Four-Dimensional Gravity on a Covariant Noncommutative Space (II)

TL;DR

This paper extends a 4-dimensional noncommutative gravity model by describing a fuzzy de Sitter space, deriving field equations, and analyzing symmetry breaking effects in the commutative limit.

Contribution

It provides a detailed construction of a covariant noncommutative space and explores the implications of symmetry breaking via an auxiliary scalar field.

Findings

Derived field equations for the noncommutative gravity model

Analyzed symmetry breaking effects in the commutative limit

Extended the description of fuzzy 4-dimensional de Sitter space

Abstract

Based on the construction of the 4-dim noncommutative gravity model described in our previous work, first, a more extended description of the covariant noncommutative space (fuzzy 4-dim de Sitter space), which accommodates the gravity model, is presented and then the corresponding field equations, which are obtained after variation of the previously proposed action, are extracted. Also, a spontaneous breaking of the initial symmetry is performed, this time induced by the introduction of an auxiliary scalar field, and its implications in the reduced theory, which is produced after considering the commutative limit, are examined.