Integral F(R) gravity and saddle point condition as a remedy for the H0-tension
Shin’ichi Nojiri, Sergei D. Odintsov, V. K. Oikonomou
Abstract
In this work, we shall provide an F(R) gravity theoretical framework for solving the H0-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 H0-tension is alleviated. The condition that remedies the H0-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 H0-tension is based on the existence of a metastable de Sitter point that occurs for redshifts near the recombination. This metastable de Sitter vacuum restricts the functional form of the F(R) gravity in the Jordan frame. We also show that by appropriately choosing the F(R) gravity, along with the theoretical solution offered for the H0-tension problem, one may also provide a unified description of the inflationary era with the late-time accelerating era, in terms of two extra de Sitter vacua. We propose a new approach to F(R) gravity by introducing a new class of integral F(R) gravity functions, which may be wider than the usual class expressed in terms of elementary F(R) gravity functions. Finally, the Einstein frame inflationary dynamics formalism is briefly discussed.