  The solution for an inflationary universe without singularities is derived
from the Einstein-Lemaitre equations. The present state of the universe evolved
from a steady state solution for a tiny, but classical micro-universe with
large cosmological constant or large equivalent vacuum energy density and with
an equal energy density of radiation and/or some kind of relativistic
primordial matter in the infinite past. An instability of this state outside
the quantum regime caused a "soft bang" by triggering an expansion that
smoothly started with zero expansion rate, continuously increased, culminated
in an exponentially inflating phase and ended through a phase transition, the
further evolution being a Friedmann-Lemaitre evolution as in big bang models.
As a necessary implication of the model the universe must be closed. All other
parameters of the model are very similar to those of big bang models and comply
with observational constraints.
