  Probing the Higgs potential and new physics behind the electroweak symmetry
breaking is one of the most important issues of particle physics. In
particular, nature of electroweak phase transition is essential for
understanding physics at the early Universe, such that the strongly first order
phase transition is required for a successful scenario of electroweak
baryogenesis. The strongly first order phase transition is expected to be
tested by precisely measuring the triple Higgs boson coupling at future
colliders like the International Linear Collider. It can also be explored via
the spectrum of stochastic gravitational waves to be measured at future
space-based interferometers such as eLISA and DECIGO. We discuss
complementarity of both the methods in testing the strongly first order phase
transition of the electroweak symmetry in models with additional isospin
singlet scalar fields with and without classical scale invariance. We find that
they are synergetic in identifying specific models of electroweak symmetry
breaking in more details.
