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

To investigate whether f ( R ) gravity can relieve current H 0 and σ 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 σ 8 tensions, and that its two typical parameters log 10 f R 0 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 R 0 < - 6.75 at the 2 σ confidence level.