A polynomial model of purely affine gravity
  We present a purely affine gravitational model in four dimensions built up entirely on the bases of full diffeomorphism invariance, and power- counting renormalizability. We show that its non-relativistic limit around a homogeneous and isotropic spacetime yields to a Newtonian gravity. 
Oscar Castillo-Felisola and Aureliano Skirzewski
gr-qc hep-th