An An Interacting Dark Energy Model with Nonminimal Derivative Coupling in the Parameterized Post-Friedmannian Framework

We investigation the parameterization of the cosmological model with the nonminimal derivative coupling of a scalar field where gravity is coupled nonminimally with the derivatives of dark energy components in the form of a scalar field. We follow the parameterized post-Friedmannian approach for the interacting dark energy theories. We show how the big number of free functions can be reduced by limiting certain assumptions to a few non-zero coefficients. We only consider the case that the dark sector contains at most second order in time derivatives of the metric and scalar fields. In this paper, we demonstrate their use through an example of the dark sector interactions model and classify them according to the current literature.