A natural fuzzyness of de Sitter space-time

Abstract

A non-commutative structure for de Sitter spacetime is naturally introduced by replacing ("fuzzyfication") the classical variables of the bulk in terms of the dS analogs of the Pauli-Lubanski operators. The dimensionality of the fuzzy variables is determined by a Compton length and the commutative limit is recovered for distances much larger than the Compton distance. The choice of the Compton length determines different scenarios. In scenario I the Compton length is determined by the limiting Minkowski spacetime. A fuzzy dS in scenario I implies a lower bound (of the order of the Hubble mass) for the observed masses of all massive particles (including massive neutrinos) of spin s>0. In scenario II the Compton length is fixed in the de Sitter spacetime itself and grossly determines the number of finite elements ("pixels" or "granularity") of a de Sitter spacetime of a given curvature.