  We analyze the vacuum stability in the inert Higgs doublet extension of the
Standard Model (SM), augmented by right-handed neutrinos (RHNs) to explain
neutrino masses at tree level by the seesaw mechanism. We make a comparative
study of the high- and low-scale seesaw scenarios and the effect of the Dirac
neutrino Yukawa couplings on the stability of the Higgs potential. Bounds on
the scalar quartic couplings and Dirac Yukawa couplings are obtained from
vacuum stability and perturbativity considerations. The regions corresponding
to stability, metastability and instability of the electroweak vacuum are
identified. These theoretical constraints give a very predictive parameter
space for the couplings and masses of the new scalars and RHNs which can be
tested at the LHC and future colliders. The lightest non-SM neutral CP-even/odd
scalar can be a good dark matter candidate and the corresponding collider
signatures are also predicted for the model.
