  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.
