Paper detail

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

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.