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

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