An Interacting Dark Energy Model with Nonminimal Derivative Coupling
  We study cosmological dynamics of an extended gravitational theory that
gravity is coupled non-minimally with derivatives of a dark energy component
and there is also a phenomenological interaction between the dark energy and
dark matter. Depending on the direction of energy flow between the dark
sectors, the phenomenological interaction gets two different signs. We show
that this feature affects the existence of attractor solution, the rate of
growth of perturbations and stability of the solutions. By considering an
exponential potential as a self-interaction potential of the scalar field, we
obtain accelerated scaling solutions that are attractors and have the potential
to alleviate the coincidence problem. While in the absence of the nonminimal
derivative coupling there is no attractor solution for phantom field when
energy transfers from dark matter to dark energy, we show an attractor solution
exists if one considers an explicit nonminimal derivative coupling for phantom
field in this case of energy transfer. We treat the cosmological perturbations
in this setup with details to show that with phenomenological interaction,
perturbations can grow faster than the minimal case.\\ {\bf Keywords}:
Dynamical Systems; Dark Energy; Dark Matter; Non-Minimal Derivative Coupling,
Statefinder Diagnostic, Cosmological Perturbations.
