Cosmological Constraints on $f(G)$ Dark Energy Models

TL;DR

This paper analyzes $f(G)$ modified gravity models with the Gauss-Bonnet term, deriving conditions for their cosmological viability, identifying stable accelerated solutions, and exploring toy models that mimic standard cosmology with late-time deviations.

Contribution

It provides a phase space analysis of $f(G)$ models, establishing geometric viability conditions and identifying stable accelerated solutions, including de Sitter and phantom-like states.

Findings

Existence of stable de Sitter and phantom solutions.

Conditions for cosmological viability based on derivatives of $f(G)$.

Toy models that replicate $\Lambda$CDM during early epochs with distinctive late-time behavior.

Abstract

Modified gravity theories with the Gauss-Bonnet term $G=R^2-4R^{\mu\nu}R_{\mu\nu}+R^{\mu\nu\rho\sigma}R_{\mu\nu\rho\sigma}$ have recently gained a lot of attention as a possible explanation of dark energy. We perform a thorough phase space analysis on the so-called $f(G)$ models, where $f(G)$ is some general function of the Gauss-Bonnet term, and derive conditions for the cosmological viability of $f(G)$ dark energy models. Following the $f(R)$ case, we show that these conditions can be nicely presented as geometrical constraints on the derivatives of $f(G)$. We find that for general $f(G)$ models there are two kinds of stable accelerated solutions, a de Sitter solution and a phantom-like solution. They co-exist with each other and which solution the universe evolves to depends on the initial conditions. Finally, several toy models of $f(G)$ dark energy are explored. Cosmologically viable trajectories that mimic the $\Lambda$CDM model in the radiation and matter dominated periods, but have distinctive signatures at late times, are obtained.