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 is based on the course of general relativity and cosmology of M1.

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

The basic notions acquired in M1 in the course "General relativity and cosmology", statistical physics, thermodynamics.

Recommended prerequisites :

(Classical) field theory.

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

• The homogeneous universe: Copernican principle and cosmological principle; reminder of the Friedmann-Lemaître-Robertson-Walker geometry; evolution of the expansion of the universe; eras dominated by radiation, by matter and by 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 diffuse 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.