
Course unit
THEORETICAL COSMOLOGY
SCP9086384, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
Mutuated
Course unit code 
Course unit name 
Teacher in charge 
Degree course code 
SCN1035989 
COSMOLOGY 
SABINO MATARRESE 
SC2443 
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
1 Commissione Theoretical Cosmology 2019/2020 
01/10/2019 
30/11/2020 
MATARRESE
SABINO
(Presidente)
GIUSTO
STEFANO
(Membro Effettivo)
MARTUCCI
LUCA
(Supplente)

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 RobertsonWalker lineelement.
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
• Superhorizon evolution
• Acoustic oscillations and tight coupling
• Freestreaming – role of the visibility function
• Evolution of gravitazional potential and Silk damping
• Temperature anisotropy multipoles
• Angular powerspectrum of the temperature anisotropy
• SachsWolfe 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
• Npoint correlation functions
• Powerspectrum and WienerKhintchine theorem
• Lowpass filtering techniques
• Upcrossing regions and peaks of the density fluctuation field
• Gaussian and nonGaussian random fields
• The pathintegral 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.

Coles P. and Lucchin F., Cosmology: The Origin and Evolution of Cosmic Structure. Chichester: Wiley and Sons, 2001.

Vittorio N., Cosmology. Boca Raton  London  New York: CRC Press  Taylor & Francis Group, 2018.


