Cosmology

This course is an introduction to the standard model of cosmology in its theoretical and phenomenological aspects. It focuses on the hot inflationary Big Bang model. It builds on the M1 course in general relativity and cosmology.

By the end of this course, students will be able to understand the standard model of cosmology, in particular the theory of linear perturbations, which is used to understand the formation of structures in the universe.

Basic concepts acquired in M1 in the course "General Relativity and Cosmology," statistical physics, thermodynamics.

Recommended prerequisites :

(Classical) field theory.

Midterm (3 hours) + Final exam (3 hours)

• The homogeneous universe: Copernican principle and cosmological principle; review of Friedmann-Lemaître-Robertson-Walker geometry; evolution of the expansion of the universe; eras dominated by radiation, matter, and the cosmological constant; dark matter and dark energy; hot Big Bang model; limitations of the hot Big Bang model and principle of inflation.
• Thermal history of the Universe: thermodynamics in an expanding universe; effective relativistic degrees of freedom; decoupling and approach to non-equilibrium physics; Boltzmann equation; applications: primordial nucleosynthesis; cosmic microwave background; a model of cold dark matter.
• Linear perturbation theory: perturbed metric; scalar, vector, and tensor degrees of freedom; gauge concepts and gauge transformations; perturbed Einstein equations.
• Structure formation: matter model; adiabatic fluctuations and isocurves; Bardeen equation; adiabatic evolution during the radiation-dominated era; adiabatic evolution during the matter-dominated era; connecting the two eras; transfer function; initial conditions and power spectrum of fluctuations; effects of the cosmological constant.
• Large galaxy surveys: galaxy counting; matter power spectrum; bias; distortion effect in the redshift space.
• Inflation: minimal model with one scalar degree of freedom; slow-rolling conditions; inflaton perturbations and generation of classical fluctuations from quantum fluctuations of the inflaton; scalar and tensor modes.