Abstract
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.
Highlights
The paradigm of symmetry underlies the construction of the Standard Model and General Relativity (SM+GR) and arguably, the most successful scientific effective field theory ever created
We describe a new phenomenon in quantum cosmology: self-organised localisation
The Self-Organised Localisation (SOL) reasoning is that some Effective Field Theories (EFT) parameters, which are functions of scalar fields belonging to an underlying theory, are attracted towards their critical values as the result of the evolution during inflation of the fields governing the dynamics of the corresponding quantum phase transition
Summary
The paradigm of symmetry underlies the construction of the Standard Model and General Relativity (SM+GR) and arguably, the most successful scientific effective field theory ever created. An obvious difference with cosmology is that in the laboratory one has the freedom to increase or decrease temperatures, background fields, or other parameters at will, and sit as close to, or far from, the critical points of classical or quantum phase transitions as desired. We find that, under circumstances which are not atypical, inflation in general relativity, quantum fluctuations of scalar fields seeded by the inflating geometry and the discontinuities present at a quantum critical point conspire in a special interplay that leads to a universal phenomenon. The SOL reasoning is that some EFT parameters, which are functions of scalar fields belonging to an underlying theory, are attracted towards their critical values as the result of the evolution during inflation of the fields governing the dynamics of the corresponding quantum phase transition. The appendix, written in a self-contained form, outlines some general properties of the stochastic equation and gives a compendium of analytical solutions
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