Practical solutions for perturbed f(R) gravity
  We examine the accuracy of the quasi-static approximation and a parametric form commonly employed for evolving linear perturbations in f(R) gravity theories and placing cosmological constraints. In particular, we analyze the nature and the importance of the near horizon effects that are often neglected. We find that for viable models, with a small present value of the scalaron field, such corrections are entirely negligible with no impact on observables. We also find that the one-parameter form, commonly used to represent the modified equations for linear perturbations in f(R), leads to theoretical systematic errors that are relatively small and, therefore, is adequate for placing constraint on f(R) models. 
Alireza Hojjati, Levon Pogosian, Alessandra Silvestri, and Starla   Talbot
astro-ph.CO gr-qc