Synergy between measurements of gravitational waves and the triple-Higgs coupling in probing the first-order electroweak phase transition

Probing the Higgs potential and new physics behind the electroweak symmetry breaking is one of the most important issues of particle physics. In particular, the nature of the electroweak phase transition is essential for understanding the physics of 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 the 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 detail.