Energy conditions constraints on a class of f(R)-gravity
  We present and discuss the bounds from the energy conditions on a general f(R) functional form in the framework of metric variational approach. As a concrete application of the energy conditions to locally homogeneous and isotropic f(R)-cosmology, the recent estimated values of the deceleration and jerk parameters are used to examine the bounds from the weak energy condition on the free parameter of the family of f(R)=\sqrt{R^2 - R_0^2} gravity theory. 
J. Santos, M.J. Reboucas, J.S. Alcaniz