Statefinder diagnostic and constraints on the Palatini f(R) gravity theories. (March 2018) - Cao, Shu-Lei; Li, Song; Yu, Hao-Ran; Zhang, Tong-Jie
Abstract: We focus on a series of f ( R ) gravity theories in Palatini formalism to investigate the probabilities of producing late-time acceleration for the flat Friedmann-Robertson-Walker (FRW) universe. We apply a statefinder diagnostic to these cosmological models for chosen series of parameters to see if they can be distinguished 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 + αR m – βR − n and (ii) f ( R ) = R + α ln R – β 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 the 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 in case (i), α = 0 in case (i) and case (ii) allow the ΛCDM model to exist in the 1 σ confidence region. After applying the statefinder diagnostic to the best-fit models, we find that all the best-fit models are capable of going through the deceleration/acceleration transition stage with a late-time acceleration epoch, and all these models turn to the de Sitter point ( r, s = 1, 0) in the future. Also, the evolutionary differences between these models are distinct, especially in the r – s plane, which makes the statefinder diagnostic more reliable in discriminating cosmological models.