  In light of no discovered new physics 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 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 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 with increasing number of brane
charges. Moreover, we show that for late times the inclusion of more charges is
equivalent to additional brane nucleations.
