Abstract The extension of the Standard Model Higgs doublet with three non-zero hypercharge triplets is examined in this article. The triplets are charged under additional U (1) ₋_ -L symmetry. We investigate the stability of the electroweak vacuum both at the tree-level, and the two-loop level. It is observed that the vacuum stability can be satisfied till Planck scale using two-loop β-functions. In contrary, due to the increase in positive effect from triplet degrees of freedom, the perturbative unitarity can be satisfied only till 1012 GeV. The parameter space allowed from the Planck scale stability is checked for the strongly electroweak first-order phase transition. The model satisfies the strongly first order phase transition for the triplet bare mass parameters till TeV scale due to the enough contribution to the cubic term from the triplet degrees of freedom. It is observed that this model foresee strongly first-order phase transition for all mass ranges until the degrees of freedom becomes heavy enough to decouple from the thermal bath. The benchmark points satisfying the strongly first-order phase transition are tested for the Gravitational wave signatures. The benchmark points allowed from Planck scale stability, strongly first-order phase transition also comes out to lie in the detectable frequency range of the LISA and BBO experiments.
Jho et al. (Mon,) studied this question.