The theory named ‘special relativity (SR) with a preferred frame’ integrates the preferred frame into special relativity while preserving the basic symmetry of space-time that expresses itself as Lorentz invariance in the regular SR. At the cost of the right to allocate the one-way speeds of light that exist in special relativity, the synthesis of such apparently contradictory principles as the nature of the chosen frame and the theory of relativity is feasible. A degree of anisotropy of the one-way speed acquires significance in the established context of a feature of the genuinely existing anisotropy induced by the movement of an inertial frame relative to the chosen frame. The anisotropic special relativity kinematics was generated on the basis of the principles of symmetry: (1) space-time transformations between inertial frames leave the invariant equation of anisotropic light propagation and (2) a group structure has a set of transformations. Modified kinematics is applied to particle dynamics based on the modified spacetime symmetry’ principle, which enables the theory to be built along the lines of the standard theory of relativity. The theory can also be generalised to the general relativity (GR) definition, which like the traditional GR, is based on the principle of equivalence, but with the local symmetry of space-time properly modified. The chosen frame is identified with an asking frame of cosmology or the CMB frame to align the theory to the observational evidence, indicating that the theory should be applied on cosmological scales. The following applications are considered: the distribution of the CMB temperature as seen by an observer moving with respect to the CMB frame; the interactions with the CMB photons of the Ultra High Energy Cosmic Rays (UHECR); cosmological models. Applying changed SR Kinematics to the problem of measuring the distribution of the CMB temperature results in a relationship in which the angular dependence is measured. It coincides with that observed on the basis of the standard theory of relativity, but in the observer velocity, the mean temperature is corrected by the second order terms. The application of modified relativistic dynamics to the explanation of UHECR interactions with universal diffuse background radiation results in the Greisen-Zatsepin-Kuzmin (GZK) energy suppression threshold due to pion photoproduction by UHECR protons depending on the distance to the particle source (cosmological redshift ⁇ ). This impact may contribute to the interpretation of Auger’s recently published data on the UHECR mass composition. The application of the modified GR to cosmology results in a correction of the luminosity distance – redshift relation such that the deceleration parameter observed can be negative as it is derived from the data for type Ia supernovae. Within the matter-dominated cosmological model of Friedman-Robertson-Walker, the observed negative values of the deceleration parameter can be clarified. Without adding dark energies to the universe. A variety of other observations may also be well adapted to the cosmological model resulting from the GR based on the SR with a privileged frame, such as Baryon Acoustic Oscillations and Cosmic Microwave Background. The ‘relativity with a chosen frame designed to reconcile the theory of relativity with the nature of the preferred cosmological frame, thus offers explanations of both the groundbreaking SNIa data and the recently published Auger data on mass composition without the implementation of new physics and with the only new universal constant, which in all applications is within the same range.

**Author (s) Details**

**Georgy I. Burde
**Alexandre Yersin Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben- Gurion, Israel.

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