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 the crossing of a phantom barrier occurs. Similar cosmological regimes are considered for the universe with two interacting fluids and for the universe with implicit EOS. For instance, the crossing of the phantom barrier is realized in an 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 the phantom era as a result of the crossing of the $w=\ensuremath{-}1$ barrier.