Geodesic congruences in the Palatini f(R) theory

We shall investigate the properties of a congruence of geodesics in the framework of Palatini f(R) theories. We shall evaluate the modified geodesic deviation equation and the Raychaudhuri's equation and show that f(R) Palatini theories do not necessarily lead to attractive forces. Also, we shall study energy condition for f(R) Palatini gravity via a perturbative analysis of the Raychaudhuri's equation.