Generation of Caustics in Self-Gravitating N-Body Systems and Large Scale Structure of the Universe

by Prof. George Savvidy (INPP, NCSR "Demokritos" (Greece))

Monday 30 Sept 2024, 14:00 → 15:00 Europe/Rome

AULA GRASSANO

We demonstrated that the dynamical mechanism of caustics generation in self-gravitating N-body systems is responsible for the formation of the cosmological Large Scale Structure of the Universe that consists of matter concentrations in the form of galaxies, galactic clusters, filaments, and vast regions devoid of galaxies. The gravitational caustics are space regions where the density of matter is higher than the average density in the surrounding space.
We formulated the dynamics of a self-gravitating N-body system in terms of a geodesic flow on a Riemannian manifold of dimension 3N equipped by the Maupertuis's metric. The sign of the sectional curvatures defines the stability of geodesic trajectories in different parts of the phase space. The regions of negative sectional curvatures are responsible for the exponential instability of geodesic trajectories, deterministic chaos and relaxation phenomena of globular clusters and galaxies, while the regions of positive sectional curvatures are responsible for the gravitational geodesic focusing and generation of caustics. We estimated the characteristic time scale of generation of gravitational caustics, calculated the density contrast on the caustics and compared it with the density contrasts generated by the Jeans–Bonnor–Lifshitz–Khalatnikov gravitational instability.