The Palatini $f(R)$ gravity, is able to probably explain the late time cosmicacceleration without the need for dark energy, is studied. In this paper, weinvestigate a number of $f(R)$ gravity theories in Palatini formalism by meansof 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 findthat the evolutionary trajectories in the $s-r$ and $q-r$ planes for varioustypes of the Palatini $f(R)$ theories reveal different evolutionary propertiesof the universe. Additionally, we use the observational $H(z)$ data toconstrain models of $f(R)$ gravity.
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机译：研究了Palatini重力，它可以解释晚时的宇宙加速而无需暗能量。在本文中，我们通过状态查找器诊断研究了Palatini形式主义中的许多$ f（R）$引力理论。我们考虑两种类型的$ f（R）$理论：（i）$ f（R）= R + \ alpha R ^ {m}-\ beta R ^ {-n} $和（ii）$ f（R）= R + \ alpha ln R + \ beta $。我们发现，对于各种类型的帕拉蒂尼$ f（R）$理论，在$ s-r $和$ q-r $平面中的演化轨迹揭示了宇宙的不同演化特性。此外，我们使用观测数据$ H（z）$来约束$ f（R）$重力模型。
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