Local dark matter and dark energy as estimated on a scale of ∼1 Mpc in a self-consistent way

Context. Dark energy was first detected from large distances on gigaparsec scales. If it is vacuum energy (or Einstein's.), it should also exist in very local space. Here we discuss its measurement on megaparsec scales of the Local Group. Aims. We combine the modified Kahn-Woltjer method for the Milky Way-M 31 binary and the HST observations of the expansion flow around the Local Group in order to study in a self-consistent way and simultaneously the local density of dark energy and the dark matter mass contained within the Local Group. Methods. A theoretical model is used that accounts for the dynamical effects of dark energy on a scale of similar to 1 Mpc. Results. The local dark energy density is put into the range 0.8-3.7 rho(v) (rho(v) is the globally measured density), and the Local Group mass lies within 3.1-5.8 x 10(12) M-circle dot. The lower limit of the local dark energy density, about 4/5x the global value, is determined by the natural binding condition for the group binary and the maximal zero-gravity radius. The near coincidence of two values measured with independent methods on scales differing by similar to 1000 times is remarkable. The mass similar to 4 x 10(12) M-circle dot and the local dark energy density similar to rho(v) are also consistent with the expansion flow close to the Local Group, within the standard cosmological model. Conclusions. One should take into account the dark energy in dynamical mass estimation methods for galaxy groups, including the virial theorem. Our analysis gives new strong evidence in favor of Einstein's idea of the universal antigravity described by the cosmological constant.