Palatini approach to $1/R$ gravity and its implications to the late universe

By applying the Palatini approach to the $1/R$ gravity model it is possible to explain the present accelerated expansion of the Universe. Investigation of the late Universe limiting case shows that (i) due to the curvature effects the energy-momentum tensor of the matter field is not covariantly conserved; (ii) however, it is possible to reinterpret the curvature corrections as sources of the gravitational field, by defining a modified energy-momentum tensor; (iii) with the adoption of this modified energy-momentum tensor the Einstein field equations are recovered with two main modifications: the first one is the weakening of the gravitational effects of matter whereas the second is the emergence of an effective varying “cosmological constant;” (iv) there is a transition in the evolution of the cosmic scale factor from a power-law scaling $a\propto t^{11/18}$ to an asymptotically exponential scaling $a\propto \exp \mathrm{}\left(t\right);$ (v) the energy density of the matter field scales as ${\rho }_m\propto {\mathrm{}(1/a)\mathrm{}}^{36/11};$ (vi) the present age of the Universe and the decelerated-accelerated transition redshift are smaller than the corresponding ones in the cold dark matter with a cosmological constant model.