  The simplest extension of the Standard Model by only one real singlet scalar
can explain the observed dark matter relic density while giving simultaneously
a strongly first-order electroweak phase transition in the early universe.
However, after imposing the invisible Higgs decay constraint from the LHC, the
parameter space of the single scalar model shrinks to regions with only a few
percent of the DM relic abundance and when adding the direct detection bound,
e.g. from XENON100, it gets excluded completely. In this paper, we extend the
Standard Model with two real guage singlet scalars, here $s$ and $s'$, and show
that the electroweak symmetry breaking may occur via different channels.
Despite very restrictive first-order phase transition conditions for the
two-scalar model in comparison to the single scalar model, there is a viable
space of parameters in different phase transition channels that simultaneously
explains a fraction or the whole dark matter relic density, a strongly
first-order electroweak phase transition and still evading the direct detection
bounds from the latest LUX/XENON experiments while respecting the invisible
Higgs decay width constraint from the LHC.
