COSMOLOGY

Second cycle degree in PHYSICS

Campus: PADOVA

Language: English

Teaching period: Second Semester

Lecturer: SABINO MATARRESE

Number of ECTS credits allocated: 6


Syllabus
Prerequisites: Fundamentals of Cosmology and Astrophysics
Examination methods: The exam of this course can be made in two alternative ways:
1. Oral interview on the main topics analyzed during the course.
2. (only for the students who attended the course) Short writtenm dissertation on a topic discussed during the course, to be agreed with the lecturer. The dissertation should contain a detailed of the chosen sunbject, based upon one or a few review articles (and or some cosmology textbook chapters).
The content of this dissertation, to be discussed with the professor is expected to show how much the student has
becokem acquainted with the main concepts presented in the lectures.
Course unit contents: General introduction

• Derivation of the Friedmann eqs. from Einstein's eqs. (after a very synthetic introduction to the latter), assuming the Robertson-Walker line-element.

The Cosmic Microwave Background (CMB) Radiation

• Boltzmann eq. and hydrogen recombination: beyond Saha equation
• The Boltzmann eq. in the perturbed universe: the photon distribution function
• The collision term
• Boltzmann eq. for photons in the linear approximation
• Boltzmann eq. for cold dark matter (CDM) in the linear approximation
• Boltzmann eq. for baryons in the linear approx.
• Evolution eq. for the photon brightness function
• Linearly perturbed Einstein's equations (scalar modes)
• Initial conditions
• Super-horizon evolution
• Acoustic oscillations and tight coupling
• Free-streaming – role of the visibility function
• Evolution of gravitazional potential and Silk damping
• Temperature anisotropy multipoles
• Angular power-spectrum of the temperature anisotropy
• Sachs-Wolfe effect
• Small angular scales: acoustic peaks and their dependence on cosmological parameters

The gravitational instability

• Gravitational instability in the expanding Universe
• Boltzmann eq. for a system of collisionless particles and the fluid limit
• The Zel’dovich approximation
• The adhesion approximation
• Solution of the 3D Burgers equation

Statistical methods in cosmology

• The ergodic and the “fair sample” hypotheses
• N-point correlation functions
• Power-spectrum and Wiener-Khintchine theorem
• Low-pass filtering techniques
• Up-crossing regions and peaks of the density fluctuation field
• Gaussian and non-Gaussian random fields
• The path-integral approach to cosmological fluctuation fields