Cosmology

This course is an introduction to the theoretical and phenomenological aspects of the Standard Model of Cosmology. It focuses on the inflationary hot Big-Bang model. It is based on the M1 course on general relativity and cosmology.

At 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.

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

Recommended prerequisites :

(Classical) field theory.

Partial (3 hours) + Written exam (3 hours)

• The homogeneous universe: Copernican principle and cosmological principle; 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; limits of the hot Big Bang model and the inflation principle.
• Thermal history of the Universe: thermodynamics in an expanding universe; effective relativistic degrees of freedom; decoupling and non-equilibrium physics approach; Boltzmann equation; applications: primordial nucleosynthesis; cosmological microwave background; a cold dark matter model.
• Linear perturbation theory: perturbed metrics; scalar degrees of freedom, vectors and tensors; gauge concepts and gauge transformations; perturbed Einstein equations.
• Structure formation: matter model; adiabatic fluctuations and isocurves; Bardeen equation; adiabatic evolution in the radiation-dominated era; adiabatic evolution in 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: counting galaxies; power spectrum of matter; bias; distortion effect in spectral shift space.
• Inflation: minimal model with one scalar degree of freedom; slow rolling conditions; inflaton perturbations and generation of classical fluctuations from quantum inflaton fluctuations; scalar and tensor modes.