The Hubble diagram for a system within dark energy: the location of the zero-gravity radius and the global Hubble rate
Tuorla Observatory, Department of Physics and Astronomy, University of Turku, 21500 Piikkiö, Finland e-mail: email@example.com
2 Sternberg Astronomical Institute, Moscow University, Moscow 119899, Russia
Accepted: 18 April 2010
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 ρloc) and discuss the position of the zero-gravity distance Rv in the Hubble diagram.
Results. Our main conclusion are: 1) when the local DE density ρloc is equal to the global DE density ρv, the outflow reaches the global Hubble rate at the distance R2 = (1+zv)Rv, where zv 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 ρloc/ρv, the local flow reaches the known global rate (the Hubble constant) at a distance R2 1.5 × Rv. Hence, Rv will be between R2/2 and R2, giving upper and lower limits to ρloc/M. For the Local Group, this supports the view that the local density is near the global one.
Key words: Local Group / dark energy / cosmological parameters
© ESO, 2010