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A natural fuzzyness of de Sitter space-time
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.Comment: 16 page