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

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 + alpha R-m - beta R-n and (ii) f (R) = R + alpha ln R - beta 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), alpha = 0 in case (i) and case (ii) allow the Lambda CDM model to exist in the 1 sigma 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 thedeceleration/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.