  A new kind of accelerating flat model with no dark energy that is fully
dominated by cold dark matter (CDM) is investigated. The number of CDM
particles is not conserved and the present accelerating stage is a consequence
of the negative pressure describing the irreversible process of gravitational
particle creation. A related work involving accelerating CDM cosmology has been
discussed before the SNe observations [Lima, Abramo & Germano, Phys. Rev. D53,
4287 (1996)]. However, in order to have a transition from a decelerating to an
accelerating regime at low redshifts, the matter creation rate proposed here
includes a constant term of the order of the Hubble parameter. In this case,
$H_0$ does not need to be small in order to solve the age problem and the
transition happens even if the matter creation is negligible during the
radiation and part of the matter dominated phase. Therefore, instead of the
vacuum dominance at redshifts of the order of a few, the present accelerating
stage in this sort of Einstein-de Sitter CDM cosmology is a consequence of the
gravitational particle creation process. As an extra bonus, in the present
scenario does not exist the coincidence problem that plagues models with
dominance of dark energy. The model is able to harmonize a CDM picture with the
present age of the universe, the latest measurements of the Hubble parameter
and the Supernovae observations.
