Dark clouds to silver linings over the hyperchargeless scalar triplets

A real scalar triplet with zero hypercharge offers a minimal nontrivial extension of the Standard Model (SM) with a charged Higgs and a possible dark matter or custodial symmetry breaking signature. The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>Z</a:mi><a:mn>2</a:mn></a:msub></a:math>-odd inert triplet model (ITM) provides a dark matter, while the noninert Higgs triplet model (HTM) breaks the custodial symmetry, enabling rich collider signatures. Both these models also promise the viability of a first-order phase transition (FOPT). This article revisits both models under various theoretical and current experimental constraints, revealing a trade-off between DM and FOPT viability, and explores the resulting gravitational wave signals and collider prospects.