Cosmological constraints on f(G) dark energy models

Modified gravity theories with the Gauss-Bonnet term G = R²−4R^μνR_μν+R^μνρσR_μνρσ 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 ΛCDM model in the radiation and matter dominated periods, but have distinctive signatures at late times, are obtained.