  Relations between the Friedmann observables of the expanding Universe and the
Dirac observables in the generalized Hamiltonian approach are established for
the Friedmann cosmological model of the Universe with the field excitations
imitating radiation. A full separation of the physical sector from the gauge
one is fulfilled by the method of the gaugeless reduction in which the
gravitational part of the energy constraint is considered as a new momentum. We
show that this reduction removes an infinite factor from the Hartle -- Hawking
functional integral, provides the normalizability of the Wheeler -- DeWitt wave
function, clarifies its relation to the observational cosmology, and picks out
a conformal frame of Narlikar.
