  The study of interactions between dark matter and the Higgs field opens an
exciting connection between cosmology and particle physics, since such
scenarios can impact the features of dark matter as well as interfering with
the spontaneous breaking of the electroweak symmetry. Furthermore, such
Higgs-portal models of dark matter should be suitably harmonised with the
various epochs of the universe and the phenomenological constraints imposed by
collider experiments. At the same time, the prospect of a stochastic
gravitational wave background offers a promising new window into the primordial
universe, which can complement the insights gained from accelerators. In this
study, we examined whether gravitational waves can be generated from a
curvature-induced phase transition of a non-minimally coupled dark scalar field
with a portal coupling to the Higgs field. The main requirement is that the
phase transition is of first order, which can be achieved through the
introduction of a cubic term on the scalar potential and the sign change of the
curvature scalar. This mechanism was investigated in the context of a dynamical
spacetime during the transition from inflation to kination, while also
considering the possibility for inducing electroweak symmetry breaking in this
manner for a sufficiently low reheating temperature when the Higgs-portal
coupling is extremely weak. We considered a large range of inflationary scales
and both cases of positive and negative values for the non-minimal coupling,
while taking into account the bound imposed by Big Bang Nucleosythesis. The
resulting gravitational wave amplitudes are boosted by kination and thus
constrain the parameter space of the couplings significantly. Even though the
spectra lie at high frequencies for the standard high inflationary scales,
there are combinations of parameter space where they could be probed with
future experiments.
