Statefinder diagnosis for the Palatini $f(R)$ gravity theories

Abstract: The Palatini $f(R)$ gravity, is able to probably explain the late time cosmic acceleration without the need for dark energy, is studied. In this paper, we investigate a number of $f(R)$ gravity theories in Palatini formalism by means of statefinder diagnosis. We consider two types of $f(R)$ theories: (i) $f(R)=R+\alpha R^{m}-\beta R^{-n}$ and (ii) $f(R)=R+\alpha ln R+\beta$. We find that the evolutionary trajectories in the $s-r$ and $q-r$ planes for various types of the Palatini $f(R)$ theories reveal different evolutionary properties of the universe. Additionally, we use the observational $H(z)$ data to constrain models of $f(R)$ gravity.