Non-minimal kinetic coupling and the phenomenology of dark energy

We study a model of scalar field with a general non-minimal kinetic coupling to itself and to the curvature. The cosmological dynamics of this model and the issue of accelerated expansion is analyzed. Solutions giving rise to power law expansion have been found. By constraining the potential of the model, we obtained a variety of solutions corresponding to phenomenologically acceptable models of dark energy, like the $\Lambda$CDM model, variable cosmological constant model VCC, FRW with two dimensional topological defects, FRW with phantom dark energy, showing that this model with the appropriate potential in each case, can describe a rich variety of dynamical scenarios.