Cosmic Evolution as Inertial Motion in the Field Space of GR
  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. 
V.N. Pervushin and D.V. Proskurin