ON QUANTUM PROPERTIES OF THE LARGE-SCALE INHOMOGENEITIES OF METRIC IN THE VICINITY OF COSMOLOGICAL SINGULARITY

Abstract

The question on the influence of quantum effects on the properties of large-scale inhomogeneities of metric is analyzed. A model with short-distance fluctuations omitted is considered. An assumption of absence of short-scale perturbations allows one to solve the Wheeler-DeWitt equation exactly, for the case of asymptotical closeness to a singularity. Probability interpretation of the wave function is discussed. In the framework of the model it is possible to define the stationary states. It is found that the metric inhomogeneities are spatially delta-correlated in a stationary state. In contrast to the classical theory, the properties of inhomogeneities are essentially dependent upon the choice of initial conditions.