{Lambda}CDM universe in f(R) gravity

Several different explicit reconstructions of f(R) gravity are obtained from the background Friedmann-Laimatre-Robertson-Walker expansion history. It is shown that the only theory whose Lagrangian is a simple function of the Ricci scalar R, that admits an exact {Lambda}CDM expansion history, is standard general relativity with a positive cosmological constant and the only way to obtain this behavior of the scale factor for more general functions of R is to add additional degrees of freedom to the matter sector.