Cosmic acceleration from modified gravity with Palatini formalism

We study new FRW type cosmological models of modified gravity treated on the background of Palatini approach. These models are generalization of Einstein gravity by the presence of a scalar field non-minimally coupled to the curvature. The models employ Starobinsky's term in the Lagrangian and (lust matter. Therefore, as a by-product, an exhausted cosmological analysis of general relativity amended by quadratic term is presented. We investigate dynamics of our models, confront them with the currently available astrophysical data as well as against ACDM model. We have used the dynamical system methods order to investigate) dynamics of the models. It reveals the presence of a final sudden singularity. Fitting free parameters we have demonstrated by statistical analysis that this class of models is in a very good agreement with the data (including CMB measurements as well as with the standard ACDM model predictions. One has to use statefinder diagnostic in order to discriminate among them. Therefore Bayesian methods of model selection have been employed in order to indicate preferred model. Only in the light of (CMB data the concordance model remains invincible.