CosmoPyro: Gradients for Gravitational-Wave Cosmology

Abstract: Gravitational-wave (GW) observations of stellar-mass compact binary coalescences directly measure the source luminosity distance. Combined with the source redshift, these measurements constrain the current expansion rate of the Universe, the Hubble constant, $H_0$, or $$h=H_0 / [100 \,{\rm km \,s^{-1} \, Mpc<sup>{-1}}]$$. For most GW signals no electromagnetic redshift measurement is expected, but the GW signal itself depends on the redshifted (detector-frame) masses. Assuming a source-frame mass distribution therefore enables a redshift estimate for each source. Combining the redshift estimates with the distance measurements provides a weak constraint on $H_0$ for each individual source that tightens with the number of sources in the catalog. However, the shape of the source-frame mass distribution is not known a priori, and previous work has relied on parametric models (piecewise power-laws with Gaussian components), and one-dimensional Gaussian processes. Here, we introduce CosmoPyro, a fully differentiable hierarchical Bayesian inference code that models the mass distribution using either one- or two-dimensional Gaussian processes. With the latest GW transient catalog (GWTC-5) we find $h = 0.66<sup>{+0.17}_{-0.20}$ and $h = 0.57<sup>{+0.20}_{-0.15}$ (median with $1σ$ uncertainty), for the one- and two-dimensional case, respectively. Despite the noticeably different inferred mass distributions, both models yield $H_0$ values consistent with the latest LVK measurements within $1 σ$. While our main results marginalize over the Gaussian-process power-spectrum hyperparameters, the measurement is also robust against fixing these hyperparameters over a range comparable to their measured uncertainty.