Numerical study of a cosmological relaxation model of the Higgs boson mass

In light of no new physics being discovered at the LHC, ideas which tackle the hierarchy problem without novelties around the TeV scale must be taken seriously. Such is a cosmological relaxation model of the Higgs boson mass, proposed in the pre-LHC era, which does not rely on new physics below the Planck scale. This scenario introduces a different notion of naturalness according to which the vacuum with a small expectation value of the Higgs field corresponds to an infinitely enhanced entropy point of the vacuum landscape that becomes an attractor of cosmological inflationary evolution. In this framework we study numerically the evolution of the Higgs vacuum expectation value (VEV). We model the inflationary vacuum-to-vacuum transitions that are triggered by nucleation of branes charged under three-form fields as a random walk. In particular, we investigate the impact of the number of coupled three-forms on the convergence rate of the Higgs VEV. We discover an enhanced rate when increasing the number of brane charges. Moreover, we show that for late times the inclusion of more charges is equivalent to additional brane nucleations.