Remarks on the Propagation of Light in the Universe

Taking into account the three geometrical cases which are possible for the Universe (characterized by positive, negative or zero curvature), a fundamental formula which expresses the property of light of being independent from its source in the point where it is measured is deduced. From this formula it follows that: the classical law of composition of velocities holds true; if the velocity of light for an observer were the same in any point of the Universe, the latter must necessarily be static; the formula relating the red-shift to the expansion; the theory of the horizons and all the various and well-known results of relativistic cosmography connected to the propagation of light. Besides, the local character of special relativity is highlighted by observing that such a theory holds true only at the level of clusters of galaxies, which do not participate in the expansion of the Universe. Finally, once the Friedmann–Robertson–Walker metric is deduced, it is observed that, in agreement with what we have now said, at the level of clusters of galaxies this metric becomes the metric of the Minkowski space-time. In the first part of the paper, for the sake of clarity and for the role that they play in the paper itself, some well-known metrics of the three-dimensional manifolds of constant curvature are deduced.