[en] The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space-time is obtained. The classical cosmology of a Universe and the Faddeev-Popov-DeWitt functional correspond to different orders of decomposition of this functional over the inverse 'mass' of a Universe. It is shown that the invariant content of general relativity as a constrained system can be covered by two 'equivalent' unconstrained systems: the 'dynamic' (with 'dynamic' time as the cosmic scale factor and conformal field variables) and 'geometric' (given by the Levi-Civita type canonical transformation to the action-angle variables which determine initial cosmological states with the arrow of the proper time measured by the watch of an observer in the comoving frame). 'Big Bang', the Hubble evolution, and creation of 'dynamic' particles by the 'geometric' vacuum are determined by 'relations' between the dynamic and geometric systems as pure relativistic phenomena, like the Lorentz-type 'relation' between the rest and comoving frames in special relativity