Probing the electroweak symmetry breaking history with Gravitational waves

We perform a three dimensional lattice simulation of the electroweak symmetry breaking process through a two-step phase transition, where one of the two steps is a first order phase transition. Our results show that: 1) when the electroweak symmetry breaking is driven by the beyond Standard Model sector around $\sim \mathcal{O}(10^{2-3})$ GeV, the gravitational wave spectra produced from the phase transitions are of broken power-law double-peak shapes; 2) when the electroweak symmetry breaking is induced by a first-order phase transition of a high-scale global U(1) theory, cosmic strings can form and then disappear through particle radiation, and the yielded gravitational wave spectra are of plateau shapes. The two scenarios can be distinguished through probing gravitational wave spectra. Our study suggests that the stochastic gravitational waves provide an alternative way to probe the beyond Standard Model sector relevant to the electroweak symmetry breaking pattern in the early Universe.