Can $f(R)$ gravity relieve $H_0$ and $\sigma_8$ tensions?

TL;DR

This study tests whether Hu-Sawicki $f(R)$ gravity can resolve the discrepancies in $H_0$ and $\sigma_8$ measurements, finding it ineffective in alleviating these tensions with current observational data.

Contribution

It provides the first comprehensive constraint on Hu-Sawicki $f(R)$ gravity using combined cosmological observations, showing it cannot resolve existing tensions.

Findings

Hu-Sawicki $f(R)$ gravity does not relieve $H_0$ and $\sigma_8$ tensions.

Model parameters are insensitive to other cosmological parameters.

Best constraint: $\log_{10}f_{R0} < -6.75$ at 2$\sigma$ confidence.

Abstract

To investigate whether $f(R)$ gravity can relieve current $H_0$ and $\sigma_8$ tensions, we constrain the Hu-Sawicki $f(R)$ gravity with Planck-2018 cosmic microwave background and redshift space distortions observations. We find that this model fails to relieve both $H_0$ and $\sigma_8$ tensions, and that its two typical parameters $\log_{10}f_{R0}$ and $n$ are insensitive to other cosmological parameters. Combining the cosmic microwave background, baryon acoustic oscillations, Type Ia supernovae, cosmic chronometers with redshift space distortions observations, we give our best constraint $\log_{10}f_{R0}<-6.75$ at the $2\sigma$ confidence level.