Noncommutative de Sitter and FRW spaces

TL;DR

This paper constructs various fuzzy four-dimensional de Sitter spaces using noncommutative geometry, analyzing their algebraic structures and differential calculi, all converging to classical de Sitter space in the commutative limit.

Contribution

It introduces multiple models of fuzzy de Sitter space within the noncommutative frame formalism, highlighting their algebraic differences and classical limits.

Findings

Different noncommutative algebras for fuzzy de Sitter spaces are derived.

The differential calculi for these spaces show significant variations.

All models reduce to classical de Sitter space in the commutative limit.

Abstract

Several versions of fuzzy four-dimensional de Sitter space are constructed using the noncommutative frame formalism. Although all noncommutative spacetimes which are found have commutative de Sitter metric as a classical limit, the algebras and the differential calculi which define them have many differences which we derive and discuss.