Cosmology I and II

FYS2081 Cosmology I
PAP326 Cosmology II

This is the permanent openly accessible Cosmology I and II homepage at University of Helsinki. Some information here may be outdated. For current information on the ongoing lecture courses see their Moodle pages.
Latest course pages on Moodle: Cosmology I (2022) and Cosmology II (2022)

Lecturer: Hannu Kurki-Suonio, C329
Assistants (exercises): Aula Al-Adulrazzaq, Jenni Häkkinen
The lecturer and assistant can be contacted by e-mail at firstname.lastname(at)

Lectures: Physicum A315, Mo 14-16 and Tu 12-14
Exercise sessions: Physicum A315, Fr 12-14
The course is lectured in English.

Exams and grades

The grade is based on both the homework (weight TBD) and the exam (weight TBD).
Note that the exams begin sharp on the hour, not quarter past.
A help sheet with information on units and key equations and a particle data table will be handed out in the exam. Students may not bring books or their own notes to the exam. Note that many equations in the help sheet are for Cosmology II.
You need to bring your own calculator (function calculator without internet connection) to the exam.
Exam questions may be of similar nature to homework problems or similar to derivations in the lecture notes. There may also be an essay question.
If the exam date is impossible, students can agree with the lecturer (this must be done before the exam) to take it later, at a departmental exam. In this case the exercise points will contribute to the grade as usual. It is possible to retake the exam twice, at a departmental exam (aka general exam), without retaking the course. The grade will then be based entirely on the exam, the exercise points no longer count. In both cases the exam has to be taken before the course is lectured again.

Lecture notes

Introductory slide show (first lecture)
Chapter 1: Introduction
Read Chapter 1 by yourself before the second lecture and before doing the first homework.
We begin from Chapter 2 in the second lecture.
Chapter 2: General Relativity
Chapter 3: Friedmann-Robertson-Walker Universe
Chapter 4: Thermal History of the Early Universe
Chapter 5: Big Bang Nucleosynthesis
Chapter 6: Dark Matter
Appendix A: Vectors and tensors in general relativity; Einstein equation (not required in Cosmology I)
Appendix C: Numerical Constants

Cosmology II

Chapter 7: Inflation
Chapter 8: Structure Formation
Chapter 9: Cosmic Microwave Background (2021 version; will be uodated soon)
Appendix B: Quantum Fluctuations during Inflation (not required in Cosmology II)

Homework problem sets

Problem sets appear on Tuesdays (at the latest), and they are due on the following Monday before the lecture. Solutions to the problems will be discussed in the exercise session on the following Friday.

Course description

This is the basic course on cosmology. It is divided into two parts, Cosmology I and II, of which Cosmology I should be easier.

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 the universe is treated in the approximation, where it is assumed homogeneous and isotropic. This approximation can be used for large scales and the early universe. This gives a basic picture of the composition and evolution of the universe. In Cosmology II we study deviations from homogeneity and isotropy.

Cosmology I is intended for the third (last) year of Bachelor studies or the first year of Master studies. The recommended background for Cosmology I includes mathematical methods (differential and integral calculus, e.g. Mapu I and II), classical mechanics, special relativity, quantum mechanics and statistical physics. Quantum mechanics and statistical physics are not necessary, if the student is willing to accept some results taken from these fields, which are presented in Chapter 4 of lecture notes. Chapter 3 presents the results from general relativity that are needed for Cosmology I. Students who prefer not to have many results presented to them without derivation could take general relativity first (but that would likely push Cosmology I to the second year of Master studies).

Cosmology II is intended for Master studies, to be taken after Cosmology I, but you can take it already with your Bachelor studies if you like, and if you would like to do your Bachelor's thesis in cosmology, this is recommended. Cosmology II requires additional mathematical methods (vector calculus, Fourier analysis and spherical harmonic analysis, e.g. Fymm I and Fymm II, assumed background) and borrows some results from cosmological (general relativistic) perturbation theory and quantum field theory (not assumed).


Here is a list of some cosmology textbooks. The oldest are already partially out of date. It is not necessary to buy any of these books; the lecture notes are sufficient.
E.W. Kolb, M.S. Turner: The Early Universe (Addison-Wesley 1990)
T. Padmanabhan: Structure formation in the universe (Cambridge University Press 1993)
P. Coles, F. Lucchin: Cosmology - The Origin and Evolution of Cosmic Structure (Wiley 1995)
L. Bergström and A. Goobar: Cosmology and Particle Astrophysic (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)
M. Roos: Introduction to Cosmology, 3rd ed. (Wiley 2003)
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)

Other courses related to cosmology

Galaksit ja kosmologia (Galaxies and Cosmology, in Finnish): An astronomy course with some overlap with Cosmology I (mainly with our Chapters 1 and 3), but mostly about galaxies and their evolution.
Galaxy Formation and Evolution
General Relativity: Not needed for Cosmology I and II but essential if you want to study cosmology further. Lectured every spring term.
Cosmological Perturbation Theory: An advanced course in cosmology, covering Cosmology II material (except CMB) at a much deeper level. Prerequisites: Cosmology I and II, General Relativity. Lectured on even year spring terms.
CMB Physics: An advanced course where the physics of the Cosmic Microwave Background and its anisotropy is discussed in detail. Last lectured fall 2007. Was motivated by the Finnish participation in the Planck satellite project. Currently not in the teaching program.
Cosmological Parameter and Model Estimation: A hands-on course on using observational data to determine cosmological parameters and compare cosmological models. Was lectured in spring 2013. Currently not in the teaching program.
Galaxy Survey Cosmology: An advanced course in cosmology motivated by the Finnish participation in the Euclid satellite project. Concentrates on the distribution of galaxies (their correlation function and its power spectrum) and weak gravitational lensing. Prerequisites: Cosmology I and II and mathematical methods (FYMM I and II). Lectured on odd year spring terms. In 2023 the course will be divided into two parts, the first part (period III) will still be called Galaxy Survey Cosmology; the second part (period IV) is called Gravitational Lensing and will require also General Relativity as prerequisite.

Last updated: November 24, 2022