  We propose an alternative, nonsingular, cosmic scenario based on
gravitationally induced particle production. The model is an attempt to evade
the coincidence and cosmological constant problems of the standard model
($\Lambda$CDM) and also to connect the early and late time accelerating stages
of the Universe. Our space-time emerges from a pure initial de Sitter stage
thereby providing a natural solution to the horizon problem. Subsequently, due
to an instability provoked by the production of massless particles, the
Universe evolves smoothly to the standard radiation dominated era thereby
ending the production of radiation as required by the conformal invariance.
Next, the radiation becomes sub-dominant with the Universe entering in the cold
dark matter dominated era. Finally, the negative pressure associated with the
creation of cold dark matter (CCDM model) particles accelerates the expansion
and drives the Universe to a final de Sitter stage. The late time cosmic
expansion history of the CCDM model is exactly like in the standard
$\Lambda$CDM model, however, there is no dark energy. This complete scenario is
fully determined by two extreme energy densities, or equivalently, the
associated de Sitter Hubble scales connected by $\rho_I/\rho_f=(H_I/H_f)^{2}
\sim 10^{122}$, a result that has no correlation with the cosmological constant
problem. We also study the linear growth of matter perturbations at the final
accelerating stage. It is found that the CCDM growth index can be written as a
function of the $\Lambda$ growth index, $\gamma_{\Lambda} \simeq 6/11$. In this
framework, we also compare the observed growth rate of clustering with that
predicted by the current CCDM model. Performing a $\chi^{2}$ statistical test
we show that the CCDM model provides growth rates that match sufficiently well
with the observed growth rate of structure.
