  In this work we discuss two different phases of a complex singlet extension
of the Standard Model (SM) together with an extension that also includes new
fermion fields, in particular, a Majoron model equipped with an inverse seesaw
mechanism. All considered scenarios contain a global $\mathrm{U}(1)$ symmetry
and allow for first-order phase transitions while only two of them are strong
enough to favour the detection of primordial gravitational waves (GWs) in
planned experiments such as LISA. In particular, this is shown to be possible
in the singlet extension with a non vanishing real VEV at zero temperature and
also in the model with extra fermions. In the singlet extension with no
additional fermions, the detection of GWs strongly depends on the
$\mathrm{U}(1)$ symmetry breaking pattern of the scalar potential at zero
temperature. We study for the first time the impact of the precision in the
determination of the SM parameters on the strength of the GWs spectrum. It
turns out that the variation of the SM parameters such as the Higgs boson mass
and top quark Yukawa coupling in their allowed experimental ranges has a
notable impact on GWs detectability prospects.
