A characteristic signature of fourth order gravity
  We present for the first time the complete matter power spectrum for $R^n$ gravity which has been derived from the fourth order scalar perturbation equations. This leads to the discovery of a characteristic signature of fourth order gravity in the matter power spectrum, the details of which have not seen before in other studies in this area and therefore provides a crucial test for fourth order gravity on cosmological scales. 
Kishore N. Ananda, Sante Carloni, Peter K. S. Dunsby