Noncommutative gravity via SO(2;3) noncommutative Gauge theory

Abstract

In this paper the noncommutative gravity is treated as a gauge theory of the noncommutative SO(2; 3)* group on the noncommutative space with the constant noncommutativity. The enveloping algebra approach and the Seiberg-Witten map are used to relate noncommutative and the commutative gauge theory. By combining different actions a noncommutative gravity model is constructed in such a way that the cosmological constant term is not present in the commutative limit, but it is generated by the noncommutativity and it appears in the higher order expansion. We calculate the second order correction to this model and obtain terms that are zero-th, first, . . . and fourth power of the curvature tensor. Finally, we discuss physical consequences of those correction terms in the low energy limit.