  The extension of the standard model by a real gauge singlet scalar is the
simplest but the most studied model with sometimes controversial ideas on the
ability of the model to address the dark matter and the electroweak phase
transition issues simultaneously. For this model, we obtain analytically
slightly different conditions for strongly first-order electroweak phase
transition and apply that in computation of the dark matter relic density where
the real scalar plays the role of the dark matter particle. We show that the
scalar in this model before imposing the invisible Higgs decay constraint, can
be responsible for all or part of the dark matter abundance, while at the same
time gives rise to a strongly first-order electroweak phase transition required
for the baryogenesis. When the constraints from the direct detection
experiments such as XENON100 or LUX/XENON1t are considered, the model is
excluded completely.
