Non-Parametric Reconstruction of the Hubble Parameter from the Fourth Gravitational Wave Transient Catalog and DESI Baryonic Acoustic Oscillations

Abstract The release of the fourth Gravitational-Wave Transient Catalog (GWTC-4.0) by the LIGO-Virgo-KAGRA collaboration includes more than 200 compact binary coalescence (CBC) candidates that can be used to probe the cosmic expansion. The population of merging binary black holes has been used so far to provide a constraint on the Hubble constant and dark matter fraction under the hypothesis of a flat-Λ-Cold-Dark-Matter Universe. In this work, we provide the first non-parametric constrain on the Hubble parameter from 137 dark sirens reported in GWTC-4.0. We employ the relation between detector and source frame masses for detected GW signals, to obtain a statistical redshift evaluation for the population of binary black holes (BBHs). We model the Hubble parameter as a non-parametric autoregressive process in terms of the scale factor, using splines. In addition, we introduce two novel features: the use of anchor points for H(z) derived from an external probe -here, Baryon Acoustic Oscillations (BAOs) -and a constraining power coefficient that quantifies where the inference is most data-driven by GW detections. We highlight three key findings: (i) using GWs alone, the Hubble parameter determination is the most GW-data-driven around redshift z = 0.44, yielding to H(0.44) = 92.3 +29.9-36.6 kms -1 Mpc -1 . Its value at z = 0, the Hubble constant, is therefore less constrained by the GW data. (ii) The Hubble parameter inferred from analyses assuming a flat-ΛCDM cosmological model is strongly affected by the cosmological model assumption. (iii) Introducing an anchor point for H(z) enhances the inferred constraints and provides a clear visualization of the redshift range where GWs contribute most to the constraining power.