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

TL;DR

This paper explores how $f(R)$ modified gravity models can produce a redshift-dependent effective Hubble constant, potentially resolving the tension between different cosmological measurements of $H_0$ by mimicking dark energy effects.

Contribution

It introduces a scalar field in $f(R)$ gravity that causes an effective, redshift-dependent Hubble constant, offering a new approach to address the Hubble tension.

Findings

The $f(R)$ model can mimic dark energy effects.

The effective Hubble constant decreases with redshift.

Results align with recent cosmological data.

Abstract

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. Our results align with recent cosmological data analysis in redshift bins, indicating a decreasing trend of the Hubble constant. The redshift dependence of $H_{0}^{\text{eff}}(z)$ might potentially reconcile measurements of the Hubble constant from probes at different redshifts.