  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.
