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Statefinder diagnostic and constraints on the Palatini f(R) gravity theories | | Shu-Lei Cao
; Song Li
; Hao-Ran Yu
; Tong-Jie Zhang
; | | Date: |
20 Nov 2017 | | Abstract: | In this paper, we focus on a series of $f(R)$ gravity theories in Palatini
formalism to investigate the probabilities of producing the late-time
acceleration for the flat Friedmann-Robertson-Walker (FRW) universe. We apply
statefinder diagnostic to these cosmological models for chosen series of
parameters to see if they distinguish from one another. The diagnostic involves
the 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 $s$ is
expressed by $r$ and the deceleration parameter $q$. In conclusion, we find
that although two types of $f(R)$ theories: (i) $f(R) = R + alpha R^m - eta
R^{-n}$ and (ii) $f(R) = R + alpha ln R - eta$ can lead to late-time
acceleration, their evolutionary trajectories in the $r-s$ and $r-q$ planes
reveal different evolutionary properties, which certainly justify the merits of
statefinder diagnostic. Additionally, we utilize the observational Hubble
parameter 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 adopting
statefinder diagnostic to the best-fit models, we find that all the best-fit
models are capable of going through deceleration/acceleration transition stage
with late-time acceleration epoch, and all these models turn to de-Sitter point
(${r,s}={1,0}$) in the future. Also, the evolutionary differences between
these models are distinct, especially in $r-s$ plane, which makes the
statefinder diagnostic more reliable in discriminating cosmological models. | | Source: | arXiv, 1711.8329 | | Services: | Forum | Review | PDF | Favorites | |
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