  We discuss the gravitational wave (GW) spectra predicted from the electroweak
scalegenesis of the Higgs portal type with a large number of dark chiral
flavors, which many flavor QCD would underlie and give the dynamical
explanation of the negative Higgs portal coupling required to trigger the
electroweak symmetry breaking. We employ the linear-sigma model as the
low-energy description of dark many flavor QCD and show that the model
undergoes ultra-supercooling due to the produced strong first-order thermal
phase transition along the (approximately realized) flat direction based on the
Gildener-Weinberg mechanism. Passing through evaluation of the bubble
nucleation/percolation, we address the reheating and relaxation processes,
which are generically non-thermal and nonadiabatic. Parametrizing the reheating
epoch in terms of the e-folding number, we propose proper formulae for the
redshift effects on the GW frequencies and signal spectra. It then turns out
that the ultra-supercooling predicted from the Higgs-portal scalegenesis
generically yields none of GW signals with the frequencies as low as nano Hz,
unless the released latent heat is transported into another sector other than
reheating the universe. Instead, models of this class prefer to give the higher
frequency signals and still keeps the future prospected detection sensitivity,
like at LISA, BBO, and DECIGO, etc. We also find that with large flavors in the
dark sector, the GW signals are made further smaller and the peak frequencies
higher. Characteristic phenomenological consequences related to the multiple
chiral scalars include the prediction of dark pions with the mass much less
than TeV scale, which is also briefly addressed.
