Galaxy clusters and structure formation in quintessence versus phantom
  dark energy universe
  The self-gravitating gas in the Newtonian limit is studied in the presence of
dark energy with a linear and constant equation of state. Entropy extremization
associates to the isothermal Boltzmann distribution an effective density that
includes `dark energy particles', which either strengthen or weaken mutual
gravitational attraction, in case of quintessence or phantom dark energy,
respectively, that satisfy a linear equation of state. Stability is studied for
microcanonical (fixed energy) and canonical (fixed temperature) ensembles.
Compared to the previously studied cosmological constant case, in the present
work it is found that quintessence increases, while phantom dark energy
decreases the instability domain under gravitational collapse. Thus, structures
are more easily formed in a quintessence rather than in a phantom dominated
Universe. Assuming that galaxy clusters are spherical, nearly isothermal and in
hydrostatic equilibrium we find that dark energy with a linear and constant
equation of state, for fixed radius, mass and temperature, steepens their total
density profile. In case of a cosmological constant, this effect accounts for a
1.5% increase in the density contrast, that is the center to edge density ratio
of the cluster. We also propose a method to constrain phantom dark energy.
