Mind the peak: improving cosmological constraints from GWTC-4.0 spectral sirens using semiparametric mass models

Gravitational wave spectral sirens can provide cosmological constraints by using the shape of the binary black hole (BBH) mass distribution (MD). However, the precision and accuracy of these constraints depends critically on the capturing all the MD features. In this work, we analyze 137 BBH events from the latest GWTC-4.0 with a novel data-driven semiparametric approach based on \textsc{Bspline} that adaptively places knots around the most informative structures in the MD, while keeping the dimensionality of the parameter space moderate. Our flexible models resolve three distinct peaks at $\sim10$, $18$, and $33\,\mathrm{M}_\odot$ and are statistically preferred over standard parametric models, with Bayes factors up to 226. Because these features are correlated with $H_0$, the semiparametric model yields, under different prior assumptions, 12%-21% improvement in the precision of $H_0$ relative to parametric models, providing $H_0 = 57.8^{+21.9}_{-20.6}\,\mathrm{km/s/Mpc}$ in the best case. Our results demonstrate that capturing the full complexity of the BBH mass distribution is essential for realizing the cosmological potential of spectral sirens as gravitational wave catalogs continue to grow.