Analyzing the $H_0$ tension in $F(R)$ gravity models
  The Hubble constant tension problem is analysed in the framework of a class
of modified gravity, the so-called $F(R)$ gravity. To do so, we explore two
models: an exponential and a power-law $F(R)$ gravities, which includes an
early dark energy (EDE) term in the latter. These models can describe both an
early time inflationary epoch and the late time accelerating expansion of the
universe. We confront both models with recent observational data including the
Pantheon Type Ia supernovae sample, the latest measurements of the Hubble
parameter $H(z)$ from differential ages of galaxies (cosmic chronometers) and
separately from baryon acoustic oscillations. Standard rulers data set from the
Cosmic Microwave Background radiation are also included in our analysis. The
estimations of the Hubble constant appear to be essentially depending on the
set of observational data and vary in the range from 68 to 70{.}3
km\,/(s$\cdot$Mpc). The fits of the other free parameters of the models are
also obtained, revealing interesting consequences.
