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

TL;DR

This paper investigates Palatini $f(R)$ gravity theories using the statefinder diagnostic to distinguish their cosmic evolution and constrains models with observational $H(z)$ data, aiming to explain late-time acceleration without dark energy.

Contribution

It applies statefinder diagnostics to specific Palatini $f(R)$ models and constrains them using observational data, highlighting their different evolutionary behaviors.

Findings

Different $f(R)$ models show distinct trajectories in $s-r$ and $q-r$ planes.

Models are constrained by observational $H(z)$ data.

Some models can explain late-time acceleration without dark energy.

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.