Abstract: Based on the anisotropies of CMB (Cosmic Microwave Background Radiation, CMB) on the large scale and Mach's principle,this paper proposed that the Lorentz invariance is violated from the length scale of galaxy. SIM(2) gauge theory was taken as an example of such motivation to illustrate the so called dark matter effect,the deviation of astronomical observation from Newton-Einstein prediction, which can be emerged from the accumulated Lorentz violation effect on the short scale. SIM(2) gauge theory was analyzed and 8 additional constrain equations were obtained in addition to the equation of motion, while the independent components of contorsion were also reduced to 8. It can lead us to the conclusion that the contorsion is non-trivial and can contribute an
effective energy-momentum distribution even in the region devoid of matter. Finally, the cylindrical symmetrized solution of metric under weak field expansion was given and its property was analyzed.

Key words: SIM(2) group, Lorentz breaking, gravitational gauge theory, contorsion