Strong phase transition, dark matter and vacuum stability from simple
  hidden sectors
  Motivated by the possibility to explain dark matter abundance and strong
electroweak phase transition, we consider simple extensions of the Standard
Model containing singlet fields coupled with the Standard Model via a scalar
portal. Concretely, we consider a basic portal model consisting of a singlet
scalar with $Z_2$ symmetry and a model containing a singlet fermion connected
with the Standard Model fields via a singlet scalar portal. We perform a Monte
Carlo analysis of the parameter space of each model, and we find that in both
cases the dark matter abundance can be produced either via freeze-out or
freeze-in mechanisms, but only in the latter model one can obtain also a strong
electroweak phase transition required by the successful electroweak
baryogenesis. We impose the direct search limits and consider systematically
the possibility that the model produces only a subdominant portion of the dark
matter abundance. We also study the renormalization group evolution of the
couplings of the model to determine if the scalar sector of the model remains
stable and perturbative up to high scales. With explicit examples of benchmark
values of the couplings at weak scale, we show that this is possible. Models of
this type are further motivated by the possibility that the excursions of the
Higgs field at the end of inflation are large and could directly probe the
instability region of the Standard Model.
