  We describe a new phenomenon in quantum cosmology: self-organised
localisation. When the fundamental parameters of a theory are functions of a
scalar field subject to large fluctuations during inflation, quantum phase
transitions can act as dynamical attractors. As a result, the theory parameters
are probabilistically localised around the critical value and the Universe
finds itself at the edge of a phase transition. We illustrate how
self-organised localisation could account for the observed near-criticality of
the Higgs self-coupling, the naturalness of the Higgs mass, or the smallness of
the cosmological constant.
