Consistency off(R)=R2−R02gravity with cosmological observations in the Palatini formalism

Abstract

In this work we study the dynamics of the Universe in $f(R)=\sqrt{{R}^{2}\ensuremath{-}{R}_{0}^{2}}$ modified gravity with the Palatini formalism. We use data from recent observations, such as the supernova type Ia Gold sample and Supernova Legacy Survey data, the size of the baryonic acoustic peak from the Sloan Digital Sky Survey , the position of the acoustic peak from the cosmic microwave background observations, and large-scale structure formation from the 2dFGRS survey, to put constraints on the parameters of the model. To check the consistency of this action, we compare the age of old cosmological objects with the age of the Universe. In the combined analysis with all the observations, we find the parameters of the model as ${R}_{0}={6.192}_{\ensuremath{-}0.177}^{+0.167}\ifmmode\times\else\texttimes\fi{}{H}_{0}^{2}$ and ${\ensuremath{\Omega}}_{m}={0.278}_{\ensuremath{-}0.278}^{+0.273}$.