The Stochastic Siren: Astrophysical Gravitational-Wave Background Measurements of the Hubble Constant

Gravitational waves from individually resolved compact object mergers can be used as standard sirens, offering a novel self-calibrating precision probe of cosmology. While the standard siren method has been well-explored, the gravitational-wave background arising from unresolved mergers offers a novel alternative to probing cosmology. We demonstrate that the combination of resolved binary black hole mergers with the unresolved signals composing the stochastic gravitational-wave background can be used to measure cosmological parameters, including the Hubble constant, $H_0$. We apply this ``stochastic siren'' method to existing gravitational-wave data and find that including the current non-detection of the background increases the accuracy at which $H_0$ can be measured, relative to using resolved mergers alone. We also provide projections for upcoming detectors to highlight their ability to probe cosmology with the background. With the anticipated detection of the astrophysical gravitational-wave background, the stochastic siren approach can be expected to improve future standard siren cosmological measurements.