Spectral sirens cosmology from binary black holes populations with sharper mass features

Spectral-sirens inference enables the extraction of cosmological parameters from gravitational-wave data alone, without electromagnetic counterparts or galaxy catalogs. We introduce new parametric mass functions for the binary black hole population that capture significant structure across the mass spectrum and are moderately favoured by Bayesian evidence over simpler models. Analysing the latest gravitational-wave transient catalog, GWTC-4.0, we show that powerlaws-only population models constrain the Hubble constant to $23%$ precision, $H_0 = 53.3^{+14.0}_{-10.8} ~\rm km ,s^{-1} ,Mpc^{-1}$ at $68%$ confidence level. This represents a $\sim 50%$ improvement over the corresponding binary black hole-only analysis by the LIGO-Virgo-KAGRA collaboration, achieving precision comparable to their joint analyses including neutron stars and galaxy catalogs. We further test alternative cosmological models, establishing competitive constraints on modified gravitational-wave propagation, while bounds on the dark energy equation-of-state parameters remain uninformative. Projecting to future O5 observing run, we forecast substantial improvements in $H_0$ and modified propagation parameters with larger datasets at higher redshifts. Our results highlight the strong interplay between the black hole mass distribution and inferred cosmology, underscoring the need for suitable population models to fully exploit gravitational-wave data.

💡 Research Summary

This paper presents a state‑of‑the‑art analysis of “spectral‑sirens” cosmology using only gravitational‑wave (GW) data, without any electromagnetic (EM) counterparts or galaxy‑catalog redshift information. The authors introduce two new parametric models for the binary black‑hole (BBH) primary‑mass distribution—named 3sPL (three‑component smooth power‑law) and 4sPL (four‑component smooth power‑law). Each model is a linear combination of three or four truncated power‑law components that are tapered at low mass, allowing very steep slopes (up to ~200) to capture sharp features observed in the BBH mass spectrum around ~10 M⊙ and ~35 M⊙, as well as additional low‑ and high‑mass structure reported in recent literature. For comparison they retain the previously used “smooth power‑law + two Gaussians” (sPL2G) model.

The hierarchical Bayesian framework follows the standard formulation: the joint posterior on population parameters Λ (including mass‑distribution hyper‑parameters, merger‑rate evolution ψ(z), and cosmology) is proportional to the prior times the product over events of the likelihood integrated over the individual‑event posterior samples, corrected for selection effects via injection campaigns. The authors use the icarogw package for the hierarchical likelihood, the nessai nested‑sampling engine (augmented with normalising flows), and the bilby infrastructure for GW parameter estimation. They employ 3 × 10³ posterior samples per event and 10⁶–5 × 10⁷ injection samples to evaluate the selection integrals, ensuring numerical stability (see Appendix D).

Population modeling details:

• Primary‑mass distribution p(m₁|Λ) is given by either 3sPL, 4sPL, or sPL2G. The former two have 14 and 19 hyper‑parameters respectively, while sPL2G has 10.
• Mass‑ratio distribution p(q|Λ) is a truncated Gaussian on