In a novel standard model extension it has been suggested that, even in the absence of right-handed neutrinos and type-I seesaw, purely triplet leptogenesis leading to baryon asymmetry of the universe can be realised by two heavy Higgs triplets which also provide type-II seesaw ansatz for neutrino masses. In this work we discuss this model for hierarchical neutrino masses in concordance with recently determined cosmologocal bounds and oscillation data including $theta_{23}$ in the second octant and large Dirac CP phases. We also address the issues on dark matter and vacuum stability of the scalar potential in a minimal extension of this model. We find that for both normal and inverted orderings the model fits the oscillation data with the sum of the three neutrino masses consistent with cosmological bounds determined from Planck satellite data. In addition using this model ansatz for CP-asymmetry and solutions of Boltzmann equations, we also show how successful prediction of baryon asymmetry emerges in the cases of both unflavoured and two-flavoured leptogeneses. With additional $Z_2$ discrete symmetry, a minimal extension of this model is shown to be capable of predicting a scalar singlet WIMP dark matter in agreement with direct and indirect observations. Whereas in the original model, the renormalization group running of the scalar potential renders it negatve leading to vacuum instability, the presence of the dark matter in the minimally extended model ensures stability. Although the combined constraints due to relic density and direct detection cross section allow this scalar singlet dark matter mass to be $m_{xi}=750$ GeV, the additional vacuum stability constraint pushes this limiting value to $m_{xi}=1.3$ TeV which is verifiable by ongoing experiments. We also dicuss constraint on the model parameters for the radiative stability of the standard Higgs mass.
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