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

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

2009-03-26

arxiv.org/abs/0903.4610v3

JCAP 0907:009,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 3 figures; typos corrected

Scientific paper

10.1088/1475-7516/2009/07/009

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.

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