Inhomogeneous Equation of State of the Universe: Phantom Era, Future   Singularity and Crossing the Phantom Barrier
  The dark energy universe equation of state (EOS) with inhomogeneous,Hubble parameter dependent term is considered. The motivation to introduce such a term comes from time-dependent viscosity considerations and modifications of general relativity. For several explicit examples of such EOS it is demonstrated how the type of future singularity changes, how the phantom epoch emerges and how crossing of phantom barrier occurs. Similar cosmological regimes are considered for the universe with two interacting fluids and for universe with implicit EOS. For instance, the crossing of phantom barrier is realized in easier way, thanks to the presence of inhomogeneous term. The thermodynamical dark energy model is presented where the universe entropy may be positive even at phantom era as a result of crossing of w=-1 barrier. 
Shin'ichi Nojiri and Sergei D. Odintsov