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’s 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 ∝ t to an asymptotically exponential scaling a ∝ exp(t); (v) the energy density of the matter field scales as ρm ∝ (1/a) ; (vi) the present age of the Universe and the decelerated-accelerated transition redshift are smaller than the corresponding ones in the ΛCDM model.