Cosmological relativity: A special relativity for cosmology

Under the assumption that Hubble's constant H₀ is constant in cosmic time, there is an analogy between the equation of propagation of light and that of expansion of the universe. Using this analogy, and assuming that the laws of physics are the same at all cosmic times, a new special relativity, a cosmological relativity, is developed. As a result, a transformation is obtained that relates physical quantities at different cosmic times. In a one-dimensional motion, the new transformation is given by {Mathematical expression} where x and v are the coordinate and velocity, T is the cosmic time measured backward with respect to our present time T=0, tand T₀ is Hubble's time. Some consequences of this transformation are given, and its applicability limitation is pointed out.