f(R,T) gravity
  We consider f(R,T) modified theories of gravity, where the gravitational
Lagrangian is given by an arbitrary function of the Ricci scalar R and of the
trace of the stress-energy tensor T. We obtain the gravitational field
equations in the metric formalism, as well as the equations of motion for test
particles, which follow from the covariant divergence of the stress-energy
tensor. Generally, the gravitational field equations depend on the nature of
the matter source. The field equations of several particular models,
corresponding to some explicit forms of the function f(R,T), are also
presented. An important case, which is analyzed in detail, is represented by
scalar field models. We write down the action and briefly consider the
cosmological implications of the $f(R,T^{\phi})$ models, where $T^{\phi}$ is
the trace of the stress-energy tensor of a self-interacting scalar field. The
equations of motion of the test particles are also obtained from a variational
principle. The motion of massive test particles is non-geodesic, and takes
place in the presence of an extra force orthogonal to the four-velocity. The
Newtonian limit of the equation of motion is further analyzed. Finally, we
provide a constraint on the magnitude of the extra-acceleration by analyzing
the perihelion precession of the planet Mercury in the framework of the present
model.
