  In order to study quantum dynamics of the FRW-universe of closed type,
definitions of velocity, Hubble function and duration of the evolved universe
are introduced into cosmology. The proposed definitions are characterized by
high stability of calculations and easy for use. The introduced characteristics
are supported by calculations of wave function in the fully quantum
(non-semiclassical) approach. We achieve high precision agreement between the
classical and quantum calculations after the formation of Universe with
classical spacetime (i.e. Big Bang). Such an agreement confirms efficiency of
the proposed definitions, and classical-quantum correspondence allows to obtain
quantum information before Big Bang, to study dynamics of evolution of universe
in the first stage and later times.
