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We review the increasing evidence for the cosmological relevance of the coldlocal Hubble flow. New observations, N-body simulations and other theoreticalarguments are discussed, supporting our previous suggestion that thecosmological vacuum or uniform dark energy can have locally observableconsequencies, especially a lower velocity scatter in DE dominated regions. Theapparent contradiction between the slight dependence of the growth factor on$\Omega_{\Lambda}$ and the significant influence of dark energy in realisticN-body calculations is clarified. An interesting new result is that in thestandard $\Lambda$ cosmology, gravitation dominates around a typical matterfluctuation up to about the correlation length $r_0$, and we tentatively linkthis with the high pairwise velocity dispersion on scales up to several Mpc, asmeasured from galaxy redshift-space correlations. Locally, the smooth Hubbleflow 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 andgroups. We introduce a useful way to view the Hubble flow in terms of "zerogravity" spheres aound galaxies: e.g. a set of non-intersecting spheres,observed to be expanding, actually participates in accelerating expansion. Theobserved insensitiveness of the local velocity dispersion to galaxy mass isexplained as an effect of the vacuum, too.Comment: 8 pages, no figures; accepted for Astronomy & Astrophysic

The quiescent Hubble flow, local dark energy tests, and pairwise velocity dispersion in a $ \mathsf{\Omega} = {\mathsf 1}$ universe