Cosmological phase transitions, gravitational waves and self-interacting dark matter in the singlet extension of MSSM

In the minimal supersymmetric standard model (MSSM) extended by a singlet superfield, when coupling between sector and MSSM is tiny, can be quasi dark with supersymmetry (SUSY). We investigate cosmological phenomena in this scenario obtain following observations: (i) parameter space solving small scale anomalies via self-interacting singlino matter (SIDM), first-order phase transition (FOPT) readily happen but requires rather light below MeV; (ii) The corresponding indicated FOPT SIDM partially covered detecting phase-transition gravitational waves (GWs) at near-future projects, such as LISA, TianQin Taiji. Therefore, recently developed GW astronomy could novel probe to SUSY scenario.