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

¹ Dipartimento di Fisica e Astronomia “Augusto Righi”–Università di Bologna, via Piero Gobetti 93/2, I-40129 Bologna, Italy
² INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via Piero Gobetti 93/3, I-40129 Bologna, Italy
³ INFN – Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 23 December 2025
Accepted: 20 April 2026

Abstract

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 depend critically on the capturing all the MD features. In this work, we analyzed 137 BBH events from the latest GWTC-4.0 with a novel data-driven semiparametric approach based on 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 resolved three distinct peaks at ∼10, 18, and 33 M_⊙ and are statistically preferred over standard parametric models, with Bayes factors up to 226. Because these features are correlated with H₀, the semiparametric model yielded, under different prior assumptions, 12%–21% improvement in the precision of H₀ relative to parametric models, providing H₀ = 57.8^+21.9_−20.6 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.