I am considering Veltman's 'The Infrared - Ultraviolet Connection' addressing the issue of quadratic divergences and the related huge radiative correction predicted by the electroweak Standard Model (SM) in the relationship between the bare and the renormalized theory, commonly called 'the hierarchy problem' which usually is claimed that this has to be cured. After the discovery of the Higgs particle at CERN, which essentially completed the SM, an amazing interrelation of the leading interaction strengths of the gauge bosons, the top-quark and the Higgs boson showed up amounting that the SM allows for a perturbative extrapolation of the running couplings up to the Planck scale. The central question concerns the stability of the electroweak vacuum, which requires that the running Higgs self-coupling stays positive. Although several evaluations seem to favor the meta-stability within the experimental and theoretical parameter-uncertainties, one should not exclude the possibility that other experiments and improved matching conditions will be able to establish the absolute stability of the SM vacuum in the future. I will discuss the stable vacuum scenario and its impact on early cosmology, revealing the Higgs boson as the inflaton. It turns out that the Standard Model's presumed 'hierarchy problem' and similarly the 'cosmological constant problem' resolve themselves when we understand the SM as a low energy effective tail that is emergent from a cutoff-medium at the Planck scale. 'The Infrared - Ultraviolet Connection' conveyed by the Higgs boson mass renormalization appears in a new light when the energy dependence of the SM couplings is taken into account. The bare Higgs boson mass square then changes sign below the Planck scale where it is activating the Higgs mechanism. At the same time, it reveals that the SM towards the Planck scale is in the symmetric phase, where the Higgs potential provides a high dark energy density triggering inflation, and four heavy Higgs bosons which decay and thereby are reheating the inflated early universe.

Workshop on Naturalness, Hierarchy, and Fine Tuning, Aachen, Germany, 28 Feb 2018 - 2 Mar 2018; Acta physica Polonica / B 52(6-7), 575 - 605 (2021). doi:10.5506/APhysPolB.52.575

Published by Inst. of Physics, Jagellonian Univ., Cracow