It is shown that the homogeneous and isotropic Universe is spatially flat in the limit which takes into account the moments of infinitely large orders of probabilistic distribution of a scale factor with respect to its mean value in the state with large quantum numbers. The quantum mechanism of fine tuning of the total energy density in the Universe to the critical value at the early stage of its evolution is proposed and the reason of possible small difference between these densities during the subsequent expansion is indicated. A comparison of the predictions of the quantum model with the real Universe is given.
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