Can $f(R)$ gravity relieve $H_0$ and ${\sigma }_8$ 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.

arXiv comment9 pages, 7 figures. Accepted in EPJC

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