SO(2, 3) noncommutative gravity model

Abstract

In this paper the noncommutative gravity is treated as a gauge theory of the non-commutative SO(2, 3)★ group, while the noncommutativity is canonical. The Seiberg-Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are zeroth, first,.. and fourth power of the curvature tensor. Finally, we discuss physical consequences of those correction terms in the limit of big cosmological constant.