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

TL;DR

This work advances spectral-siren cosmology by introducing a data-driven semiparametric BSpline model to reconstruct the BBH primary-mass distribution from GWTC-4.0. By adaptively placing knots where the mass distribution exhibits informative features, the authors uncover three substructures in $p(m_1)$ that are missed by traditional parametric templates, leading to substantially tighter $H_0$ constraints. Across Bayes factors and DIC, the flexible SP models deliver improved cosmological inferences, with notable gains of ~12–21% in $H_0$ precision. The study demonstrates the crucial role of accurately modeling the full MD complexity to maximize the cosmological potential of spectral sirens as GW catalogs expand.

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 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.

Figures (5)

• Figure 1: Mean observed source-frame primary MD for different $H_0$ values (top) and its log-derivative (bottom) used to determine knot positions (dots) at different thresholds (dashed lines). Green points are knots for the pls-log-14 model.
• Figure 2: Median of the PPD of the primary mass and $H_0$ posterior derived from GWTC-4.0 using different models. Top: Results for the 14 data-driven knots (pls-dd-14) with varying prior widths ($\sigma$) on the spline coefficients. Bottom: the data-driven knot sets with different knot counts $N$ (red curves), alongside the logarithmic case (pls-log-14-$\mathcal{G}_2$; green curve), all using $\sigma = 2$.
• Figure 3: Spearman correlation coefficients between $H_0$ and the parameters of $p(m_1)$ (medians in black).
• Figure 4: Posterior predictive check for all the models tested in this work. In darker colors are shown the observed cumulative distribution of the BBH population, while in lighter colors the predicted one, given the considered models (reported at the top of each panel). Solid black lines are the medians of the predicted CDFs of $m_1$.
• Figure 5: Median and 68% confidence interval of the PPD for the primary mass for each model. We compare these results with those found using another weakly-parametrized approach by LIGOScientific:2025pvj (black dashed line).