  The evidence of the acceleration of universe at present time has lead to
investigate modified theories of gravity and alternative theories of gravity,
which are able to explain acceleration from a theoretical viewpoint without the
need of introducing dark energy. In this paper we study alternative
gravitational theories defined by Lagrangians which depend on general functions
of the Ricci scalar invariant in minimal interaction with matter, in view of
their possible cosmological applications. Structural equations for the
spacetimes described by such theories are solved and the corresponding field
equations are investigated in the Palatini formalism, which prevents
instability problems. Particular examples of these theories are also shown to
provide, under suitable hypotheses, a coherent theoretical explanation of
earlier results concerning the present acceleration of the universe and
cosmological inflation. We suggest moreover a new possible Lagrangian,
depending on the inverse of sinh(R), which gives an explanation to the present
acceleration of the universe.
