Secondary-Mass Features improve Spectral-Siren $H_0$ Constraints

Gravitational-wave (GW) signals from compact binary coalescences (CBCs) enable independent measurements of the Hubble constant $H_0$ via the spectral siren method, which critically depends on an accurate model of the source-frame mass distribution. While the primary mass function has been extensively studied, the impact of the secondary mass distribution on cosmological inference has been largely overlooked. Here, we perform a joint inference of population and cosmological parameters using 142 confident CBC detections from GWTC-4.0, adopting a new parametric model that flexibly describes features in both the component-mass spectrum and the pairing function, with particular emphasis on the secondary masses. We find $H_0=71.4_{-13.4}^{+13.8}\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$ (68% CL) from spectral sirens alone, and $H_0=73.5_{-7.2}^{+9.2}\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$ when combined with the bright siren GW170817. Compared to the standard LVK Fullpop-4.0 analysis, these constraints represent improvements of $\sim 29.8\mathrm{\%}$ and $\sim 22.2\mathrm{\%}$ in $H_0$ uncertainty, respectively. The enhanced precision is driven by previously unmodeled features, including peaks near $18M_{\odot }$ and $65M_{\odot }$ as well as mass-dependent pairing transitions at $28M_{\odot }$ and $52M_{\odot }$. Our results demonstrate that the secondary mass function is also a key ingredient for precision standard siren cosmology.