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

Abstract

To investigate whether f(R) gravity can relieve current H and σ8 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 and σ8 tensions, and that its two typical parameters log 10fR 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 10fR< - 6.75 at the 2 σ confidence level.