Non-Friedmann cosmology for the Local Universe, significance of the universal Hubble constant, and short-distance indicators of dark energy

Based on the increasing evidence of the cosmological relevance of the local Hubble flow, we consider a simple analytical cosmological model for the Local Universe. This is a non-Friedmann model with a non-uniform static space-time. The major dynamical factor controlling the local expansion is the antigravity produced by the omnipresent and permanent dark energy of the cosmic vacuum (or the cosmological constant). The antigravity dominates at larger distances than 1d-2 Mpc from the center of the Local group. The model gives a natural explanation of the two key quantitative characteristics of the local expansion flow, which are the local Hubble constant and the velocity dispersion of the flow. The observed kinematical similarity of the local and global flows of expansion is clarified by the model. We analytically demonstrate the efficiency of the vacuum cooling mechanism that allows one to see the Hubble law this close to the Local group. The "universal Hubble constant" HV (approximate to 60 km s(-1) Mpc(-1)), depending only on the vacuum density, has special significance locally and globally. The model makes a number of verifiable predictions. It also unexpectedly shows that the dwarf galaxies of the local flow with the shortest distances and lowest redshifts may be the most sensitive indicators of dark energy in our neighborhood.