Quantum behaviour of long-wave inhomogeneous models of the very early Universe

The inhomogeneous Mixmaster model is shown to provide a satisfactory physical description of quantum behavior of the gravitational field near the cosmological singularity. It is also shown that near the singularity the only stable quantum characteristics of the gravitational field are the anisotropy parameters, while mean values of logarithms of scale functions are divergent in the limit t → 0. This makes it impossible to use a perturbation scheme on a classical background to describe the singularity.