Perturbed f(R) gravity coupled with neutrinos: Exploring cosmological implications

We conduct a thorough examination of cosmological parameters within the context of perturbed $f\left(R\right)$ gravity coupled with neutrinos, using a diverse array of observational datasets, including Cosmic Microwave Background (CMB), Cosmic Chronometers (CC), Baryon Acoustic Oscillations (BAO), and Pantheon supernova and Lensing data. Our analysis unveils compelling constraints on cosmological parameters such as the sum of neutrino masses ($\sum m_{\nu }$), sound speed ($c_s$), Jean’s wavenumbers ($k_J$), redshift of non-relativistic matter ($z_{\mathrm{nr}}$) and redshift of Deceleration-Acceleration phase transition ($z_{\mathrm{DA}}$). In our model the interaction strength parameter ($\Gamma$) coming from incorporation of neutrinos with the perturbed $f\left(R\right)$ gravity as a key factor significantly influencing cosmic evolution, shaping the formation of large-scale structures and the dynamics of cosmic expansion. Our study also addresses the Hubble tension problem by providing $H_0$ measurements that are in agreement with the existing research.