Energy conditions in $f(R)$ gravity

In order to shed some light on the current discussion about $f(R)$-gravity theories we derive and discuss the bounds imposed by the energy conditions on a general $f(R)$ functional form. The null and strong energy conditions in this framework are derived from Raychaudhuri’s equation along with the requirement that gravity is attractive, whereas the weak and dominant energy conditions are stated from a comparison with the energy conditions that can be obtained in a direct approach via an effective energy-momentum tensor for $f(R)$ gravity. 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 parameters of two families of $f(R)$-gravity theories.