  In the context of the recently proposed formulation of quantum
geometrodynamics in extended phase space we discuss the problem how the
behavior of the Universe, initially managed by quantum laws, has become
classical. In this version of quantum geometrodynamics we quantize gauge
gravitational degrees of freedom on an equal basis with physical degrees of
freedom. As a consequence of this approach, a wave function of the Universe
depends not only on physical fields but also on gauge degrees of freedom. From
this viewpoint, one should regard the physical Universe as a subsystem whose
properties are formed in interaction with the subsystem of gauge degrees of
freedom. We argue that the subsystem of gauge degrees of freedom may play the
role of environment, which, being taken into account, causes the density matrix
to be diagonal. We show that under physically reasonable fixing of gauge
condition the density matrix describing the physical subsystem of the Universe
may have a Gaussian peak in some variable, but it could take the Gaussian form
only within a spacetime region where a certain gauge condition is imposed. If
spacetime manifold consists of regions covered by different coordinate charts
the Universe cannot behave in a classical manner nearby borders of these
regions. Moreover, in this case the Universe could not stay in the same quantum
state, but its state would change in some irreversible way.
