  We explore the possibility of describing our universe with a
singularity--free, closed, spatially homogeneous and isotropic cosmological
model, using only general relativity and a suitable equation of state which
produces an inflationary era. A phase transition to a radiation--dominated era
occurs as a consequence of boundary conditions expressing the assumption that
the temperature cannot exceed the Planck value. We find that over a broad range
of initial conditions, the predicted value of the Hubble parameter is
approximately $47$ km$\cdot$~s$^{-1}\cdot$~Mpc$^{-1}$. Inflation is driven by a
scalar field, which must be conformally coupled to the curvature if the
Einstein equivalence principle has to be satisfied. The form of the scalar
field potential is derived, instead of being assumed a priori.
