Dark energy with a gradient coupling to the dark matter fluid:
  cosmological dynamics and structure formation
  We consider scalar field models of dark energy interacting with dark matter
through a coupling proportional to the contraction of the four-derivative of
the scalar field with the four-velocity of the dark matter fluid. The coupling
is realized at the Lagrangian level employing the formalism of Scalar-Fluid
theories, which use a consistent Lagrangian approach for relativistic fluid to
describe dark matter. This framework produces fully covariant field equations,
from which we can derive unequivocal cosmological equations at both background
and linear perturbations levels. The background evolution is analyzed in detail
applying dynamical systems techniques, which allow us to find the complete
asymptotic behavior of the universe given any set of model parameters and
initial conditions. Furthermore we study linear cosmological perturbations
investigating the growth of cosmic structures within the quasi-static
approximation. We find that these interacting dark energy models give rise to
interesting phenomenological dynamics, including late-time transitions from
dark matter to dark energy domination, matter and accelerated scaling solutions
and dynamical crossing of the phantom barrier. Moreover we obtain possible
deviations from standard $\Lambda$CDM behavior at the linear perturbations
level, which have an impact on the dynamics of structure formation and might
provide characteristic observational signatures.
