Rapid Oscillatory quintessence with variable equation of state parameter in non minimal derivative coupling model

Abstract: The rapid oscillating scalar field is considered as the quintessence in the framework of nonminimal kinetic coupling model. The scalar field behaves like a perfect fluid with a variable equation of state parameter which can be expressed as a function of the Hubble parameter. This feature enables us to study its evolution via continuity equation. The scalar field may behave as dark energy in the present epoch, while it behaves like dark matter in the future. This characteristic allows the occurrence of a decelerated expansion after the present acceleration, without invoking any interaction. The model is also studied in the presence of an interaction between dark sectors alleviating the coincidence problem. The stability of the model is investigated and the stable attractor solutions are studied.