The quiescent Hubble flow, local dark energy tests, and pairwise velocity dispersion in a Ω = 1 universe

We review the increasing evidence for the cosmological relevance of the cold local Hubble flow. New observations, N-body simulations and other theoretical arguments are discussed, supporting our previous suggestion that the cosmological vacuum or uniform dark energy can have locally observable consequencies, especially a lower velocity scatter in DE dominated regions. The apparent contradiction between the slight dependence of the growth factor on $\Omega_{\Lambda}$ and the significant influence of dark energy in realistic N-body calculations is clarified. An interesting new result is that in the standard $\Lambda$ cosmology, gravitation dominates around a typical matter fluctuation up to about the correlation length $r_0$, and we tentatively link this with the high pairwise velocity dispersion on scales up to several Mpc, as measured from galaxy redshift-space correlations. Locally, the smooth Hubble flow on similar scales is consistent with N-body simulations including $\Omega_{\Lambda} \approx 0.7$ and a low density contrast in the Local Volume, which make it generally vacuum-dominated beyond 1 - 2 Mpc from galaxies and groups. We introduce a useful way to view the Hubble flow in terms of "zero gravity" spheres aound galaxies: e.g. a set of non-intersecting spheres, observed to be expanding, actually participates in accelerating expansion. The observed insensitiveness of the local velocity dispersion to galaxy mass is explained as an effect of the vacuum, too.