Quantum dynamics of early Universe
  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. 
Sergei P. Maydanyuk
gr-qc astro-ph.CO