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

TL;DR

This paper proposes a specific $F(R)$ gravity framework with a metastable de Sitter point near recombination to address the $H_0$-tension, unifying early and late cosmic acceleration phases.

Contribution

It introduces a new integral form of $F(R)$ gravity and derives conditions for alleviating the $H_0$-tension via a metastable de Sitter vacuum.

Findings

A condition on $F(R)$ that alleviates $H_0$-tension.

A constrained form of $F(R)$ gravity in Jordan and Einstein frames.

A unified description of inflation and late-time acceleration.

Abstract

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. 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 $H_0$-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.