Effective Gravitational Theory In Lorentz Breaking Background

General relativity can be regarded as a sort of gauge theory. It could therefore be described with the theory of fiber bundle. Its structure group is the space-time symmetry group while its manifold is general pseudo-Riemannian manifold. The principal bundle is the frame bundle and the associated bundle is the tangent bundle.Utiyama proposed this point of view in 1955.It was thoroughly examined and developed by Kibble etc. later.While Lorentz group as the space-time symmetry group are probably broken. In 2006, Cohen and Glashow proposed the concept under the broken Lorentz group.In the article, we will at first introduce the concept of the space-time gauge theory with Lorentz group being the symmetry group. We will also compare with the internal gauge theory.Then, we will use SIM(2) group as the space-time symmetry group and construct its space-time gauge theory. We find that the non-zero contorsion will contribute to a non-zero matter-like field.Finally, we will solve the vacuum Einstein’s equation utilizing SIM(2) gauge theory and analyze its properties.