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In this article, we examine the Standard Model extended with a $Y=0$ Higgstriplet and a real singlet. We consider the Higgs triplet to be odd under the$Z_2$ symmetry, and hence the lightest stable particle from the inert tripletbecomes the dark matter candidate, whereas the real singlet is considered to beeven under the $Z_2$ symmetry. A dimension-5 effective term is introduced withthe help of a real singlet, which breaks the CP symmetry and gives anadditional source of CP-violation in the fermion sector. The phase transitionproceeds in two-steps, with the symmetry breaking in the singlet directionoccurring first and later leading to the usual electroweak symmetry breakingminima, while electroweak baryogenesis is associated with the second step. Theparameters chosen for the electroweak phase transition are found to beconsistent with the Planck scale stability and the perturbativity usingtwo-loop $\beta$-functions. The DM mass bound for inert triplet, i.e., 1.2 TeV(below which it is under abundance), also comes out to be consistent with thestrongly first-order phase transition, which was not possible solely with inerttriplet. The upper bound on the triplet mass comes out to be $\leq 3.8$ TeV,which satisfies the strongly first-order phase transition. This particularbenchmark point also satisfies the correct baryon asymmetry of the Universe$(6.13 \times 10^{-11})$, and the gravitational wave spectrum also lies withinthe detectable frequency range of LISA $(6.978 \times 10^{-4} - 1.690 \times10^{-2} )$ Hz and BBO $(2.80\times 10^{-3}-1.096)$ Hz experiments.

Exploring CP-violation in $Y=0$ inert triplet with real singlet