On the LCDM Universe in f(R) gravity
  Several different explicit reconstructions of f(R) gravity are obtained from
the background FRW expansion history. It is shown that the only theory whose
Lagrangian is a simple function of the Ricci scalar R, that admits an exact
LCDM expansion history is standard General Relativity with a positive
cosmological constant and the only way to obtain this behaviour of the scale
factor for more general functions of R is to add additional degrees of freedom
to the matter sector.
