Can f(R) gravity relieve H0 and σ8 tensions?

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.