# Cosmology and gravitational systems

## Informations pratiques

Discipline : |
Physique |

Niveau : |
Master 2 |

Semestre : |
S3b |

Crédits ECTS : |
6 |

Volume Horaire : |
24h Cours |

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)

## Objective

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.

## Syllabus

*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.

## Bibliography

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

## Exam

Written exam