Dilution of Dark Matter Relic abundance due to First Order Electroweak Phase Transition

We investigate the effect of a first-order electroweak phase transition (FOEWPT), which is one of the prerequisites for electroweak baryogenesis, on the thermal relic abundance of the dark matter (DM) that freezes out before the occurrence of the phase transition in the complex singlet scalar extended $Z_3$-invariant type-II seesaw model that can simultaneously provide a DM candidate, explain the non-vanishing neutrino masses and the baryon asymmetry of the Universe. Such a phase transition around the electroweak scale leaves an impact on the relic density due to the release of entropy, particularly for a TeV-scale DM. We thus concentrate on the region of parameter space of the said model, which favors an FOEWPT in the early Universe and for which the DM is heavy such that its freeze-out temperature turns out to be larger than the phase transition temperature. We further study the dependencies of the dilution factor of the DM relic density on the model parameters, the nucleation temperature, the strength and the duration of the phase transition. Such a dilution might retrieve some of the regions of parameter space that were previously ruled out by the measured value of the DM relic density and/or the latest constraints from the DM direct-detection experiments. Furthermore, a direct connection is drawn between the dilution factor and the generation of stochastic gravitational waves as a result of an FOEWPT.