Probing the Mass--Redshift Dependence of Binary Black Holes and its Implications for H 0 with GWTC-5.0

The mass and redshift distributions of merging binary black holes (BBHs) bear imprints of their astrophysical formation channels. Whether the BH mass distribution evolves with redshift, however, remains an open question. In this paper, we employ copula functions, which describe the dependence between variables independently of their marginal distributions, to probe the dependence structure between the primary mass and the redshift of BBH mergers. We construct five population models by coupling the marginal distributions of primary mass and redshift with the Gaussian copula, the Clayton copula, or one of its three rotations, and we constrain their hyperparameters using 235 BBH events from GWTC-5.0. For comparison, we also adopt a baseline model in which the primary mass and redshift are assumed independent. Among the copula-based models, only the model with the 180 rotated Clayton copula, which couples higher primary masses preferentially with high redshifts, exhibits evidence for a nonzero correlation, with its copula parameter deviating from the independence limit at more than 1σ significance. Importantly, the constraints on the Hubble constant (H 0) derived from these models are mutually consistent within the 68% confidence level; the baseline model yields H 0=74.3+13.7-19.6 km s-1 Mpc-1, indicating that allowing for a mass--redshift dependence does not significantly bias the H 0 inference with the current dataset. Bayesian model comparison favors the baseline model over all copula-based alternatives, with log-Bayes factors corresponding to weak to moderate evidence against the latter on the Jeffreys scale. Our results thus imply that the current GWTC-5.0 sample remains consistent with no redshift evolution of the primary mass distribution over the redshift range probed.