  Higher order curvature gravity has recently received a lot of attention due
to the fact that it gives rise to cosmological models which seem capable of
solving dark energy and quintessence issues without using "ad hoc" scalar
fields. Such an approach is naturally related to fundamental theories of
quantum gravity which predict higher order terms for loop expansions of quantum
fields in curved spacetimes. In this framework, we obtain a class of
cosmological solutions which are fitted against cosmological data. We reproduce
reliable models able to fit high redshift supernovae and WMAP observations. The
age of the universe and other cosmological parameters are recovered in this
context. Furthermore, in the weak field limit, we obtain gravitational
potentials which differ from the Newtonian one because of repulsive corrections
increasing with distance. We evaluate the rotation curve of our Galaxy and
compare it with the observed data in order to test the viability of these
theories and to estimate the scale-length of the correction. It is remarkable
that the Milky Way rotation curve is well fitted without the need of any dark
matter halo and similar results hold also for other galaxies.
