  This manuscript deals with a model of the evolution of an event space
represented by the fundamental solution of a N-dimensional generalized
Schrodinger equation for free matter. Specifically this solution can be applied
to describe the 3D space evolution of the Universe in the forward direction in
time. The model which is based on the presented solution is close to the well
known Inflation theory, but is nonsingular, does not violate the conservation
laws and is finite throughout the whole space at any moment of time. According
to this model, the evolution progresses non-uniformly with a positive
acceleration. Moreover, the model correctly approaches Hubble's law in the
long-time limit. It is also shown that any source functions which describe
substance and its physical fields set space topology of the Universe, but do
not influence the general dynamics of its evolution.
