  The nearly aligned Higgs Effective Field Theory (naHEFT) is based on the
general assumption: all deviations in the Higgs boson couplings are originated
from quantum one-loop effects of new particles that are integrated out. If the
new particles integrated out have the same non-decoupling property, physics of
the electroweak symmetry breaking can be then described by several parameters
in the naHEFT, so that there is a correlation among the Higgs boson couplings
such as $h \gamma \gamma$, $hWW$ and $hhh$ couplings. In this paper, we analyze
the strongly first-order electroweak phase transition (EWPT) with the condition
of sphaleron decoupling and the completion condition of the phase transition,
and investigate the relation among the deviations in the Higgs boson couplings
and the dynamics of the EWPTs. We also take into account the gravitational wave
spectrum as well as the primordial black hole predicted at the EWPT. We show
that if the new particles integrated out include charged scalar states future
precision measurements of the $h \gamma \gamma$ coupling can give a useful
prediction on the $hhh$ coupling to realize the strongly first-order EWPT. We
can explore the nature of EWPT and the new physics behind it by the combination
of precision measurements of various Higgs boson couplings at future collider
experiments, gravitational wave observations at future space-based
interferometers and searches for primordial black holes.
