Semi-classical Universe Near Initial Singularity
  The properties of the quantum universe on extremely small spacetime scales
are studied in the semi-classical approach to the well-defined quantum model.
It is shown that near the initial cosmological singularity point quantum
gravity effects ~ h exhibit themselves in the form of additional matter source
with the negative pressure and the equation of state as for ultrastiff matter.
The analytical solution of the equations of theory of gravity, in which matter
is represented by the radiation and additional matter source of quantum nature,
is found. It is shown that in the stage of the evolution of the universe, when
quantum corrections ~ h dominate over the radiation, the geometry of the
universe is described by the metric which is conformal to a metric of a unit
four-sphere in a five-dimensional Euclidean flat space. In the radiation
dominated era the metric is found to be conformal to a unit hyperboloid
embedded in a five-dimensional Lorentz-signatured flat space. The origin of the
universe can be interpreted as a quantum transition of the system from the
region in a phase space with a trajectory in imaginary time into the region,
where the equations of motion have the solution in real time. Near the boundary
between two regions the universe undergoes almost an exponential expansion
which passes smoothly into the expansion under the action of radiation
dominating over matter. As a result of such a quantum transition the geometry
of the universe changes. This agrees with the hypothesis about the possible
change of geometry after the nucleation of expanding universe from `nothing'.
