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

Abstract

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. We calculate the present locus of test particles injected a fixed time ago (\sim 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. Our main conclusions 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 (\approx 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 \ga 1.5 \times 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.

4 pages, 3 figures, A&A in press

References in corpus (3)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• The Hubble flow around the Local Group
• Non-Friedmann cosmology for the Local Universe, significance of the universal Hubble constant and short-distance indicators of dark energy

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• Tracking the Local Group Dynamics by Extended Gravity
• Timing Argument take on the Milky Way and Andromeda past-encounter
• Dark Energy as a Critical Period in Binary Motion: Bounds from Multi-scale Binaries
• Galaxy groups in the presence of Cosmological Constant: Increasing the Masses of Groups
• The Velocity Field Around Groups of Galaxies
• Bounding the Cosmological Constant using Galactic Rotation Curves from the SPARC Dataset
• Islands in Simulated Cosmos: Probing the Hubble Flow around Groups and Clusters