  In this article we examine the prospect of first order phase transition with
a Y=0 real $SU(2)$ triplet extension of the Standard Model, which remains odd
under $Z_2$, considering the observed Higgs boson mass, perturbative unitarity,
dark matter constraints, etc. Especially we investigate the role of
Higgs-triplet quartic coupling considering one- and two-loop beta functions and
compare the results with the complex singlet extension case. It is observed
that at the one-loop level, no solution can be found for both, demanding the
Planck scale perturbativity. However, for a much lower scale of $10^4$ GeV, the
singlet case predicts first order phase transition consistent with the observed
Higgs boson mass. On the contrary, at the two-loop, both the scenarios foresee
strongly first order phase transition consistent with the observed Higgs mass
with upper bounds of 310, 909 GeV on the triplet and singlet masses,
respectively. This puts the triplet in apparent contradiction with the observed
dark matter relic bound and thus requires additional field for that. The
preferred regions of the parameter space in both cases are identified by
benchmark points, that predict the Gravitational Waves with detectable
frequencies in the present and future experiments.
