Electroweak phase transition in the 2HDM: Collider and gravitational wave complementarity

The knowledge of the Higgs potential is crucial for understanding origin mass and thermal history our Universe. We show how collider measurements observations stochastic gravitational wave signals can complement each other to explore multiform scalar in two doublet model (2HDM). Accounting theoretical current experimental constraints, we analyze key ingredients shape triggering transmutation phase transition, from smooth crossover strong first-order transition (${\ensuremath{\xi}}_{c}>1$), focusing on barrier formation upliftment true vacuum. In particular, observe that ${\ensuremath{\xi}}_{c}>1$ regime favored lower masses, rendering extra motivation searches. contrast dominant at HL-LHC (high-luminosity LHC) with observable LISA. obtain will be able cover a vast range parameter space, decays heavy fermions $(H,A,{H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}tt,tb)$ being most promising smoking gun signature electroweak 2HDM.