Symmetries are the useful tools to explain the physical rules of the nature. On the other hand each discrepancy of them helps to concept the events and to extend the physics. We have checked some deviation from the Lorentz symmetry in the context of the Standard Model Extension (SME). We have shown that if the Lorentz violation exists, the circular polarization of the cosmic microwave background will be observed in the future. There are some percentages of the circular polarization in the pulsars’ profiles. There isn’t any theory to explain the origin and the mechanism to produce the circular polarization in the pulsars. We have calculated the photon interactions in the presence of the Lorentz violation. Using the huge magnetic fields of the pulsars and the relation between the Lorentz violation parameter (k F ) ???? and the Non-commutative parameter ? ?? we have demonstrated the production of circular polarization. Furthermore, changing the direction of the circular polarization can occur. The CPT even Lorentz violation parameter d ?? violates the CP symmetry. Electric Dipole Moment (EDM) of electron has calculated in the presence of this parameter and it has shown the electric dipole moment of the electron can be as large as 10 -14 e cm. Finally the evolution equations of the vorticities of the electrons, ions and photons in a pre-decoupling plasma are derived, in a fully inhomogeneous geometry. The maximal magnetic field induced by the total vorticity turns out to be, at most, of the order of 10 -37 G. Keywords: Lorentz invariance violation, Standard Model extension, circular polarization of Cosmic Microwave Background Radiation, Pulsars’ circular polarization, Electric Dipole Moment of Electron, Magnetic field from the pre-decoupling plasma.