Matter instabilities in general Gauss-Bonnet gravity

We study the evolution of cosmological perturbations in f(G) gravity, where the Lagrangian is the sum of a Ricci scalar R and an arbitrary function f in terms of a Gauss-Bonnet term G. We derive the equations for perturbations assuming matter to be described by a perfect fluid with a constant equation of state w. We show that density perturbations in perfect fluids exhibit negative instabilities during both the radiation and the matter domination, irrespective of the form of f(G). This growth of perturbations gets stronger on smaller scales, which is difficult to be compatible with the observed galaxy spectrum unless the deviation from general relativity is very small. Thus f(G) cosmological models are effectively ruled out from this ultraviolet instability, even though they can be compatible with the late-time cosmic acceleration and local gravity constraints.