We construct models of universe with a generalized equation of state p = ( \alpha \rho + k \rho ^ { 1 + 1 / n } ) c ^ { 2 } having a linear component and a polytropic component .
The linear equation of state p = \alpha \rho c ^ { 2 } with -1 \leq \alpha \leq 1 describes radiation ( \alpha = 1 / 3 ) , pressureless matter ( \alpha = 0 ) , stiff matter ( \alpha = 1 ) , and vacuum energy ( \alpha = -1 ) .
The polytropic equation of state p = k \rho ^ { 1 + 1 / n } c ^ { 2 } may be due to Bose-Einstein condensates with repulsive ( k > 0 ) or attractive ( k < 0 ) self-interaction , or have another origin .
In this paper , we consider the case where the density increases as the universe expands .
This corresponds to a “ phantom universe ” for which w = p / \rho c ^ { 2 } < -1 ( this requires k < 0 ) .
We complete previous investigations on this problem and analyze in detail the different possibilities .
We describe the singularities using the classification of [ S. Nojiri , S.D .
Odintsov , S. Tsujikawa , Phys .
Rev .
D 71 , 063004 ( 2005 ) ] .
We show that for \alpha > -1 there is no Big Rip singularity although w \leq - 1 .
For n = -1 , we provide an analytical model of phantom bouncing universe “ disappearing ” at t = 0 .
We also determine the potential of the phantom scalar field and phantom tachyon field corresponding to the generalized equation of state p = ( \alpha \rho + k \rho ^ { 1 + 1 / n } ) c ^ { 2 } .