Probing the electroweak symmetry breaking history with gravitational waves

We perform three dimensional lattice simulation of the electroweak symmetry breaking process through two-step vacuum-like phase transitions with one step being first-order. Our results show that: 1) when the electroweak symmetry breaking is driven by the beyond Standard Model theories through the Higgs-portal, the gravitational wave spectra produced from the phase transitions are of broken power-law shape; 2) when the electroweak symmetry breaking is induced by a first-order phase transition of a high-scale theory respecting the global U(1) symmetry, cosmic strings can form and then decay through particle radiation. The two scenarios can be distinguished through probing the stochastic gravitational wave backgrounds. Our study suggests that the stochastic gravitational wave backgrounds provide an alternative way to probe the beyond Standard Model theories relevant to the electroweak symmetry breaking in the early Universe.