Holographic dark energy with non-minimal derivative coupling to gravity
  effects
  Non-minimal derivative coupling (NMDC) to gravity in flat FLRW universe is
investigated in the scenario of holographic dark energy. Kinetic term is
coupled to the Einstein tensor under potential $V = (1/2)m^2 \phi^2$. The free
kinetic term is allowed to be canonical and phantom. Gravitational constant is
modified with the NMDC coupling. Holographic cutoff at Hubble horizon gives
modification to dark energy density. We evaluate dark energy equation of state
and the variation of gravitational constant of the theory such that the theory
can be constrained. It is found that positive NMDC coupling is favored rather
than the negative one. The model with purely NMDC theory and the potential is
favored with positive sub-Planckian NMDC coupling and decaying scalar field.
The canonical scalar field with positive NMDC coupling under the scalar
potential is also viable under some conditions that result in oscillating
scalar field. The phantom field case is not favored in this model since the
coupling and scalar mass are required to be super-Planckian while it is tightly
constrained by gravitational constant variation observations.
