Cosmological constraints on f(G) dark energy models

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.