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School of Science
Course unit
SCP9086384, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
SC2490, Degree course structure A.Y. 2019/20, A.Y. 2019/20
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Degree course track THEORY AND MODELLING [001PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination THEORETICAL COSMOLOGY
Website of the academic structure
Department of reference Department of Physics and Astronomy
Mandatory attendance
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge SABINO MATARRESE FIS/05

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses FIS/05 Astronomy and Astrophysics 6.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2019 course timetable

Examination board
Examination board not defined

Prerequisites: Fundamentals of Cosmology and Astrophysics
Target skills and knowledge: The goal of this lecture course is to make the students familiar with some of the most important research subjects of modern cosmology, as well as provifding them with some of the fundamental tools used to analyse and interpret cosmological data.
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 classes) Short written dissertation on a topic discussed during the course, to be agreed with the lecturer. The dissertation should contain a detailed of the chosen subject, 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
become acquainted with the main concepts presented in the lectures.
Assessment criteria: Ability of the student to elaborate on and make use of the subjects presented in the course.
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
• Approach based on the Schroedinger 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
Planned learning activities and teaching methods: Classrooms, including some computer worked examples.
Additional notes about suggested reading: Professor's notes on esentially all the subjects covered during the course.
Textbooks (and optional supplementary readings)
  • Dodelson, S., Modern Cosmology. Amsterdam: Academic Press, 2003. Cerca nel catalogo
  • Coles P. and Lucchin F., Cosmology: The Origin and Evolution of Cosmic Structure. Chichester: Wiley and Sons, 2001. Cerca nel catalogo
  • Vittorio N., Cosmology. Boca Raton - London - New York: CRC Press - Taylor & Francis Group, 2018. Cerca nel catalogo