Lorentz-Violating Electrodynamic In Static De Sitter Space-time

Recently, the luminosity observations of the farthest supernovas [1,2,3,4] indicate that our universe is accelerated expanding , asymptotic de Sitter (dS)[5] with a positive cosmological constant. In the early universe, existing cosmological constant also provides an intriguing idea, inflationary cosmology, to fix long-standing cosmological problems in the Big-bang scenario. The fact our universe is accelerated expanding indicates that there is a mysterious anti-gravity which was called as "dark energy" [6,7,8,9]. "dark energy" was first introduced by Einstain for the purpose of obtaining a static homogeneous universe, it is coincided with the cosmological constant term in Einstain's gravitational field equation. In 1917, de Sitter obtained a static solution of the equation, the corresponding space-time which was named as de Sitter space-time is the 4-d maximal symmetric space-time with a positive constant curvature. However, when Edwin Hubble found that our universe was expanding in 1926, physicists lost there interesting on this static homogeneous cosmological model. Einstain once said that the cosmological constant was the biggest mistake he made in his whole life, but now the biggest mistake maybe become a biggest discovery. When the abnormal press produced by "dark energy" overcome the gravitational press, the universe cannot but accelerated expanding asymptotic de Sitter universe, so it is reasonable to believe that it should be important to research the electrodynamics in de Sitter space-time.In another way, since Minkowski matric was not the exact depiction of space-time, the important concomitant problem is that some fundamental properties of Minkowski space-time maybe not remained in de Sitter space-time, the most important property of Minkowski space-time is Lorentz symmetry. Lorentz invariance is one of the most great discoveries of physics in the history of physics and has been confirmed to ever greater precision. Most of the evidence comes from short distance tests. However there are plenty of signs that something strange may happen at large distance (for example,dark energy), where the constraints on Lorentz symmetry are much weaker. It is reasonable that many researchers are interesting in Lorentz violation from various points of views [24, 25, 26, 27, 28]. They pointed out that Lorentz invariance can be viewed as...