Exploring Hubble Tension Alleviation through Neutrino-Coupled Perturbed $f(R)$ Gravity

This work examines the Hubble constant ($H_0$) tension within the frameworks of perturbed $f(R)$ gravity and perturbed $f(R)$ gravity coupled with neutrinos, using lastest observational data. The datasets incorporate the Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), Cosmic Chronometers (CC), lensing, and Pantheon supernovae. We compare the ability of these models to bridge the discrepancy between Planck 2018 ($H_0 = 67.4 \pm 0.5 \ \text{km/s/Mpc}$) and the local R22 measurement ($H_0 = 73.5 \pm 1.04 \ \text{km/s/Mpc}$). In perturbed $f(R)$ gravity, the derived $H_0$ values align closely with Planck, leaving a substantial tension with R22. The inclusion of neutrino interactions introduces additional parameters that shift $H_0$ toward higher values, reducing the tension with local measurements. Notably, the coupled model achieves a smaller residual tension compared to the standalone perturbed $f(R)$ model, indicating that neutrino physics plays a significant role in modifying the late-time expansion dynamics. While both models provide insights into addressing the Hubble tension, the coupled $f(R)$ gravity with neutrinos offers a more consistent alignment across the datasets.