  We study the gravitational waves (GWs) spectrum produced during the
electroweak phase transition in a scale-invariant extension of the Standard
Model (SM), enlarged by a dark $ U(1)_{D} $ gauge symmetry. This symmetry
incorporates a vector dark matter (DM) candidate and a scalar field (scalon).
Because of scale invariance, the model has only two independent parameters and
for the parameter space constrained by DM relic density, strongly first-order
electroweak phase transition can take place. In this model, for a narrow part
of the parameter space, DM-nucleon cross section is below the neutrino-floor
limit, and therefore, it cannot be probed by the future direct detection
experiments. However, for a benchmark point form this narrow region, we show
the amplitude and frequency of phase transition GW spectrum fall within the
observational window of space-based GW detectors such as eLISA.
