Neutrino Interactions with perturbed Rastall Gravity: A Novel Approach to Reducing the Hubble Tension

Abstract

We investigate the cosmological implications of coupling neutrinos to perturbed Rastall gravity, focusing on its impact on the Hubble constant ($H_0$) and the associated tension between early- and late-universe measurements with MCMC and 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 $\Lambda$CDM model, as indicated by lower Akaike Information Criterion (AIC) values in both early and late-universe regimes. The model introduces a deviation parameter $\alpha$, which remains consistent with existing literature and differs across epochs, supporting a dynamic gravitational framework. Combining all datasets, the Rastall model yields $H_0 = 70.23 \pm 2.01$ km,s$^{-1}$,Mpc$^{-1}$, significantly reducing the tension with Planck ($1.34\sigma$) and SH0ES ($1.16\sigma$) compared to the $\sim 4\sigma$ discrepancy in $\Lambda$CDM. Additional dataset combinations confirm this alleviation, with Planck tensions consistently below $1.6\sigma$. Overall, our results highlight Rastall gravity with neutrino coupling as a promising alternative to $\Lambda$CDM, capable of addressing current cosmological tensions while aligning with observational data, it can be concluded that the Hubble tension may be resolved.