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

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.