The phase-space of generalized Gauss-Bonnet dark energy

TL;DR

This paper analyzes the phase space of generalized Gauss-Bonnet gravity models to identify conditions for stable de-Sitter solutions, revealing critical curves and attractors relevant for dark energy explanations.

Contribution

It investigates the stability conditions of de-Sitter solutions in F(R,G) gravity by analyzing the R-H phase space, highlighting the existence of critical curves and multiple attractors.

Findings

Existence of stable de-Sitter attractors in F(R,G) models.

Identification of critical curves R=12H^2 as attractors.

Numerical examples illustrating stability conditions.

Abstract

The generalized Gauss-Bonnet theory, introduced by Lagrangian F(R,G), has been considered as a general modified gravity for explanation of the dark energy. G is the Gauss-Bonnet invariant. For this model, we seek the situations under which the late-time behavior of the theory is the de-Sitter space-time. This is done by studying the two dimensional phase space of this theory, i.e. the R-H plane. By obtaining the conditions under which the de-Sitter space-time is the stable attractor of this theory, several aspects of this problem have been investigated. It has been shown that there exist at least two classes of stable attractors : the singularities of the F(R,G), and the cases in which the model has a critical curve, instead of critical points. This curve is R=12H^2 in R-H plane. Several examples, including their numerical calculations, have been discussed.