  After decades of successful hot big-bang paradigm, Cosmology still lacks a
framework in which the early inflationary phase of the universe smoothly
matches the radiation epoch and evolves to the present `quasi' de Sitter
spacetime. No less intriguing is that the current value of the effective vacuum
energy density is vastly smaller than the value that triggered inflation. In
this Essay we propose a new class of cosmologies capable of overcoming, or
highly alleviating, some of these acute cosmic puzzles. Powered by a decaying
vacuum energy density, the spacetime emerges from a pure nonsingular de Sitter
vacuum stage, "gracefully" exits from inflation to a radiation phase followed
by dark matter and vacuum regimes, and, finally, evolves to a late time de
Sitter phase.
