Statefinder diagnostic and constraints on the Palatini f(R) gravity theories

摘要

In this paper, we focus on a series of $f(R)$ gravity theories in Palatiniformalism to investigate the probabilities of producing the late-timeacceleration for the flat Friedmann-Robertson-Walker (FRW) universe. We applystatefinder diagnostic to these cosmological models for chosen series ofparameters to see if they distinguish from one another. The diagnostic involvesthe statefinder pair $\{r,s\}$, where $r$ is derived from the scale factor $a$and its higher derivatives with respect to the cosmic time $t$, and $s$ isexpressed by $r$ and the deceleration parameter $q$. In conclusion, we findthat although two types of $f(R)$ theories: (i) $f(R) = R + \alpha R^m - \betaR^{-n}$ and (ii) $f(R) = R + \alpha \ln R - \beta$ can lead to late-timeacceleration, their evolutionary trajectories in the $r-s$ and $r-q$ planesreveal different evolutionary properties, which certainly justify the merits ofstatefinder diagnostic. Additionally, we utilize the observational Hubbleparameter data (OHD) to constrain these models of $f(R)$ gravity. As a result,except for $m=n=1/2$ of (i) case, $\alpha=0$ of (i) case and (ii) case allow$\Lambda$CDM model to exist in 1$\sigma$ confidence region. After adoptingstatefinder diagnostic to the best-fit models, we find that all the best-fitmodels are capable of going through deceleration/acceleration transition stagewith late-time acceleration epoch, and all these models turn to de-Sitter point($\{r,s\}=\{1,0\}$) in the future. Also, the evolutionary differences betweenthese models are distinct, especially in $r-s$ plane, which makes thestatefinder diagnostic more reliable in discriminating cosmological models.