To the theory of the Universe evolution
  Self-consistent account of the most simple non-gauge vector fields leads to a
broad spectrum of regular scenarios of temporal evolution of the Universe
completely within the frames of the Einstein's General relativity. The
longitudinal non-gauge vector field is "the missing link in the chain",
displaying the repulsive elasticity and allowing the macroscopic description of
the main features of the Universe evolution. The singular Big Bang turns into a
regular inflation-like state of maximum compression with the further
accelerated expansion at late times. The parametric freedom of the theory
allows to forget the troubles of fine tuning. In the most interesting cases the
analytical solutions of the Einstein's equations are found.
