  We give a rigorous and mathematically well defined presentation of the
Covariant and Gauge Invariant theory of scalar perturbations of a
Friedmann-Lemaitre-Robertson-Walker universe for Fourth Order Gravity, where
the matter is described by a perfect fluid with a barotropic equation of state.
The general perturbations equations are applied to a simple background solution
of R^n gravity. We obtain exact solutions of the perturbations equations for
scales much bigger than the Hubble radius. These solutions have a number of
interesting features. In particular, we find that for all values of n there is
always a growing mode for the density contrast, even if the universe undergoes
an accelerated expansion. Such a behaviour does not occur in standard General
Relativity, where as soon as Dark Energy dominates, the density contrast
experiences an unrelenting decay. This peculiarity is sufficiently novel to
warrant further investigation on fourth order gravity models.
