  The identification of a cosmic scale function with the volume integral of a
spacelike hypersurface defines the cosmic evolution in General Relativity as a
collective motion along a geodesic in the field space of the metric components,
considered as the coset of the affine group over the Lorentz one.
  The Friedmann equations are derived out of the homogeneous approximation by
the Gibbs averaging exact equations over the relative constant spatial volume.
  A direct correspondence between the collective cosmic motion and Special
  Relativity is established, to solve the problem of time and energy by analogy
with the solution of this problem for a relativistic particle by Poincare and
Einstein.
  A geometrical time interval is introduced into quantum theory of the
relativistic collective motion by the canonical Levi-Civita -- type
transformation in agreement with the correspondence principle with quantum
field theory. In this context the problem of quantum cosmological creation of
visible matter is formulated.
  We show that latest observational data can testify to the relative
measurement standard, and the cosmic evolution as an inertial motion along
geodesic in the field space.
