Prospects of a Strong first-order Electroweak Phase Transition in the $Z_3$-NMSSM

We have studied the viability and possible patterns of a strong first-order electroweak phase transition (SFOEWPT) within the $Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model (NMSSM), in view of the latest experimental results from the dark matter (DM) sector, Higgs sector and the searches of the lighter chargino and neutralinos at the Large Hadron Collider (LHC). We show that the region of parameter space with relatively small $\mu_\mathrm{eff}$ that favors an SFOEWPT has started to get excluded from the searches at the LHC and various DM experiments. However, there still remain phenomenologically much involved and compatible regions for an SFOEWPT that are yet not sensitive to the latest LHC and DM searches. We further estimate the production of stochastic gravitational waves (GW) from an SFOEWPT within and without the bag model and the prospects of detecting such signals at various future/proposed GW experiments.