Generalization of the de Sitter Cosmos

Abstract

First of all, we investigate whether the transformation of Lema ? tre inevitably leads from the static de Sitter cosmos to an expanding cosmos. A Lorentz transformation which can be assigned to the Lema ? tre transformation results in a frame of reference that moves relatively to the static dS system. Because of the homogeneity of space, this applies to every point in the space which does not itself undergo any change. We interpret the “expansion” of the cosmos Milne-like. It is not the space that expands, but the mesh of the Lema ? tre coordinate system. The velocity parameter of the associated Lorentz transformation is geometrically based and shows that the joined observer systems are moving in free fall. We also discuss the question of whether the speed of light for free-falling observers in the universe can be reached or can be exceeded, respectively. We raise the question of whether the model can be extended in such a way that the motions take place with a velocity that is lower than the one of the free fall. We believe that the method we have derived can be generalized to models with genuine expansion.