  We assume that current state of the Universe can be described by the Inert
Doublet Model, containing two scalar doublets, one of which is responsible for
EWSB and masses of particles and the second one having no couplings to fermions
and being responsible for dark matter. We consider possible evolutions of the
Universe to this state during cooling down of the Universe after inflation. We
found that in the past Universe could pass through phase states having no DM
candidate. In the evolution via such states in addition to a possible EWSB
phase transition (2-nd order) the Universe sustained one 1-st order phase
transition or two phase transitions of the 2-nd order.
