Evolution of an effective Hubble constant in $f$ modified gravity

We investigate the Hubble constant tension within f(R) modified gravity in the Jordan frame, focusing on its application to the dynamics of an isotropic Universe. A scalar field, non-minimally coupled to the metric, provides an extra degree of freedom compared to General Relativity. We analyze the impact of such a scalar field on the cosmic expansion, leading to an effective Hubble constant Heff 0 (z), dependent on redshift z. We show that our f(R) model might mimic dark energy and provide an apparent variation of the Hubble constant. Our results align with recent cosmological data analysis in redshift bins, indicating a decreasing trend of the Hubble constant. The redshift dependence of Heff 0 (z) might potentially reconcile measurements of the Hubble constant from probes at different redshifts.