Cosmology I & II, fall 2026
Cosmology I & II, fall 2026
FYS2081 Cosmology I (5 op) (1.9.-20.10.)
PAP326 Cosmology II (5 op) (26.10.-17.12.)
Lecturer: Syksy Räsänen (Physicum C326)
Assistants: Selda Koivula (Physicum C304) and (for Cosmology I only) Jichao Li (Physicum A314)
The lecturer and assistants can be reached at firstname.lastname at helsinki.fi. You can also drop by our offices.
Cosmology I
Lectures: Monday 14.15-16.00 at Physicum E204, Tuesday 14.15-16.00 at Exactum D123
Exercises: Thursday and Friday 12.15-14.00 at Physicum D112.
First lecture: Tuesday September 1
Last lecture: Tuesday October 13
First exercise session: Thursday September 3
Last exercise session: Friday October 16
Exam: Tuesday October 20 13.00-17.00 in Exactum B123.
Students have to register for the course on Sisu. Registered students have access to the courses Moodle pages.
This page has the correct up-to-date information about the course. Updates will also be sent to registered students via email. (The automatically generated course webpage is not necessarily updated.)
Cosmology II
Lectures: Monday and Tuesday 14.15-16.00 at Physicum A315
Exercises: Thursday 16.15-18.00 at Exactum A315.
First lecture: Monday October 26
Last lecture: Tuesday December 8
First exercise session: Wednesday October 28
Last exercise session: Thursday December 9
Exam: Thursday December 17 13.00-17.00 in Physicum E207.
Students have to register for the course on Sisu. Registered students have access to the course Moodle pages.
This page has the correct up-to-date information about the course. Updates will also be sent to registered students via email. (The automatically generated course webpage is not necessarily updated.)
Practicalities
Language: English
Exams and grades: For both Cosmology I and II, the grade is based on the weekly exercises (1/3) and the exam (2/3). (Exception: for students who have taken the course before, the grade is based entirely on the exam.) There are 6 weekly exercises for each course. You need 45% of the maximum points to pass the course (grade 1). When retaking the exam, the exercise points are not counted towards the grade.
Use of machine learning algorithms ("AI"): Doing homework exercises with machine learning algorithms ("AI") is not allowed on the courses Cosmology I and II. (General guidelines of the University of Helsinki on AI can be found here.) Prompting an AI to do them and passing the answers as your own constitutes cheating. More importantly, doing so means that you not learn how to do the calculations, which is the main method of learning cosmology. Hence, you will also have difficulty passing the exam. I advise caution if consulting AI even for general understanding of the topic, because of the lack of error control in the answers: they may seem convincing, and can sometimes be right, but can also be false or even nonsensical.
Contents
These courses provide the basics of cosmology. Unlike on 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 consider deviations from homogeneity and isotropy. We consider cosmic inflation, the origin of structures and the cosmic microwave background.
Cosmology I is intended for the third (last) year of Bachelor studies or the first year of Master studies. The recommended prerequisities are Matemaattiset apuneuvot I ja II, Analyyttinen mekaniikka and Statistinen fysiikka I. The statistical physics course is not really necessary, but it will make some parts of Cosmology I easier to follow. Quantum mechanics and statistical physics are not necessary, if the student is willing to accept some results taken from these fields without deriva. 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 the courses General relativity I & II. But they can also be taken afterwards.
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 would like to do your Bachelor's thesis in cosmology, this is recommended. Prerequisites are Cosmology I, FYMM Ia, FYMM Ib and FYMM IIa. We also need a bit of quantum mechanics; the course Kvanttimekaniikka I is more than sufficient.
Literature: Lecture notes. No textbook is required. However, it is always useful to have more then one perspective, and some cosmology textbooks are listed below.
E.W. Kolb, M.S. Turner: The Early Universe (Addison-Wesley 1990).
T. Padmanabhan: Structure formation in the universe (Cambridge University Press 1993).
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).
M. Roos: Introduction to Cosmology, 3rd ed. (Wiley 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).
D. Baumann: Cosmology (Cambridge University Press 2022).
Lecture notes
Lecture notes appear here before the lectures. Lecture notes from 2025 can be found here.
Cosmology I
Chapter 1: Introduction
Chapter 2: Basics of general relativity
Chapter 3: The Friedmann-Lemaître-Robertson-Walker model
Chapter 4: Thermodynamics in the expanding universe
Chapter 5: Big Bang nucleosynthesis
Chapter 6: Dark matter
Cosmology II
Chapter 7: Inflation: background
Chapter 8: Inflation: perturbations
Chapter 9: Perturbations after inflation
Chapter 10: Cosmic microwave background
Homework problem sets
The homework problems appear here on Monday or Tuesday. The solutions are returned via Moodle by the next Monday lecture. Solutions have to be handwritten, LaTeXed solutions are not accepted.
Related courses
General relativity I & II: Not needed for Cosmology I and II but essential if you want to study cosmology further. Also fun. Lectured every spring term.
Galaxy Survey Cosmology and Gravitational Lensing: Two advanced courses in cosmology motivated by Finnish participation in ESA's Euclid satellite project. They focus on the distribution of galaxies (their correlation function and power spectrum) and weak gravitational lensing. Galaxy Survey has Cosmology I and II as prerequisites, Gravitational Lensing has Cosmology I and General Relativity I. Lectured every odd year spring term, next in 2027.
Galaxy formation and evolution: If you want to know how the linear perturbations discussed in Cosmology II eventually turn into galaxies, this is the course for you. Lectured every even year fall term, so right now in fall 2026.
Galactic dynamics: This course looks into galaxies in detail. Lectured every odd year spring term, next in 2027.
A cosmology helpsheet that will be available in the exams.
A dictionary of general relativity and cosmology terms from English to Finnish.
Last updated: August 14, 2026