On the Newtonian Limit in Gravity Models with Inverse Powers of R

I reconsider the problem of the Newtonian limit in nonlinear gravity models in the light of recently proposed models with inverse powers of the Ricci scalar. Expansion around a maximally symmetric local background with positive curvature scalar R_0 gives the correct Newtonian limit on length scales << R_0^{-1/2} if the gravitational Lagrangian f(R) satisfies |f(R_0)f''(R_0)|<< 1. I propose two models with f''(R_0)=0.