We study the standard model (SM) in its full perturbative validity range
between ΛQCD and the U(1)Y Landau pole, assuming that a yet unknown
gravitational theory in the UV does not introduce additional particle
thresholds, as suggested by the tiny cosmological constant and the absence of
new stabilising physics at the EW scale. We find that, due to dimensional
transmutation, the SM Higgs potential has a global minimum at 10^26 GeV,
invalidating the SM as a phenomenologically acceptable model in this energy
range. We show that extending the classically scale invariant SM with one
complex singlet scalar S allows us to: (i) stabilise the SM Higgs potential;
(ii) induce a scale in the singlet sector via dimensional transmutation that
generates the negative SM Higgs mass term via the Higgs portal; (iii) provide a
stable CP-odd singlet as the thermal relic dark matter due to CP-conservation
of the scalar potential; (iv) provide a degree of freedom that can act as an
inflaton in the form of the CP-even singlet. The logarithmic behaviour of
dimensional transmutation allows one to accommodate the large hierarchy between
the electroweak scale and the Landau pole, while understanding the latter
requires a new non-perturbative view on the SM.Comment: 15 pages, 9 figures. Final version to be published in Physical Review
