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Abstract. The Local Group environment at 1-10 Mpc expands linearly and smoothly, as if ruled by uniform matter, while observations show on the same scales the very lumpy local galaxy universe. This enigma in cosmology has also been demonstrated by high-resolution N-body CDM simulations. We suggest that the homogeneous dark energy component, revealed by SNIa observations, may resolve the problem of the local cold Hubble flow within the highly non-uniform environment. Linear density perturbations on a homogeneous background with the equation of state pQ = wρQc 2 are decaying for w < −1/3. Exact non-linear Einstein's equations for a spherically symmetric matter concentration, show that there is a zero-mass surface where the positive mass of the local cloud is compensated by the negative dark energy mass, and beyond this surface dark energy dominates dynamically. In such regions the velocity dispersion is adiabatically cooling, and this may explain why the Hubble law starts on the outskirts of the Local Group, with the same H0 as globally and with a remarkably small velocity dispersion.

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