Abstract:
Cosmological model of the Friedmann world filled by ideal liquid with the equation
of state $p=K\rho$ is studied in the framework of explicit canonical quantization of gravitation
by the Arnowitt–Deser–Misner (ADM) method and in the framework of the
superspatial Dirac method. It is shown that the collapse does not take place in the
model (the Dirac method and the ADM method when the time is chosen out of matter
variables). If the time is chosen out of geometrical variables, the Friedmann Universe
can be in the eigen-state of the Hamiltonian with the energy eigen-values depending
on time. Physical interpretation of the results obtained is discussed.