Cosmology of modified Gauss-Bonnet gravity

We consider the cosmology where some function f (G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations are derived with a method which could also be applied to general f (R, R^abR₀₁, R^abcdR₀₁₂₃) gravitational theories. It is pointed out that, despite their fourth-order character, such f (G) gravity models generally cannot reproduce arbitrary background cosmic evolutions; for example, the standard paradigm with ₃₄=0. 76 cannot be realized in f (G) gravity theories unless f is a true cosmological constant because it imposes exclusionary constraints on the form of f (G). We analyze the perturbation equations and find that, as in the f (R) model, the stability of early-time perturbation growth puts some constraints on the functional form of f (G), in this case ^2f/G^2<0. Furthermore, the stability of small-scale perturbations also requires that f not deviate significantly from a constant. These analyses are illustrated by numerically propagating the perturbation equations with a specific model reproducing a representative cosmic history. Our results show how the f (G) models are highly constrained by cosmological data.