Dark Energy: the equation of state description versus scalar-tensor or   modified gravity
  Dark energy dynamics of the universe can be achieved by equivalent mathematical descriptions taking into account generalized fluid equations of state in General Relativity, scalar-tensor theories or modified F(R) gravity in Einstein or Jordan frames. The corresponding technique transforming equation of state description to scalar-tensor or modified gravity is explicitly presented. We show that such equivalent pictures can be discriminated by matching solutions with data capable of selecting the true physical frame. 
S. Capozziello, S. Nojiri, and S.D. Odintsov