Evolution of an effective Hubble constant in $f(R)$ modified gravity

Understand

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 $H_{0}^{\text{eff}}(z)$, dependent on redshift $z$.
• We show that our $f(R)$ model might mimic dark energy and provide an apparent variation of the Hubble constant.