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,(RRab)-R-ab,(RRabcd)-R-abcd) 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 Lambda CDM paradigm with Omega(DE)=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 partial derivative(2)f/partial derivative 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 Lambda CDM cosmic history. Our results show how the f(G) models are highly constrained by cosmological data.