  We present a class of non-supersymmetric models in which so-called critical
Higgs inflation ($\xi<100$) naturally can be realized without using specific
values for Higgs and top quark masses. In these scenarios, the Standard Model
(SM) vacuum stability problem, gauge coupling unification, neutrino mass
generation and Higgs inflation mechanism are linked to each other. We adopt in
our models Type I seesaw mechanism for neutrino masses. An appropriate choice
of the Type I Seesaw scale allows us to have an arbitrarily small but positive
value of SM Higgs quartic coupling around the inflation scale. We present a few
benchmark points where we show that the scalar spectral indices are around
0.9626 and 0.9685 for the number of e-folding $N=50$ and $N=60$ respectively.
The tensor-to-scalar ratios are order of $10^{-3}$. The running of the scalar
spectral index is negative and is order of $10^{-4}$.
