Inferring astrophysics and cosmology with individual compact binary coalescences and their gravitational-wave stochastic background

Gravitational waves (GWs) from compact binary coalescences (CBCs) provide a new avenue to probe the cosmic expansion, in particular the Hubble constant, H₀. The spectral sirens method is one of the most used techniques for GW cosmology. It consists of obtaining cosmological information from the GW luminosity distance, directly inferred from data, and the redshift, which can be implicitly obtained from the source frame mass distribution of the CBC population. With GW detectors, populations of CBCs can be observed either as resolved individual sources or implicitly as a stochastic gravitational-wave background (SGWB) from the unresolved ones. We studied how resolved and unresolved sources of CBCs can be employed in the spectral siren framework to constrain cosmic expansion. The idea stems from the fact that the SGWB can constrain additional population properties of the CBCs, thus potentially improving the measurement precision of the cosmic expansion parameters. We show that with a five-detector network at O5-designed sensitivity, the inclusion of the SGWB will improve our ability to exclude low values of H₀ and the dark matter energy fraction, Ωₘ, while also improving the determination of a possible CBC peak in redshift. Although low values of H₀ and Ωₘ will be better constrained, we find that most of the precision on H₀ will be provided by resolved spectral sirens. For the four-detector network, the population posterior is instead entirely dominated by resolved sources, and the inclusion of the SGWB does not lead to any noticeable improvement in the precision of H₀ across its range. We also performed a spectral siren analysis of 59 resolved binary black hole sources detected during the third observing run with an inverse false alarm rate higher than 1 per year jointly with the SGWB. We find that with current sensitivities, the cosmological and population results are not impacted by the inclusion of the SGWB.