  In the Emergent scenario, the Universe should evolve from a non-singular
state replacing the typical singularity of General Relativity, for any initial
condition. For the scalar field model in [1] we show that only a subset of
initial conditions leads to emergence, either from a static state (an Einstein
model), or from a de Sitter state.
  Assuming a scenario based on CDM interacting with a Dark Energy fluid, we
show that in general flat and open models expand from a non-singular unstable
de Sitter state at high energies; for closed models this state is a transition
phase with a bounce. A subset of these models are qualitatively in agreement
with the observable Universe, accelerating at high energies, going through a
matter-dominated decelerated era, then accelerating toward a de Sitter phase.
