Galaxy clusters and structure formation in quintessence versus phantom dark energy universe

Abstract

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.

Astrophysical constraints on dark energy

“…In the event that dark energy is dynamical [19], as opposed to a rigid cosmological constant, it might form inhomogeneous clumps on galactic length scales. This behavior could, in principle, be detectable through the effects discussed here: Λ from astrophysical measurements would be larger than the known cosmological value.…”

The Gravothermal Instability at All Scales: From Turnaround Radius to Supernovae

“…Therefore, a spherical non-homogeneous perturbation will decouple from the expansion and collapse only below a threshold radius, the turnaround radius (an incomplete list on the subject includes [11][12][13][14][15][16]). This radius estimated by equilibria of an isothermal sphere as we did in [8,10] is smaller and thus stricter-rendering our estimation more accurate-than the one estimated considering only homogeneous equilibria (e.g., published later [14]). Thermodynamic equilibria of an ideal gas cannot exist below the turnaround radius Rturn for a fixed energy E. We assume here a dark energy density with the equation of state corresponding to the cosmological constant Λ.…”

“…we find in addition that quintessential dark energy (w > −1) favors the formation of structures with respect to the phantom-type dark energy (w < −1), as depicted in Figure 1b. The diagrams of Figure 1 are generated by solving numerically the following equation (for a general derivation, see [10], and for the case w = −1, see [9]):…”

“…for several R boundary values, keeping the total number of particles fixed. This equation is the modification of the Emden equation due to dark energy, i.e., the Poisson equation for a density corresponding to an isothermal distribution plus the constant energy density and gravitating pressure of dark energy [10].…”

The turnaround radius as a probe of dark energy and modified gravity

“…It was suggested recently that the turnaround radius is a possible probe of dark energy or modified gravity scenarios [3,4,5,6] but the concept of turnaround radius is older [7].…”