Cosmology

This course is an introduction to the standard model of cosmology, covering 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, particularly the theory of linear perturbations, which is used to understand the formation of structures in the universe.

The basic concepts covered in the first year of the master's program (M1) in the course “General Relativity and Cosmology,” as well as statistical physics and thermodynamics.

Recommended Prerequisites :

(Classical) Field Theory.

Midterm (3 hours) + Written exam (3 hours)

• The homogeneous universe: the Copernican principle and the cosmological principle; a review of Friedmann-Lemaître-Robertson-Walker geometry; the evolution of the universe’s expansion; the radiation-dominated, matter-dominated, and cosmological-constant-dominated eras; dark matter and dark energy; the hot Big Bang model; the limitations of the hot Big Bang model and the principle of inflation.
• Thermal History of the Universe: thermodynamics in an expanding universe; effective relativistic degrees of freedom; decoupling and the non-equilibrium approach; the Boltzmann equation; applications: primordial nucleosynthesis; the 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.
• Formation of structures: matter model; adiabatic fluctuations and isocurves; the 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 spectral shift space.
• Inflation: minimal model with one scalar degree of freedom; slow-roll conditions; inflaton perturbations and the generation of classical fluctuations from quantum inflaton fluctuations; scalar and tensor modes.