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

TL;DR

This paper develops a modified special relativity theory incorporating a preferred frame related to the CMB, maintaining the relativity principle and invariance of light speed, and explores its cosmological implications.

Contribution

It introduces an anisotropic special relativity framework consistent with a preferred frame and applies Lie group theory to derive transformation laws and cosmological effects.

Findings

Angular dependence of CMB temperature matches standard relativity

Mean temperature correction is second order in observer velocity

Eliminates inconsistency in applying standard relativity formulas to a preferred frame

Abstract

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 (\textit{two-way}) speed of light. 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. 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.