  In the present lore of cosmology, matter and space-time emerged from a
singularity and evolved through four different regimes: inflation, radiation,
dark matter and dark energy dominated eras. In the radiation and dark matter
dominated stages, the expansion of the Universe decelerates while the inflation
and dark energy eras are accelerating regimes. So far there is no clear cut
connection between these accelerating periods. More intriguing, the substance
driving the present accelerating stage remains a mystery, and the best
available candidate (vacuum energy density) is plagued with the coincidence and
cosmological constant problems. In this paper we overcome such problems through
an alternative cosmic scenario based on gravitationally-induced particle
production. The model proposed here is non-singular with the space-time
emerging 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 (Parker's theorem). Next, the radiation
becomes subdominant with the Universe entering in the cold dark matter
dominated era. Finally, the negative pressure associated with the creation of
cold dark matter particles accelerates the expansion and drives the Universe to
a final de Sitter stage. The late time cosmic expansion history is exactly like
in the standard LCDM model, however, there is no dark energy. The model evolves
between two limiting (early and late time) de Sitter regimes. Our scenario is
fully determined by two extreme energy densities, or equivalently, the
associated de Sitter Hubble scales connected by 122 orders of magnitude.
