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Primordial gravitational waves from first order cosmological phase transitions has become a new cosmic frontier for probing particle physics beyond the standard model and can complement current direct searches at the energy and intensity frontier. This complementarity is most strikingly manifested by a blind spot in collider observables, which however can still lead to strong gravitational wave signals detectable by future space-based detectors. In this talk I will introduce the di-Higgs blind spot we recently discovered in the minimal extension of the SM with a new gauge singlet real scalar, and show that it generically exists in other models.