Cosmology I and II, fall 2015

Homepage for the 2016 Cosmology course is here.

53757 Cosmology I (Kosmologia I), 1.9.-16.10.
53758 Cosmology II (Kosmologia II), 26.10.-11.12.

Lecturer: Syksy Räsänen, C326
Assistant: Mikko Lavinto, C311

The lecturer and the assistant can be contacted by email at, or you can drop by our offices.

Cosmology I grades

Cosmology II grades

Lectures of Cosmology II: Mon and Tue 12-14 Physicum room A315
The first lecture of Cosmology II will be on Monday October 27.

Exercises of Cosmology II: Thu 16-18 Physicum room D112

Note: According to WebOodi, the exercises are on Wednesdays, but this is incorrect.

The exam of Cosmology II will be on Monday December 14 at 13.00-17.00 in Physicum room D114. (Exams begin sharp on the hour, not quarter past.)

The grade is based 33% on the exercises and 67% on the exam. (Exception: for students who have taken the course before, the grade is based only on the exam.) If the exam date is impossible, students can agree with the lecturer to take it later, at a faculty exam. The exercise points will contribute to the grade as usual. The exam has to be taken before the course is lectured again. (This must be agreed before the exam. Not showing up for the exam without such prior agreement counts as a failed attempt.)

It is possible to retake the exam once, without retaking the course. The grade will then be based entirely on the exam, the exercise points don't count. This can only be done once, nor matter how many times the course is taken. (I.e. there is one 'free' retake ever.)

Help Sheet

This sheet with information on units and key equations will be handed out in the exam. (Students may not bring books or their own notes to the exam.)

Lecture notes

Lecture notes will appear here as the lectures proceed. Reading the lecture notes before attending the lectures is recommended.
The introductory lecture Powerpoint file is here. The simulations of large scale structure are from the Max Planck Institute for Astrophysics, here and here.

Chapter 1: Introduction
Chapter 2: Basics of general relativity
Chapter 3: The Friedmann-Robertson-Walker model
Chapter 4: Thermodynamics in an expanding universe
Chapter 5: Thermal history of the early universe
Chapter 6: Big bang nucleosynthesis
Chapter 7: Dark matter

Chapter 8: Inflation: background
Chapter 9: Linear perturbation theory
Chapter 10: Inflation: perturbations
Chapter 11: Perturbations after inflation
Chapter 12: Cosmic microwave background

Homework problem sets

Problem sets are out on Mondays (at the latest) on this webpage, and they are due the following Monday by 14.15. The solutions are returned to a cardboard box of the second floor of the A-wing of Physicum.

Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6

Homework 7
Homework 8
Homework 9
Homework 10
Homework 11
Homework 12

Contents: The observable universe, homogeneous and isotropic models of the universe, thermal history of the universe, big bang nucleosynthesis, dark matter, inflation, cosmological perturbation theory, cosmic microwave background.
Textbook: Lecture notes.
Literature: E.W. Kolb, M.S. Turner: The Early Universe (Addison-Wesley 1990).
T. Padmanabhan: Structure formation in the universe (Cambridge University Press 1993).
M. Roos: Introduction to Cosmology, 3rd ed. (Wiley 2003).
L. Bergström and A. Goobar: Cosmology and Particle Astrophysics (Wiley 1999).
J.A. Peacock: Cosmological Physics (Cambridge University Press 1999).
A.R. Liddle and D.H. Lyth: Cosmological Inflation and Large-Scale Structure (Cambridge University Press 2000).
S. Dodelson: Modern Cosmology (Academic Press 2003).
V. Mukhanov: Physical Foundations of Cosmology (Cambridge University Press 2005).
S. Weinberg: Cosmology (Oxford University Press 2008).
R. Durrer: The Cosmic Microwave Background (Cambridge University Press 2008).
A.R. Liddle and D.H. Lyth: The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure (Cambridge University Press 2009).

It's not necessary to buy any of these textbooks, the lecture notes are sufficient.

Course description

This is a basic course in cosmology. It is divided into two parts, Cosmology I and II, of which the first one is easier. The course material (lecture notes, homework problems) will be in English. Lectures will be in either Finnish or English, depending on the audience. (Typically about 40% of the students are foreigners, so it's rather unlikely for the lectures to be in Finnish.)

Unlike most theoretical physics courses, in Cosmology we will not derive a self-contained theory from basic principles, but we will instead apply known theories to the study of the universe.

In Cosmology I, we look at the universe in the simplest approximation, that of spatial homogeneity and isotropy, to get a basic picture of its composition and evolution. In Cosmology II, we look at the deviations from homogeneity and isotropy. We consider the origin of structures and the evolution of perturbations, with particular attention to the cosmic microwave background.

The assumed background includes mathematical methods, mechanics, special relativity, statistical physics and some quantum mechanics. Previous knowledge of general relativity is not required, as the results that are used will be reviewed (but not derived). For students who prefer not to have many results presented to them without proper derivation, it is advisable to first take a general relativity course. In Cosmology I we will use the Friedmann-Robertson-Walker models and some basic statistical physics without derivation and in Cosmology II we'll use general relativistic perturbation theory (and a little bit of quantum field theory in curved spacetime) in the same way.

In terms of courses lectured at the university of Helsinki, recommended prerequisities are Matemaattiset apuneuvot I ja II, Analyyttinen mekaniikka, FYMM Ia, FYMM Ib, FYMM IIa and Statistinen fysiikka I. The statistical physics course is not completely necessary, but it will make Cosmology I easier to follow. On Cosmology I, we need almost no quantum mechanics, on Cosmology II we need a little bit of it. The course Kvanttimekaniikka I is sufficient background.

Some cosmology resources

Last updated: August 26, 2016