It was shown that near the singularity properties of inhomogeneities of the metric can be adequately described, from the classical point of view, by the in-homogeneous mixmaster model (IMM)~1. It was also shown that IMM provides a satisfactory physical description of the quantum evolution of the very early Universe ~2, see also multidimensional generalizations in~3. The most important feature of the quantum evolution of IMM near singularity was shown to be absence of a stable classical background geometry (it is hidden under pure quantum fluctuations)~2.
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