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.

中文翻译：

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协变非对易空间上的四维引力（II）

基于我们之前工作中描述的 4-dim 非对易引力模型的构建，首先，提出了对包含引力模型的协变非对易空间（模糊 4-dim de Sitter 空间）的更扩展描述，然后相应的场方程，这是在先前提出的动作变化后获得的，被提取出来。此外，还进行了初始对称性的自发破坏，这次是通过引入辅助标量场引起的，并检查了其在考虑交换极限后产生的简化理论中的含义。