  We propose a mechanism to solve the Higgs naturalness problem through a
cosmological selection process. The discharging of excited field configurations
through membrane nucleation leads to discrete jumps of the cosmological
constant and the Higgs mass, which vary in a correlated way. The resulting
multitude of universes are all empty, except for those in which the
cosmological constant and the Higgs mass are both nearly vanishing. Only under
these critical conditions can inflation be activated and create a non-empty
universe.
