  Special relativity (SR) with a privileged frame is a framework, which, like
the standard relativity theory, is based on the relativity principle and the
universality of the (two-way) speed of light but includes a privileged frame as
an essential element. It is developed using the following first principles: (1)
Anisotropy of the one-way speed of light in an inertial frame is due to its
motion with respect to the privileged frame; (2) Space-time transformations
between inertial frames leave the equation of anisotropic light propagation
invariant; (3) A set of the transformations possesses a group structure. The
Lie group theory apparatus is applied to define groups of transformations. The
correspondingly modified general relativity (GR), like the standard GR, is
based on the equivalence principle but with the properly modified space-time
local symmetry in which an invariant combination differs from the Minkowski
interval of the standard SR. Applying the modified GR to cosmology yields the
luminosity distance -- redshift relation corrected such that the observed
deceleration parameter can be negative as it was derived from the data for type
Ia supernovae. Thus, the observed negative values of the deceleration parameter
can be explained without introducing the dark energy. A number of other
observations, such as Baryon Acoustic Oscillations (BAO) and Cosmic Microwave
Background (CMB) also can be well fit to the cosmological model arising from
the GR based on the SR with a privileged frame.
