On curvature coupling and quintessence fine-tuning

We discuss the phenomenological model in which the potential energy of the quintessence field depends linearly on the energy density of the spatial curvature. We find that the pressure of the scalar field takes a different form when the potential of the scalar field also depends on the scale factor and the energy momentum tensor of the scalar field can be expressed as the form of a perfect fluid. A general coupling is proposed to explain the current accelerating expansion of the Universe and solve the fine-tuning problem