Interplay among gravitational waves, dark matter and collider signals in the singlet scalar extended type-II seesaw model

We study the prospect of simultaneous explanation of tiny neutrino masses, dark matter (DM), and the observed baryon asymmetry of the Universe in a $Z_3$-symmetric complex singlet scalar extended type-II seesaw model. The complex singlet scalar plays the role of DM. Analyzing the thermal history of the model, we identify the region of the parameter space that can generate a first-order electroweak phase transition (FOEWPT) in the early Universe, and the resulting stochastic gravitational waves (GW) can be detected at future space/ground-based GW experiments. First, we find that light triplet scalars do favor an FOEWPT. In our study, we choose the type-II seesaw part of the parameter space in such a way that light triplet scalars, especially the doubly charged ones, evade the strong bounds from their canonical searches at the Large Hadron Collider (LHC). However, the relevant part of the parameter space, where FOEWPT can happen only due to strong SM doublet-triplet interactions, is in tension with the SM-like Higgs decay to a pair of photons, which has already excluded the bulk of this parameter space. On the other hand, the latest spin-independent DM direct detection constraints from XENON-1T and PANDA-4T eliminate a significant amount of parameter space relevant for the dark sector assisted FOEWPT scenarios, and it is only possible when the complex scalar DM is significantly underabundant. In short, we conclude from our analysis that the absence of new physics at the HL-LHC and/or various DM experiments in the near future will severely limit the prospects of detecting a stochastic GW at future GW experiments and will exclude the possibility of electroweak baryogenesis within this model.