Integral $F(R)$ Gravity and Saddle Point Condition as a Remedy for the $H_0$-tension

Understand

In this work, we shall provide an $F(R)$ gravity theoretical framework for solving the $H_0$-tension.

• Specifically, by exploiting the $F(R)$ gravity correspondence with a scalar-tensor theory, we shall provide a condition in which when it is satisfied, the $H_0$-tension is alleviated.
• The condition that remedies the $H_0$-tension restricts the corresponding $F(R)$ gravity, and we present in brief the theoretical features of the constrained $F(R)$ gravity theory in both the Jordan and Einstein frames.
• The condition that may remedy the $H_0$-tension is based on the existence of a metastable de Sitter point that occurs for redshifts near the recombination.