Virialization of matter overdensities within dark energy subsystems: special cases

TL;DR

This paper investigates the virialization process of matter overdensities within dark energy subsystems under specific assumptions, analyzing special cases of quintessence clustering and their impact on virialization parameters.

Contribution

It introduces a detailed formulation of the virial theorem for dark energy and matter subsystems, considering various clustering scenarios and special values of the equation of state parameter w.

Findings

The fractional virialization radius  varies differently from previous models.

Fully clustered quintessence significantly affects virialization dynamics.

Discrepancies with earlier studies are explained by different assumptions.

Abstract

The virialization of matter overdensities within dark energy subsystems is considered under the restrictive assumptions (i) spherical-symmetric density profiles, (ii) time-independent quintessence equation of state parameter, w, and (iii) nothing but gravitational interaction between dark energy scalar field and matter. In addition, the quintessence subsystem is conceived as made of ``particles'' whose mutual interaction has intensity equal to G(1+3w) and scales as the inverse square of their distance. Then the virial theorem is formulated for subsystems. In the special case of fully clustered quintessence, energy conservation is assumed with regard to either the whole system (global energy conservation), or to the matter subsystem within the tidal potential induced by the quintessence subsystem (partial energy conservation). Further investigation is devoted to a few special values, w=-1/3, -1/2, -2/3, -1. The special case of fully clustered (i.e. collapsing together with the matter) quintessence is studied in detail. The general case of partially clustered quintessence is considered in terms of a degree of quintessence de-clustering, \zeta, ranging from fully clustered (\zeta=0) to completely de-clustered (\zeta=1) quintessence, respectively. The special case of unclustered (i.e. remaining homogeneous) quintessence is also discussed. The trend exhibited by the fractional (virialization to turnaround) radius, \eta, as a function of other parameters, is found to be different from its counterparts reported in earlier attempts. The reasons of the above mentioned discrepancy are discussed.