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While an additional scalar multiplet over and above the Standard Model canlead to a strong electroweak phase transition, depending on its quantumnumbers, it also potentially confronts crucial constraints from theory andexperiments. Should there exist more than one copy of such a multiplet, it ispossible to predict that number from the requirements of a strong electroweakphase transition and agreement with the latest constraints. We aim to probethis specific issue in this study in the context of $N$ degenerate scalartriplets governed by a global O$(N)$ symmetry. We fold in important constraintsfrom $h \to \gamma\gamma$ signal strength, dark matter direct detection andLandau pole behaviour. A combined analysis reveals $N \gtrsim 70$ for a strongphase transition and consistency with the constraints. We also look intopossible gravitational wave signals in the parameter regions of interest.

Limiting multiple hyperchargeless scalar triplets using electroweak phase transition and other constraints