A 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 the 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 the instability domain under gravitational collapse, while phantom dark energy decreases it. 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 the 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.

• Received 23 December 2013

DOI:https://doi.org/10.1103/PhysRevD.89.083002