  Inert Doublet Model is a minimal extension of the Standard Model with the
second scalar doublet that may provide a Dark Matter candidate. In this paper
we consider different variants of the evolution of the Universe after
inflation, that lead towards the Inert phase today. We extend our previous
analysis, in particular by discussing the co-existence of minima and providing
numerical examples of the evolutions of the mass parameters for the different
types of the history of the Universe. We take into account the existing
constraints, including the relict density data.
