Late-time acceleration and Phantom Divide Line Crossing with Non-minimal   Coupling and Lorentz Invariance Violation
  We consider two alternative dark energy models: a Lorentz invariance preserving model with a nonminimally coupled scalar field and a Lorentz invariance violating model with a minimally coupled scalar field. We study accelerated expansion and dynamics of equation of state parameter in these scenarios. While a minimally coupled scalar field has not the capability to be a successful dark energy candidate with cosmological constant line crossing, a nonminimally coupled scalar field in the presence of Lorentz invariance or a minimally coupled scalar field with Lorentz invariance violation have this capability. In the later case, accelerated expansion and phantom divide line crossing are the results of interactive nature of this Lorentz violating scenario. 
Kourosh Nozari and S. Davood Sadatian