Higgs boson and top quark masses as tests of electroweak vacuum stability

The measurements of the Higgs boson and top-quark masses can be used to extrapolate the Standard Model Higgs potential at energies up to the Planck scale. Adopting a next-to-next-to-leading-order renormalization procedure, we (i) find that electroweak vacuum stability is at present allowed and discuss the associated theoretical and experimental errors and the prospects for its future tests, (ii) determine the boundary conditions allowing for the existence of a shallow false minimum slightly below the Planck scale, which is a stable configuration that might have been relevant for primordial inflation, and (iii) derive a conservative upper bound on type-I seesaw right-handed neutrino masses, following from the requirement of electroweak vacuum stability.