7 lectures: 19, 20, 21, 22 September, 2, 3,
19 Sept: J. Silk
1a. Evidence for dark matter: galaxy rotation curves, clusters of galaxies, large-scale clustering, gravitational lensing)
1b. Baryonic dark matter: primordial nucleosynthesis, CMB, IGM, clusters, microlensing
20 Sept: JSilk
2. Nonbaryonic dark matter: candidates, direct detection, indirect detection, cold dark matter
21 Sept: J.P. Uzan
Goals of cosmology, limitations.
1. Uniformity Principles
Hypothesis underlying the construction of cosmological models.
2. nature of matter
3. cosmological and Copernician principles
2. Homogeneous and isotropic universe models
Homogeneity, isotropy, constant curvature space, FLRW spacetime, conformal time, Killing vectors.
1. Kinematics of FLRW models
Hubble law, light, redshift, test particle.
1. Dynamics of FLRW models
Geometric quantities, matter, Friedmann equations, some solutions, reduced form, dynamical system approach.
1. Time and distances
Age of the universe, look-back time, angular distance, luminosity distance, duality relation, units.
22 Sept: J.P. Uzan
Part Ib: Cosmological models (2)
Event horizon, particle horizon, Penrose-Carter diagrams.
1. The hot big-bang model
Hubble constant, age of the universe, thermal history, nucleosynthesis, cosmic microwave background.
1. Beyond FLRW models
3+1 covariant approach, generalized Hubble law, Raychaudhuri equation, generalized Friedmann equation, Killing vectors, Bianchi I, Lemaître-Tolman-Bondi.
9- Problems and
02 Oct: J. Silk
3a. Galaxy formation: Nonlinear theory, hierarchical growth, first stars, chemical evolution
3b. Formation of spiral galaxies: angular momentum, disk instability, star formation rate, Tully-Fisher relation
4a. Formation of elliptical galaxies: mergers, spheroid formation, fundamental plane
4b. Active galactic nuclei and quasars: Role of supermassive black holes, scaling relations
03 Oct: J.P. Uzan
Part IIa: cosmological perturbation theory (1)
1. Newtonian perturbation theory
Static spacetime, expanding spacetime, growth factor, toward the non-linear regime.
1. Gauge invariant cosmological perturbations
Gauge problem, gauge invariant metric perturbations, matter, perturbation equations.
1. Some solutions
Vector modes, tensor modes, scalar modes.
1. Power spectrum of density perturbation
04 Oct: J.P. Uzan
Part IIb: cosmological perturbation theory (2)
1. CMB anisotropies
Sachs-Wolfe formula, angular power spectrum, toward the kinetic approach.
See also lecture by F. Bouchet for observational aspects.
1. Weak lensing
Principle, weak lensing by large scale structures, Sachs equation, cosmic shear.
See also lecture by Y. Mellier for observational aspects
1. Origin of the perturbations: inflation
Principle, implementation, slow-roll conditions, zoo of models, origin of fluctuations, generic prediction, WMAP, eternal inflation
See also lecture by V. Mukhanov for extended discussion.
Satus of the model, open issues.
Plots shown in the lectures
Some reference articles:
G.F.R. Ellis, 1975, Cosmology and verifiability.
J. Bernstein, 1989, Cosmological helium production simplified.
D. Lyth, 1993, introduction to cosmology.
H. van Elst and G.F.R Ellis, 1998, Cosmological models.
K. Olive et al., 2000, Primordial nucleosynthesis: theory and observations.
M. Bartelmann and P. Schneider, 2001, weak gravitational lensing.
Y. Mellier, 2003, Gravitational lensing by large scale structures.
F. Bernardeau et al., 2002, large scale structures of the universe and cosmological perturbation theory.
F. Bernardeau, 2003, dark matter, dark energy...
G.F.R. Ellis, 2004, issues on the philosophy of cosmology, Issues in the Philosophy of Cosmology, astro-ph/0602280 .
A. Linde, Particle Physics and Inflationary Cosmology, hep-th/0503203.
Mukhanov, Feldmann, Brandenberger, 1992, Theory of cosmological perturbations.