Le 10 janvier 2014
De 10h30 à 11h30
Observatoire Astronomique – Grande Coupole
Giovanni MANFREDI
Institut de Physique et Chimie de Matériaux de Strasbourg (IPCMS)
Cosmological simulations should in principle adopt a four-dimensional (4D) space-time to model the evolution of large regions of the universe. However, as billions of particles are required to represent the matter distribution, significant approximations must be made, which leave the delicate issue of fractal structure largely unresolved. Here, we address this question within the framework of a class of idealized 1D models. Most existing results rely on N-body simulations, whereby one solves the equations of motion of a large number of particles that interact through the gravitational force (in the Newtonian approximation). Starting from a uniform distribution of particles, N-body simulations show the formation of a hierarchical structure. The density power spectrum displays a scale-free range, thus suggesting a fractal distribution of the particles. The analyses are robust for high density regions but give contrasted results for the low-density regions. To have a better insight into the distribution of mass in the low-density region, we propose to use a continuous probability distribution in the phase space, which evolves according to the Vlasov equation. In Vlasov simulations, the entire phase space is covered with a uniform mesh, so that regions of high and low density are sampled with equal precision and the level of numerical noise remains low. The underlying model and assumptions will be illustrated and preliminary numerical results will be presented. The Vlasov approach should allow us to extend to the low-density regions (where existing numerical evidence is inconclusive) the results obtained from the N-body simulations. Finally, I will present a few results on a different topic, namely the Schrödinger-Newton equations and their possible application to model boson or fermion stars.