  On the basis of a semi-classical analysis of vacuum energy in an expanding
spacetime, we describe a non-singular cosmological model in which the vacuum
density decays with time, with a concomitant production of matter. During an
infinitely long period we have an empty, inflationary universe, with H \approx
1. This primordial era ends in a fast phase transition, during which H and
\Lambda decrease to nearly zero in a few Planck times, with release of a huge
amount of radiation. The late-time scenario is similar to the standard model,
with the radiation phase followed by a long dust era, which tends
asymptotically to a de Sitter universe, with vacuum dominating again. An
analysis of the redshift-distance relation for supernovas Ia leads to
cosmological parameters in agreement with other current estimations.
