f(R) Gravity as a Dark Energy Fluid

Using the so-called equation of state approach to linear perturbation
 applied to f(R) gravity, we reproduce most of the results presented in 
the article "The Large Scale Structure of f(R) Gravity" (2007) by Y.-S. 
Song, W. Hu and I. Sawicki. More precisely, we study the equations for 
the evolution of cosmological perturbations in f(R) gravity
 and conclude that this modified gravity model can be interpreted as a 
dark energy fluid at background and linearised perturbation order. By 
eliminating the extra scalar degree of freedom known to be present in 
such theories, we are able to characterise the evolution of the 
perturbations in the scalar sector in terms of equations of state for 
the entropy perturbation and anisotropic stress which are written in 
terms of the density and velocity perturbations of the dark energy fluid
 and those in the matter, or the metric perturbations. We also do the 
same in the much simpler vector and tensor sectors. In order to 
illustrate the simplicity of this formulation, we numerically evolve 
cosmological perturbations in a small number of cases.