# Lorentz Violation by the Preferred Frame Effects and Cosmic and Gamma Ray Propagation

## Abstract

**:**

## 1. Introduction

## 2. Special Relativity

#### 2.1. Kinematics

#### 2.2. Free Particle Dynamics

## 3. Electromagnetic Field Dynamics

## 4. Electromagnetic Waves

## 5. Gamma-Ray Propagation

#### 5.1. Attenuation due to the Pair-Production Process

#### 5.2. Attenuation due to Other Processes

#### 5.2.1. Attenuation Processes

#### 5.2.2. The Preferred Frame Effects

#### 5.3. Astrophysical Tests for Vacuum Dispersion and Vacuum Birefringence

## 6. Discussion

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | For a discussion of the one-way vs. two-way speed of light issue and the related issues of conventionality of simultaneity and clock synchronization, see, e.g., [30,31,32,33,34,35,36,37]; a discussion of those issues in the context of the ‘relativity with a preferred frame’ can be found in [27,38]. Here, it is only worth noting that the transformations derived in the present framework differ conceptually from other transformations incorporating the anisotropy of the one-way speed of light that are repeatedly derived in the literature (e.g., [30,31,32,33]). In the latter, the anisotropy is a feature that emerges due to changing the synchronization procedure, which is equivalent to a change of coordinates, while, in the present framework, the anisotropy is governed entirely by a physical law. |

2 | |

3 | It should be noted in this connection that, in the cosmological context, the rest frame is defined by the large-scale structure; in particular, when the terms ’rest frame’ or ’CMB frame’ are used in cosmological applications, the frame more or less coinciding with our galaxy is meant. Thus, using the terms ’rest frame’ or ’CMB frame’ in that context inevitably implies the space (and time) averaging over the scales on which the assumptions of homogeneity and isotropy accepted in the cosmological models are valid. The same is implied for the theories treating propagation of astroparticles on cosmological scales, moreover that those theories should include effects of the cosmological expansion which are calculated on the basis of homogeneous and isotropic cosmological models [47]. Therefore, the experiments on the solar system scale intended to detect phenomena related to motion of the Earth, as, for example, asymmetry of lifetimes of particles parallel and antiparallel to the direction of motion of the Earth with respect to the CMB frame [44], are irrelevant to the frameworks (such as the present one) designed to describe phenomena on cosmological scales. |

4 |

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**Figure 1.**The dependence of $\frac{dl\left(z\right)}{dz}$ (multiplied by ${H}_{0}$) on z for the concordance model with ${\mathsf{\Omega}}_{M}=0.31$ (solid) and for the cosmological model, based on ‘relativity with a preferred frame’ [28], with ${\mathsf{\Omega}}_{M}=1$, $b=-0.672$ (dashed) and ${\mathsf{\Omega}}_{M}=0.5$, $b=-0.495$ (dotted) where the values of the parameters ${\mathsf{\Omega}}_{M}$ and b are chosen from those consistent with both the SNIa and BAO data (see [28]).

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Burde, G.I.
Lorentz Violation by the Preferred Frame Effects and Cosmic and Gamma Ray Propagation. *Galaxies* **2021**, *9*, 119.
https://doi.org/10.3390/galaxies9040119

**AMA Style**

Burde GI.
Lorentz Violation by the Preferred Frame Effects and Cosmic and Gamma Ray Propagation. *Galaxies*. 2021; 9(4):119.
https://doi.org/10.3390/galaxies9040119

**Chicago/Turabian Style**

Burde, Georgy I.
2021. "Lorentz Violation by the Preferred Frame Effects and Cosmic and Gamma Ray Propagation" *Galaxies* 9, no. 4: 119.
https://doi.org/10.3390/galaxies9040119