Special relativity with a preferred frame and the relativity principle: cosmological implications

The modern view, that there exists a preferred frame of reference related to the cosmic microwave background (CMB), is in apparent contradiction with the principles of special relativity. The purpose of the present study is to develop a counterpart of the special relativity theory that is consistent with the existence of a preferred frame but, like the standard relativity theory, is based on the relativity principle and universality of the (two-way) speed of light. The synthesis of those seemingly incompatible concepts is possible at the expense of the freedom in assigning the one-way speeds of light that exists in special relativity. In the framework developed, a degree of anisotropy of the one-way velocity acquires meaning of a characteristic of the really existing anisotropy caused by motion of an inertial frame relative to the preferred frame. The anisotropic special relativity kinematics is developed based on the first principles: (1) Space-time transformations between inertial frames leave the equation of anisotropic light propagation invariant and (2) A set of the transformations possesses a group structure. The Lie group theory apparatus is applied to define groups of space-time transformations between inertial frames. The correspondence principle, that the coordinate transformations should turn into the Galilean transformations in the limit of small velocities, and the argument, that the anisotropy parameter k in a particular inertial frame is determined by its velocity relative to the preferred frame, are used to specify the transformations. The parameter of anisotropy k becomes a variable which takes part in the transformations so that the preferred frame naturally arises as the frame with k = 0. The transformations between inertial frames obtained as the result of the analysis do not leave the interval between two events invariant but modify it by a conformal factor. Applying the consequences of the transformations to the problem of calculating the CMB temperature distribution yields an equation in which the angular dependence coincides with that obtained on the basis of the standard relativity theory but the mean temperature is corrected by the terms second order in the observer velocity. From conceptual point of view, it eliminates the inconsistency of the usual approach when formulas of the standard special relativity are applied to define effects caused by motion with respect to the preferred frame. PACS numbers: 03.30.+p, 98.80.Jk, 04.20.-q ∗Electronic address: [email protected]