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We study the general NMSSM with an emphasis on the parameter regions with avery strong first-order electroweak phase transition (EWPT). In the presence ofheavy fields coupled to the Higgs sector, the analysis can be problematic dueto the existence of sizable radiative corrections. In this paper we propose asubtraction scheme that helps to circumvent this problem. For simplicity wefocus on a parameter region that is by construction hidden from the currentcollider searches. The analysis proves that (at least) in the identifiedparameter region the EWPT can be very strong and striking gravitational wavesignals can be produced. The corresponding gravitational stochastic backgroundcan potentially be detected at the planned space-based gravitational waveobservatory eLISA, depending on the specific experiment design that will beapproved.

Detectable Gravitational Waves from Very Strong Phase Transitions in the General NMSSM