2015A&A...577A.144T

The current cosmological paradigm sees the formation and evolution of the cosmic large-scale structure as governed by the gravitational attraction of dark matter (DM) and the repulsion of dark energy (DE). We characterize the relative importance of uniform and constant dark energy, as given by the Λ term in the standard ΛCDM cosmology, in galaxy systems of different scales from groups to superclusters. An instructive ''Λ significance graph'' is introduced where the matter-DE density ratio <ρ_M>/ρ_Λ for different galaxy systems is plotted against the radius R. This presents gravitation- and DE-dominated regions and directly shows the zero velocity radius, the zero-gravity radius, and the Einstein-Straus radius for any fixed value of mass. Example galaxy groups and clusters from the local universe illustrate the use of the Λ significance graph. These are generally located deep in the gravity-dominated region <ρ_M>/ρ_Λ>2, and are virialized. Extended clusters and the main bodies of superclusters can reach down near the borderline between gravity-dominated and DE-dominated regions <ρ_M>/ρ_Λ=2. The scale-mass relation from the standard two-point correlation function intersects this balance line near the correlation length. The log<ρ_M >/ ρ_Λ vs. logR diagram is a useful and versatile way to characterize the dynamical state of systems of galaxies within the Λ-dominated expanding universe.