Lagrangian description of cosmic fluids: mapping dark energy into
  unified dark energy
  We investigate the appropriateness of the use of different Lagrangians to
describe various components of the cosmic energy budget, discussing the
degeneracies between them in the absence of nonminimal couplings to gravity or
other fields, and clarifying some misconceptions in the literature. We further
demonstrate that these degeneracies are generally broken for nonminimal coupled
fluids, in which case the identification of the appropriate on-shell Lagrangian
may become essential in order characterize the overall dynamics. We then show
that models with the same on-shell Lagrangian may have different proper energy
densities and use this result to map dark energy models into unified dark
energy models in which dark matter and dark energy are described by the same
perfect fluid. We determine the correspondence between their equation of state
parameters and sound speeds, briefly discussing the linear sound speed problem
of unified dark energy models as well as a possible way out associated to the
nonlinear dynamics.
