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

TL;DR

This work investigates the Hubble tension by combining dynamical dark energy via the CPL parametrization with massive neutrinos in a Bayesian PINN framework. By embedding the Friedmann background into a neural network, the authors reconstruct $H(z)$ from Pantheon+, CC, and DESI DR2 BAO data, while adopting Planck distance priors to connect early- and late-time physics. The results show a mild phantom-like $w_0$ with small $w_a$, and neutrino masses allowed up to $oldsymbol{ u}$-induced limits, collectively reducing the SH0ES tension to about 0.5–2σ depending on the dataset, though Planck constraints remain challenging. The study demonstrates that late-time dynamics and neutrino physics can coherently alleviate portions of the Hubble tension within a robust, uncertainty-quantified BPINN framework, while underscoring that a full resolution likely requires additional physics or data inputs. The BPINN approach proves to be a powerful, efficient tool for precision cosmology beyond ΛCDM, offering consistent uncertainty propagation and compatibility with traditional MCMC benchmarks.

Abstract

We present a comprehensive Bayesian analysis of the Hubble constant within the framework of Physics-Informed Neural Networks (PINNs), focusing on the standard $Λ$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 $Λ$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 $Σm_ν$, yields a balanced reconciliation between early- and late-Universe determinations of $H_0$, with tension levels typically reduced to the $\sim1$-$2σ$ 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.

Figures (7)

• Figure 1: Posterior distributions of the CPL dark energy parameters ($w_0$, $w_a$) and the Hubble constant $H_0$ derived from the Bayesian Physics-Informed Neural Network (BPINN) analysis using various low-redshift datasets. The filled contours correspond to the $68\%$ and $95\%$ confidence levels, illustrating the parameter correlations and dataset-specific constraints.
• Figure 2: Comparison the Hubble constant $H_0$ derived from the Bayesian Physics-Informed Neural Network (BPINN) analysis using various low-redshift datasets with Planck 2018 and R22.
• Figure 3: Corner plot of the CPL+$\Sigma m_\nu$ posterior distributions obtained from the Bayesian Physics-Informed Neural Network (BPINN) analysis. The filled contours correspond to the $68\%$ and $95\%$ confidence levels, showing the correlations between $H_0$, $\Omega_m$, $w_0$, $w_a$, and the sum of neutrino masses $\Sigma m_\nu$.
• Figure 4: Comparison the Hubble constant $H_0$ derived from the Bayesian Physics-Informed Neural Network (BPINN) analysis using various low-redshift datasets with Planck 2018 and R22.
• Figure 5: Corner plot of the $\Lambda$CDM posterior distributions obtained from the Bayesian Physics-Informed Neural Network (BPINN) analysis for different low-redshift datasets. The filled contours correspond to the $68\%$ and $95\%$ confidence levels. Each color represents a different dataset or combination of datasets as indicated in the legend.