Extended $f(R,L_m)$ gravity with generalized scalar field and kinetic
  term dependences
  We generalize previous work by considering a novel gravitational model with
an action given by an arbitrary function of the Ricci scalar, the matter
Lagrangian density, a scalar field and a kinetic term constructed from the
gradients of the scalar field, respectively. The gravitational field equations
in the metric formalism are obtained, as well as the equations of motion for
test particles, which follow from the covariant divergence of the stress-energy
tensor. Specific models with a nonminimal coupling between the scalar field and
the matter Lagrangian are further explored. We emphasize that these models are
extremely useful for describing an interaction between dark energy and dark
matter, and for explaining the late-time cosmic acceleration.
