Abstract
We study the evolution of cosmological perturbations in [Formula: see text] gravity, where the Lagrangian is the sum of a Ricci scalar R and an arbitrary function f in terms of a Gauss-Bonnet term [Formula: see text]. 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 [Formula: see text]. 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 [Formula: see text] cosmological models are effectively ruled out from this Ultra-Violet instability, even though they can be compatible with the late-time cosmic acceleration and local gravity constraints.
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