Diagnostic of $f(R)$ under the $Om(z)$ function

Abstract

We perform the two$-$point diagnostic for the $Om(z)$ function proposed by Sahni ${\it et al}$ in 2014 for the Starobinsky and Hu & Sawicki models in $f(R)$ gravity. We show that the observed values of the $Omh^2$ function can be explained in $f(R)$ models while in LCDM the $Omh^2$ funticon is expected to be a redshift independent number. We perform the analysis for some particular values of $\Omega_m^0$ founding a cumulative probability ($P(\chi^2 \leq \chi^2_{{\it model}})$) $P \sim 0.16$ or $\sim0.09$ for the better cases versus a cumulative probability of $P \sim 0.98$ in the $\Lambda$CDM scenario. We also show that these models present a characteristic signature around the interval between $z\sim 2$ and $z\sim 4$, that could be confronted with future observations using the same test.