A Bayesian PINN Framework for Barrow-Tsallis Holographic Dark Energy with Neutrinos: Toward a Resolution of the Hubble Tension

TL;DR

This paper applies a Bayesian Physics-Informed Neural Network framework to constrain the Barrow-Tsallis Holographic Dark Energy model using diverse cosmological data, achieving tighter parameter bounds and alleviating the Hubble tension.

Contribution

It introduces a novel Bayesian PINN approach for cosmological parameter estimation, providing more precise constraints than traditional MCMC methods and demonstrating its effectiveness in addressing the Hubble tension.

Findings

Bayesian PINN yields more precise parameter constraints than MCMC.

Hubble constant estimates lie between Planck 2018 and SH0ES values, reducing tension.

Tighter bounds on neutrino mass and consistent results across datasets.

Abstract

We investigate the Barrow-Tsallis Holographic Dark Energy (BTHDE) model using both traditional Markov Chain Monte Carlo (MCMC) methods and a Bayesian Physics-Informed Neural Network (PINN) framework, employing a range of cosmological observations. Our analysis incorporates data from Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), CMB lensing, Cosmic Chronometers (CC), and the Pantheon+ Type Ia supernova compilation. We focus on constraining the Hubble constant $ H_0 $, the nonextensive entropy index $ q $, the Barrow exponent $ \Delta $, and the Granda-Oliveros parameters $ \alpha $ and $ \beta $, along with the total neutrino mass $ \Sigma m_\nu $. The Bayesian PINN approach yields more precise constraints than MCMC, particularly for $ \beta $, and tighter upper bounds on $ \Sigma m_\nu $. The inferred values of $ H_0 $ from both methods lie between those from Planck 2018 and SH$_0$ES (R22), alleviating the Hubble tension to within $ 1.3\sigma $-$2.1\sigma $ depending on the dataset combination. Notably, the Bayesian PINN achieves consistent results across CC and Pantheon+ datasets, while maintaining physical consistency via embedded differential constraints. The combination of CMB and late-time probes leads to the most stringent constraints, with $ \Sigma m_\nu < 0.114 $ eV and $ H_0 = 70.6 \pm 1.35 $ km/s/Mpc. These findings suggest that the BTHDE model provides a viable framework for addressing cosmological tensions and probing modified entropy scenarios, while highlighting the complementary strengths of machine learning and traditional Bayesian inference in cosmological modeling.