Late-Time Resolution of the Hubble Tension in CPL Cosmology with Massive Neutrinos via Bayesian Physics-Informed Neural Networks

Abstract

We present a comprehensive Bayesian analysis of the Hubble constant within the framework of Physics-Informed Neural Networks (PINNs), focusing on the standard $\Lambda$CDM model and its dynamical dark energy extensions described by the Chevallier-Polarski-Linder (CPL) parametrization, both with and without massive neutrinos. By embedding the cosmological background equations directly into a Bayesian PINN architecture, we reconstruct the Hubble expansion history $H(z)$ in a data-driven yet physically consistent manner, while rigorously propagating epistemic uncertainties. Our analysis combines late-time observational probes, including Cosmic Chronometers, Baryon Acoustic Oscillations (BAO DESI DR2), and the Pantheon supernova sample, and quantifies the resulting tension in the inferred Hubble constant with respect to Planck 2018 Cosmic Microwave Background constraints and the SH0ES (R22) local distance ladder measurement. Within $\Lambda$CDM, we find that data combinations involving BAO tend to favor lower values of $H_0$, alleviating the tension with Planck at the expense of increased disagreement with SH0ES. Allowing for a time-evolving dark energy equation of state in the CPL framework systematically shifts the posterior of $H_0$ toward higher values, leading to a notable reduction of the SH0ES tension, particularly for combinations including supernova data. The most flexible scenario, CPL with a free total neutrino mass $\Sigma m_\nu$, yields a balanced reconciliation between early- and late-Universe determinations of $H_0$, with tension levels typically reduced to the $\sim1$-$2\sigma$ range relative to both Planck and SH0ES. Our results highlight the nontrivial interplay between dark energy dynamics and neutrino mass in addressing the Hubble tension and demonstrate the efficacy of Bayesian PINNs as a robust and versatile tool for precision cosmology beyond the standard paradigm.