Towards a Machine Learning Solution for Hubble Tension: Physics-Informed Neural Network (PINN) Analysis of Tsallis Holographic Dark Energy in Presence of Neutrinos

Abstract

We present a Physics-Informed Neural Network (PINN) framework for reconstructing the redshift-dependent Hubble parameter \(H(z)\) within the Tsallis Holographic Dark Energy (THDE) model extended by massive neutrinos. In this approach, the modified Friedmann equation is incorporated into the neural network loss function, enabling training on Cosmic Chronometers data up to \(z \leq 2\). The framework allows for the simultaneous estimation of the Hubble constant \(H_0\), the neutrino density parameter \(Ω_ν\), and the Tsallis non-extensivity index \(δ\). Uncertainty quantification is performed through dropout simulations, resulting in statistically consistent \(1σ\) confidence bands. Our results show that the THDE+$\nu$ model, reconstructed via PINN, alleviates the statistical Hubble tension from the canonical \(\sim 5σ\) level down to a range of \(0.5σ\leq T \leq 2.2σ\), depending on the redshift sampling. Additionally, we constrain the total neutrino mass to \(Σm_ν< 0.11\,\text{eV}\). A detailed comparison with the traditional Markov Chain Monte Carlo (MCMC) analysis demonstrates the consistency of both methods, while highlighting the competitiveness of the PINN-based THDE framework as a robust, data-driven approach for non-parametric cosmological inference within generalized thermodynamics.

32 pages, 9 figures

References in corpus (21)

• Dynamics of dark energy
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM
• Planck evidence for a closed Universe and a possible crisis for cosmology
• The 1% Concordance Hubble Constant
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Baryon acoustic oscillations with Lyman-$\alpha$ forests
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1
• Inferring solutions of differential equations using noisy multi-fidelity data
• The new form of the equation of state for dark energy fluid and accelerating universe
• Neutrino mass from Cosmology
• Dynamical vacuum energy, holographic quintom, and the reconstruction of scalar-field dark energy
• Modified cosmology from extended entropy with varying exponent
• Instability of holographic dark energy models
• Interacting holographic dark energy in Brans-Dicke theory
• Interacting agegraphic dark energy models in non-flat universe
• Holographic dark energy in the DGP braneworld with GO cutoff
• Correspondence between entropy-corrected holographic and Gauss-Bonnet dark energy models
• $H_0=69.8\pm 1.3$ $\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, ${\Omega }_{m0}=0.288\pm 0.017$, and other constraints from lower-redshift, non-CMB, expansion-rate data
• Reconstructing interacting entropy-corrected holographic scalar field models of dark energy in non-flat universe
• Polarized image of a rotating black hole in Scalar-Tensor-Vector-Gravity theory