  An extension of the Standard Model with three right-handed neutrinos and a
simple invisible axion model can account for all experimentally confirmed
signals of new physics (neutrino oscillations, dark matter and baryon
asymmetry) in addition to solving the strong CP problem, stabilizing the
electroweak vacuum and satisfying all current observational bounds. We show
that this model can also implement critical Higgs inflation, which corresponds
to the frontier between stability and metastability of the electroweak vacuum.
This leads to a value of the non-minimal coupling between the Higgs and the
Ricci scalar that is much lower than the one usually quoted in Higgs inflation
away from criticality. Then, an advantage is that the scale of perturbative
unitarity breaking on flat spacetime can be very close to the Planck mass,
where anyhow new physics is required. The higher dimensional operators are
under control in this inflationary setup. The dependence of the cutoff on the
Higgs background is also taken into account as appropriate when the Higgs is
identified with the inflaton. Furthermore, critical Higgs inflation enjoys a
robust inflationary attractor that makes it an appealing setup for the early
universe. In the proposed model, unlike in the Standard Model, critical Higgs
inflation can be realized without any tension with the observed quantities,
such as the top mass and the strong coupling.
