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Classical and Quantum Gravity 27 (2010) 025004
A natural fuzzyness of de Sitter spacetime
J.-P. Gazeau1, F. Toppan

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.
1:  APC - UMR 7164 - AstroParticule et Cosmologie
Physics/General Relativity and Quantum Cosmology

Physics/High Energy Physics - Theory

Physics/Mathematical Physics

Mathematics/Mathematical Physics
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