E(2) Gravitational Gauge Theory

General relativity has been tested by numerous experiments for more than one hundred years.All these tests show that general relativity is strictly exact within the solar system.While some astronomical phenomena occurring in the larger scale than solar system are obviously against general relativity.At present,the dark matter hypothesis plays a central role on explanations of the deviations between the general relativity and astronomical observations.However,no dark matter particle has been conclusively identified.Lorentz symmetry,as one of the most exact symmetries of Nature,have been challenged by numerous experiments.There is no doubt that Lorentz symmetry is satisfied under the solar system scale.But the dipole anomaly of the Cosmic Microwave Background in the power spectrum may indicate that there exists a rest frame of the Cosmic Microwave Background which breaks Lorentz invariance.That is to say,the Lorentz symmetry is violated totally at the cosmological scale.In fact the Lorentz violation has been researched by a variety of scientists for many years.In this paper,we suppose Lorentz symmetry starts to be violated partly from the scale of galaxy.By adding constraints,space-time symmetry group is limited to E(2)group which is one of subgroups in the Very Special Relativity(VSR),and E(2)group is taken as space-time gauge group to construct the corresponding gauge theory as effective gravitation theory at large scale.We can conclude that contortion is not trivial when matter source is ordinary scalar matter source.The existence of non-trivial contortion which can provide effective energy-momentum tensor distribution is likely to contribute a part of dark matter effect.