The kinematical aspect of relativistic cosmology is examined on the basis of three postulated requirements: The constancy of the velocity of light, spatial isotropy, and homogeneity. Three distinct types of cosmological models are obtained, characterized by different motions of nebulae. The metric of any universe is conformal to Minkowski space and Maxwell's equations are the same for all possible universes. In Part II, it is shown that the cosmological models are metrically, though not topologically, equivalent to those of H. P. Robertson. Next, special models are examined and their line elements brought into the conformal-Minkowskian form. The problem of the displacement of the lines of nebular spectra is discussed; formulas are obtained and applied to some special cosmological models. Finally, idealized experiments are described which indicate the physical content of the cosmological coordinates.

• Received 16 September 1945

DOI:https://doi.org/10.1103/PhysRev.68.250