Neutrino interactions with perturbed Rastall gravity: A novel approach to reducing the Hubble tension

Abstract

In this paper, we investigate the cosmological implications of coupling neutrinos to perturbed Rastall gravity, focusing on its impact on the Hubble constant ([Formula: see text]) and the associated tension between early- and late-universe measurements with Markov Chain Monte Carlo (MCMC) and Physics-Informed Neural Network (PINN) method. Utilizing observational data from the Cosmic Microwave Background (CMB), Cosmic Chronometers (CC), Baryon Acoustic Oscillations (BAO) and the Pantheon+ Type Ia supernovae, CMB Lensing, we perform a detailed statistical analysis. Our findings demonstrate that the Rastall model provides an improved fit to the data compared to the standard [Formula: see text]CDM model, as indicated by lower Akaike Information Criterion (AIC) values in both early and late-universe regimes. The model introduces a deviation parameter [Formula: see text], which remains consistent with existing literature and differs across epochs, supporting a dynamic gravitational framework. Combining all datasets, the Rastall model yields [Formula: see text][Formula: see text]km, s[Formula: see text], Mpc[Formula: see text], significantly reducing the tension with Planck ([Formula: see text]) and SH0ES ([Formula: see text]) compared to the [Formula: see text] discrepancy in [Formula: see text]CDM. Additional dataset combinations confirm this alleviation, with Planck tensions consistently below [Formula: see text]. Overall, our results highlight Rastall gravity with neutrino coupling as a promising alternative to [Formula: see text]CDM, capable of addressing current cosmological tensions while aligning with observational data.