Dark energy cosmology with generalized linear equation of state

Dark energy with the usually used equation of state $p=w\rho$, where $w=const<0$ is hydrodynamically unstable. To overcome this drawback we consider the cosmology of a perfect fluid with a linear equation of state of a more general form $p=\alpha(\rho-\rho_0)$, where the constants $\alpha$ and $\rho_0$ are free parameters. This non-homogeneous linear equation of state provides the description of both hydrodynamically stable ($\alpha>0$) and unstable ($\alpha<0$) fluids. In particular, the considered cosmological model describes the hydrodynamically stable dark (and phantom) energy. The possible types of cosmological scenarios in this model are determined and classified in terms of attractors and unstable points by the using of phase trajectories analysis. For the dark energy case there are possible some distinctive types of cosmological scenarios: (i) the universe with the de Sitter attractor at late times, (ii) the bouncing universe, (iii) the universe with the Big Rip and with the anti-Big Rip. In the framework of a linear equation of state the universe filled with an phantom energy, $w<-1$, may have either the de Sitter attractor or the Big Rip.