Cosmology and gravitational systems

Informations pratiques

Discipline :


Niveau :

Master 2

Semestre :


Crédits ECTS :


Volume Horaire :

24h Cours
10h TD

Responsable :

Thomas Buchert

Université Claude Bernard Lyon 1, Centre de Recherche d'Astrophysique de Lyon

Intervenants :

Thomas Buchert
Fosca Al Roumi

Language of instruction

The language of the course will be chosen during the first session to meet the audience preference (French or English)


We give the foundations of the theory of Newtonian gravitation in space and in phase space, a historical view of cosmology and its main issues today, an overview of the observational data and their interpretation, and a detailed view of applications in this research field at different scales (from cosmological systems to stellar systems). Emphasis is put on the formation of self-gravitating structures.


1. General Introduction:
historical overview of cosmology; homogeneous cosmology; the "concordance model" and inflation; important observational data; the problems of dark matter and dark energy; phenomenology of gravitational systems; phase space in classical mechanics; gravitational field equations; the matter model "dust"; Euler-Poisson system and its known solutions; Lagrangian picture; incompressible phase space flows.

2. Kinematical properties and gravitational instability:
the kinematics of a continuous system in space; multi-stream hydrodynamics; singularities; morphogenesis of cosmic structures; the transport equations (expansion, shear, vorticity, gravitational field, tidal force); special non-linear models and their integrals; perturbation theory (Eulerian and Lagrangian); architecture of numerical simulations and comparison with analytical approximations; session of illustrations.

3. The hierarchy of velocity moments:
velocity moments of the phase space density and of Vlasov's equation; velocity fluctuations; general treatment of the hierarchy of equations and the approach of Klimontovich; "coarse-graining"; Liouville's theorem; Euler-Jeans-Poisson system; systems with isotropic velocity dispersion; special flows (barotropic flows; diffusion equations, Burgers and Navier-Stokes equations); gravitational turbulence; dynamical state equations; non-perturbative models.

4. The hierarchy of spatial moments:
spatial moments of observables; the virial theorem of Chandrasekhar and Lee; local equilibria and the theorems of Jeans; orbital structures of dynamical systems; hydrodynamical equilibra; the Maxwell-Boltzmann distribution; the effective dynamics of inhomogeneous non-isolated systems; regional equilibra; aspects of inhomogeneous cosmology in general relativity; global gravitational instability; the curvature and topology of the Universe; interpretation of dark energy; scalar field models.


An extensive bibliography and courses notes (in english) will be given during the course


Written exam