On dark energy models of single scalar field
  In this paper we revisit the dynamical dark energy model building based on
single scalar field involving higher derivative terms. By imposing a degenerate
condition on the higher derivatives in curved spacetime, one can select the
models which are free from the ghost mode and the equation of state is able to
cross the cosmological constant boundary smoothly, dynamically violate the null
energy condition. Generally the Lagrangian of this type of dark energy models
depends on the second derivatives linearly. It behaves like an imperfect fluid,
thus its cosmological perturbation theory needs to be generalized. We also
study such a model with explicit form of degenerate Lagrangian and show that
its equation of state may cross -1 without any instability.
