On the Stability of a class of Modified Gravitational Models

TL;DR

This paper investigates the stability of modified gravitational models, including $f(R)$ and generalized Gauss-Bonnet types, in a cosmological setting, providing conditions for stability around de Sitter solutions.

Contribution

It introduces a stability condition for a broad class of modified gravity models, extending previous $f(R)$ analysis to include $F(R,G,Q)$ models and higher order invariants.

Findings

Derived stability conditions for $f(R)$ models.

Extended stability analysis to $F(R,G,Q)$ models.

Discussed potential for higher order invariants.

Abstract

Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting are investigated. Specifically, after revisiting the $f(R)$ case, $R$ being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized Gauss-Bonnet type $F(R,G,Q)$, $G$ and $Q$ being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is mentioned.