Relativity with a Preferred Frame

The theory termed 'special relativity (SR) with a preferred frame' incorporates the preferred frame into
special relativity while retaining the fundamental space-time symmetry which, in the standard SR,
manifests itself as Lorentz invariance. The synthesis of such seemingly incompatible concepts as the
existence of preferred frame and the relativity principle 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 speed 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 symmetry 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 modified kinematics is
extended to particle dynamics based on the concept of the 'modified spacetime symmetry' which
allows to develop the theory along the lines of the standard relativity theory. That concept also allows
to extend the theory to the general relativity (GR) which, like the standard GR, is based on the
equivalence principle but with the properly modified space-time local symmetry. To fit the theory to the
observational data, the preferred frame is identified with a comoving frame of cosmology or the CMB
frame which implies that the theory should be applied on cosmological scales. The following
applications are considered: the CMB temperature distribution as it is seen by a observer moving with
respect to the CMB frame; the interactions of the Ultra High Energy Cosmic Rays (UHECR) with the
CMB photons; cosmological models. Applying the modified SR Kinematics to the problem of
calculating the CMB temperature distribution yields a relation 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. Applying the modified relativistic
dynamics to describing interactions of the UHECR with universal diffuse background radiation yields
the result that the Greisen-Zatsepin-Kuzmin (GZK) threshold for the energy suppression due to pion
photoproduction by UHECR protons depends on the distance (cosmological redshift ) to the source
of particles. This effect may contribute to interpretation of the recently released Auger data on the
mass composition of UHECR. Applying the modified GR to cosmology yields the luminosity distance -
redshift relation corrected such that the observed deceleration parameter can be negative as it is
obtained from the data for type Ia supernovae. It allows to explain the observed negative values of the
deceleration parameter within the matter-dominated Friedman-Robertson-Walker cosmological model
of the universe without introducing the dark energy. A number of other observations, such as Baryon
Acoustic Oscillations and Cosmic Microwave Background, also can be well fit to the cosmological
model arising from the GR based on the SR with a privileged frame. Thus, the 'relativity with a
preferred frame', designed to reconcile the relativity principle with the existence of the cosmological
preferred frame, provides explanations of both the revolutionary SNIa data and the recently released
Auger data on the mass composition without introducing new physics and with the only new universal
constant, that is within the same range in all the applications.