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 dust
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 LCDM model. We have used the dynamical
system methods in 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 LCDM 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.
