École Nationale Supérieure de
Techniques Avancées

Abstract

In order to investigate dynamics at small cosmological scales, the dynamics of stars or massive particles in a central potential is studied. The isochrone model, first introduced by Michel Hénonin 1959, is a special case well describing the structure of numerous observed globular clusters and setting a specific link between the Coulomb and Kepler potentials which properties have been derived to highlight their duality. The reminding of Liouville integrability and generalised Gorringe-Leach equations eventually enable the further investigation of the isochrone potential.The general theory of relativity established by Einstein is on the other hand used to un- derstand the cosmological reasons that have led him to introduce a new universal constant, the cosmological constant, to describe a static universe in its whole. This is studied before examining the cosmological principle and Friedmann-Lemaˆıtre-Robertson-Walker equations that describe the fundamental properties of the universe at large scales today. The notion of observable and key elements, necessary to the numerical simulation I have made of this model and its validation,are also explained.