Tripling down on the $W$ boson mass

A new precision measurement of the $W$ boson mass has been announced by the CDF collaboration, which strongly deviates from the Standard Model prediction. In this article, we study the implications of this measurement on the parameter space of the $SU(2)_L$ triplet extension (with hypercharge $Y=1$) of the Standard Model Higgs sector, focusing on a limit where the new triplet is approximate $\mathbb{Z}_2$-odd while the SM is $\mathbb{Z}_2$-even. We study the compatibility of the triplet spectrum preferred by the $W$ boson mass measured by the CDF-II experiment with other electroweak precision observables and Higgs precision data. We comprehensively consider the signals of new Higgs states at the LHC and highlighted the promising search channels. In addition, we also investigate the cosmological implications of the case in which the lightest new Higgs particle is either late decaying or cosmologically stable.