Can f(R) gravity relieve $$H_0$$ H 0 and $$\sigma _8$$ σ 8 tensions?

Abstract

Abstract To investigate whether f(R) gravity can relieve current $$H_0$$ H 0 and $$\sigma _8$$ 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 $$H_0$$ H 0 and $$\sigma _8$$ σ 8 tensions, and that its two typical parameters $$\log _{10}f_{R0}$$ 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 $$\log _{10}f_{R0}<-6.75$$ log 10 f R 0 < - 6.75 at the $$2\sigma $$ 2 σ confidence level.