  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
$a\propto t^{11/18}$ to an asymptotically exponential scaling $a\propto
\exp(t)$; (v) the energy density of the matter field scales as $\rho_m\propto
(1/a)^{36/11}$; (vi) the present age of the Universe and the
decelerated-accelerated transition redshift are smaller than the corresponding
ones in the $\Lambda$CDM model.
