THE DESITTER UNIVERSE MODELS

The kinematical properties of the de Sitter space-time are reviewed an d investigated. The properties of the static sections are clarified. A deduction of the analytic extension, analogous to that of Kruskal and Szekeres for the Schwarzschild space-time, of the static section to t he region outside the horizon is given. The representation of the de S itter space-time as a four-dimensional hyperboloid in Minkowskian five -dimensional space-time is reviewed. Coordinate transformations betwee n different sections of the de Sitter space-time are found. By means o f the transformation formulae the different sections are mapped onto e ach other in space-time diagrams. These mappings are interpreted kinem atically. We have aimed at providing, whenever possible, an intuitive understanding of the kinematical properties of the different sections, and how they are interrelated. Among others we present real coordinat e transformations between the static and the three Robertson-Walker se ctions of the de Sitter space-time on one hand and the vacuum dominate d Bianchi type-III model on the other hand. These transformations are used to map the path of a typical Bianchi type-III reference particle into the static and the Robertson-Walker sections.