  We study a singlet scalar extension of the Standard Model. The singlet scalar
is coupled non-minimally to gravity and assumed to drive inflation, and also
couple sufficiently strongly with the SM Higgs field in order to provide for a
strong first order electroweak phase transition. Requiring the model to
describe inflation successfully, be compatible with the LHC data, and yield a
strong first order electroweak phase transition, we identify the regions of the
parameter space where the model is viable. We also include a singlet fermion
with scalar coupling to the singlet scalar to probe the sensitivity of the
constraints on additional degrees of freedom and their couplings in the singlet
sector. We also comment on the general feasibility of these fields to act as
dark matter.
