The general form of the coupled Horndeski Lagrangian that allows
  cosmological scaling solutions
  We consider the general scalar field Horndeski Lagrangian coupled to matter.
Within this class of models, we present two results that are independent of the
particular form of the model. First, we show that in a
Friedmann-Robertson-Walker metric the Horndeski Lagrangian coincides with the
pressure of the scalar field. Second, we employ the previous result to identify
the most general form of the Lagrangian that allows for cosmological scaling
solutions, i.e. solutions where the ratio of matter to field density and the
equation of state remain constant. Scaling solutions of this kind may help
solving the coincidence problem since in this case the presently observed ratio
of matter to dark energy does not depend on initial conditions, but rather on
the theoretical parameters.
