Fock-Lorentz transformations and time-varying speed of light

The theory of relativity was built up on linear Lorentz transformation. However, in his fundamental work "Theory of Space, Time and Gravitation" V.A.Fock shows that the general form of the transformation between the coordinates in the two inertial frames could be taken to be linear fractional. The implicit form of this transformation contains two constants of different space-time dimensions. They can be reduced to the constant "c" with the dimension of speed ("speed of light"), and to the constant "R" with the dimension of length (an invariant radius of the visible part of the Universe). The geometry of the "light cones" shows that "R" is a fundamental constant, but "c" depends on the time of transformation.