Globally Stable Dark Energy in $F(R)$ Gravity

TL;DR

This paper introduces a new $F(R)$ gravity model with globally positive derivatives to ensure stability, unifying early and late cosmic acceleration while passing local gravity tests.

Contribution

It develops a novel $F(R)$ model with globally positive derivatives, ensuring stability across all Ricci scalars, and extends previous models to better explain cosmic acceleration.

Findings

Model achieves global stability with positive derivatives.

Successfully explains cosmic acceleration.

Passes local gravity tests.

Abstract

$F(R)$ models for dark energy generally exhibit a weak curvature singularity, which can be cured by adding an $R^2$ term. This correction allows for a unified description of primordial and late-time accelerated expansions. However, most existing models struggle to achieve this, as they become unstable over certain negative ranges of the Ricci scalar, where either the first or second derivative of $F(R)$ turns negative. These instabilities may disrupt the post-inflationary evolution when the Ricci scalar oscillates about the vacuum state after the $R^2$ inflation. In this work, we introduce a new model-building to guarantee global stability, i.e., the first and second derivatives are positive for all real Ricci scalars. By extending the idea from Appleby and Battye, we demonstrate that viable models can be constructed by imposing a positive, bounded first derivative of $F(R)$ with a sigmoid shape. As examples, we first reformulate and generalize the original Appleby-Battye model. Then, we propose a new dark energy model, which successfully explains the acceleration of cosmic expansion and passes local gravity tests.