f(R,L_m) gravity
  We generalize the $f(R)$ type gravity models by assuming that the
gravitational Lagrangian is given by an arbitrary function of the Ricci scalar
$R$ and of the matter Lagrangian $L_m$. 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 energy-momentum
tensor. The equations of motion for test particles can also be derived from a
variational principle in the particular case in which the Lagrangian density of
the matter is an arbitrary function of the energy-density of the matter only.
Generally, the motion 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 also considered, and a procedure for obtaining the
energy-momentum tensor of the matter is presented. The gravitational field
equations and the equations of motion for a particular model in which the
action of the gravitational field has an exponential dependence on the standard
general relativistic Hilbert--Einstein Lagrange density are also derived.
