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

Abstract

We present a Bayesian analysis of the Hubble constant using Physics-Informed Neural Networks (PINNs), applied to the standard wCDM model and its dynamical extension via the Chevallier--Polarski--Linder (CPL) parametrization, with and without a free summed neutrino mass $Σm_ν$. Embedding the background Friedmann equation into a Bayesian PINN, we reconstruct $H(z)$ in a data-driven, physically consistent way while propagating epistemic uncertainty. Combining Cosmic Chronometers, DESI DR2 BAO, and Pantheon+ supernovae with Planck 2018 CMB distance priors, we quantify the Hubble tension against Planck and SH0ES (R22). For wCDM, BAO-dominated combinations favor lower $H_0$, easing the Planck tension at the cost of a larger SH0ES discrepancy. Letting the equation of state evolve within CPL shifts $H_0$ upward and consistently favors a mildly quintessence-like $w_0 \gtrsim -1$ with negative $w_a$, pointing to a slowly evolving, non-phantom dark energy component. Adding a free $Σm_ν$ stabilizes $H_0$ between $69.7$ and $71.6~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, bounds $Σm_ν\lesssim 0.16$--$0.28~\mathrm{eV}$ ($2σ$), and reduces the SH0ES tension below $1.8σ$ (down to $0.83σ$) while the Planck tension persists at $1.6$--$2.8σ$. AIC and BIC both favor CPL+$Σm_ν$ despite its extra parameters, arguing against overfitting. A full-CMB MCMC cross-check via Cobaya, including CMB lensing, reproduces the BPINN posteriors -- including the neutrino-mass bound -- within 1--2$σ$ at a fraction of the cost. A mildly evolving dark energy component combined with sub-eV neutrino masses thus substantially eases, though does not fully resolve, the Hubble tension, supporting Bayesian PINNs as an efficient, physically consistent tool for precision cosmology beyond $Λ$CDM.