The Hubble diagram for a system within dark energy: the location of the zero-gravity radius and the global Hubble rate

Abstract

Aims. Here we continue to discuss the principle of the local measurement of dark energy using the normalized Hubble diagram describing the environment of a system of galaxies. Methods. We calculate the present locus of test particles injected a fixed time ago (∼the age of the universe), in the standard Λ cosmology and for different values of the system parameters (the model includes a central point mass M and a local dark energy density ρ loc ) and discuss the position of the zero-gravity distance R v in the Hubble diagram. Results. Our main conclusion are: 1) when the local DE density ρ loc is equal to the global DE density ρ v , the outflow reaches the global Hubble rate at the distance R 2 = (1 + z v )R v , where z v is the global zero-acceleration redshift (≈0.7 for the standard model). This is also the radius of the ideal Einstein-Straus vacuole, 2) for a wide range of the local-to-global dark energy ratio ρ loc /ρ v , the local flow reaches the known global rate (the Hubble constant) at a distance R 2 > ∼ 1.5 × R v . Hence, R v will be between R 2 /2 and R 2 , giving upper and lower limits to ρ loc /M. For the Local Group, this supports the view that the local density is near the global one.

Dark energy domination in the Virgocentric flow

“…(11) in general independently of the "boundary/initial conditions" near the cluster (see Fig. 2 in Teerikorpi & Chernin 2010). In particular, strong perturbations at small distances in the flow are compatible with its regularity at larger distances.…”

“…This suggests that R ZG < 15 Mpc. The argument that the zero-gravity surface is located below the point where the local flow reaches the global expansion rate gained support from the calculations by Teerikorpi & Chernin (2010). As for the cluster mass, we adopt the range M = (0.6−1.2) × 10 15 M (Sect.…”

The Hubble diagram for a system within dark energy: influence of some relevant quantities

“…If, say, two objects with equal energies were expelled at different past times, they should still lie on the trajectory corresponding to that same energy. However, if the objects had a range of different energies when expelled at the same past time, their presently observed distance-velocity locus is made of pieces of trajectories for different E = E(R) (Chernin et al 2009;Teerikorpi & Chernin 2010). The true situation could be a mixture of these variants: a range of energies and a range of expulsion times.…”

“…Generally, the dynamical mass determination methods will underestimate the true mass of a galaxy group (e.g., the Local Group) if one does not take the presence of possible antigravitating local DE into account. Teerikorpi & Chernin (2010) further considered the expected present-day local Hubble relation within the Einstein-Straus vacuole containing different amounts of DE, and its link to the global Hubble law.…”

The Dominance of Dark Energy Leads to Reduction of the Entropy of Galaxies Flow and Entropy of the Universe

“…I.D.Karachentsev (Karachentsev & Kashlbadze, 2006;Karachentsev, 2005;Karachentsev et al, 2009;Karachentsev, Karachentseva & Huchtmeier, 2007) and A.D.Chernin (Chernin, Teerikorpi, Baryshev, 2003;Chernin et al, 2007;Chernin et al, 2009;Chernin et al, 2012;Chernin et al, 2013;Chernin et al, 2007;Chernin et al, 2012;Chernin, 2013;Teerikorpi & Chernin, 2010), studying the motions of galaxies in clusters, have shown that anti-gravity effects manifest themselves not only on a cosmic scale, but the scale of clusters of galaxies, for example -the Local Group, including our galaxy (the Milky Way) galaxy Andromeda and dozens of other smaller galaxies. M. Eingorn and A. Zhuk also studied in detail these issues (Brilenkov, Eingorn & Zhuk, 2015;Eingorn & Zhuk, 2012).…”