Possible explanations for fine-tuning of the universe

Abstract

The Froggatt–Nielsen mechanism and the multilocal field theory are interesting and promising candidates for solving the naturalness problem in the universe. These theories are based on the different physical principles: The former assumes the microcanonical partition function [Formula: see text], and the latter assumes the partition function [Formula: see text] where [Formula: see text] is the multilocal action [Formula: see text] Our main purpose is to show that they are equivalent in the sense that they predict the same fine-tuning mechanism. In order to clarify our argument, we first study (review) the similarity between the Froggatt–Nielsen mechanism and statistical mechanics in detail, and show that the dynamical fine-tuning in the former picture can be understood completely in the same way as the determination of the temperature in the latter picture. Afterward, we discuss the multilocal theory and the equivalence between it and the Froggatt–Nielsen mechanism. Because the multilocal field theory can be obtained from physics at the Planck/String scale, this equivalence indicates that the microcanonical picture can also originate in such physics. As a concrete example, we also review the IIB matrix model as an origin of the multilocal theory.