  The meaning of the wave function of the Universe was actively discussed in
1980s. In most works on quantum cosmology it is accepted that the wave function
is a probability amplitude for the Universe to have some space geometry, or to
be found in some point of the Wheeler superspace. It seems that the wave
function gives maximally objective description compatible with quantum theory.
However, the probability distribution does not depend on time and does not take
into account the existing of our macroscopic evolving Universe. What we wish to
know is how quantum processes in the Early Universe determined the state of the
present Universe in which we are able to observe macroscopic consequences of
these quantum processes. As an alternative to the Wheeler - DeWitt quantum
geometrodynamics we consider the picture that can be obtained in the extended
phase space approach to quantization of gravity. The wave function in this
approach describes different states of the Universe which correspond to
different stages of its evolution.
