% in a more flexible $w_0{w}_a$CDM model. The method also shows remarkable robustness against systematic effects such as the modeling of non-linear structure formation.

v2: clarified the methodology. Accepted for publication in JCAP

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• The Science of the Einstein Telescope
• Cosmic Cartography II: completing galaxy catalogs for gravitational-wave cosmology
• Inferring astrophysics and cosmology with individual compact binary coalescences and their gravitational-wave stochastic background
• Echoes from the dark: Galaxy catalog incompleteness in standard siren cosmology
• Measurement of the Hubble constant using the Dark Energy Survey Year 6 Gold galaxy catalogue and the fourth Gravitational-Wave Transient Catalogue
• Exploring future synergies for large-scale structure between gravitational waves and radio sources
• Constraining the lensing dispersion from the angular clustering of binary black hole mergers