Cosmology I & II, 2025
Cosmology I & II 2025
FYS2081 Cosmology I (5 op) (2.9.-17.10.)
PAP326 Cosmology II (5 op) (27.10.-10.12.)
Lecturer: Kari Rummukainen (kari.rummukainen, Physicum C323)
Assistants: Riikka Seppä Kalliokoski (riikka.seppa, Physicum C315) and (only for Cosmology I) Laura Laine (laura.sz.laine)
To get e-mail addresses append @helsinki.fi.
Cosmology I
Lectures: Monday 14.15-16.00 at Exactum CK112, Tuesday 14.15-16.00 at Physicum E204
Exercises: 12.15-14.00 Thursday Exactum BK114, 12.15-14.00 Friday Physicum D112. (this was wrong way around before!)
Exam: Tuesday October 21 13.00-17.00 in Exactum B123.
Course has (Cosmology I) Moodle pages, where the homework exercises are returned.
Students have to register for the course on Sisu.
Cosmology II
Lectures: Monday and Tuesday 14.15-16.00 at Physicum A315
Exercises: Wednesday 16.15-18.00 at Physicum A315.
Exam: Thursday December 18 9.00-13.00 in Exactum D123.
Cosmology II Moodle pages, where homework exercises are returned.
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.
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 t\item a) Derive the Saha equation (given below) for the ionisation fraction
$x\equiv n_p/n_B$ at recombination.
\bea
{1-x\over x^2} = {4\sqrt2\,\zeta(3)\over\sqrt\pi}\eta
\left({T\over m_{\rm e}}\right)^{3/2}e^{B/T} \nonumber
\eea
b) Explain what effect the small value of the baryon-photon ratio has on the recombination temperature. If the ratio were larger, would recombination happen sooner or later, and why?
o 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 sufficient background.
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).
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).
D. Baumann: Cosmology (Cambridge University Press 2022).
Lecture notes
We're using the lecture notes by Syksy Räsänen from 2024 below.
Introductory notes (warning, 460MB pdf file).
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. The solutions are discussed on exercise sessions and returned via Moodle by the following Monday lecture (14.00).
Cosmology I
Homework 1 (return 8.9)
Homework 2 (return 15.9)
Homework 3 (return 22.9)
Homework 4 (return 29.9)
Homework 5 (return 6.10)
Homework 6 (return 13.10)
Cosmology II
Homework 1 (return 3.11)
Homework 2 (return 10.11)
Homework 3 (return 17.11)
Homework 4 (return 24.11)
Homework 5 (return 1.12)
Homework 6 (return 8.12)
A cosmology helpsheet that will be available in the exams.
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. Concentrates on the distribution of galaxies (their correlation function and power spectrum) and weak gravitational lensing. Prerequisites: Cosmology I and II and mathematical methods (FYMM I and II); for Gravitational Lensing also General Relativity I and II. Lectured every odd year spring term, next in 2025.
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 2024.
Galactic dynamics: This course looks into galaxies in detail. Lectured every odd year spring term, next in 2025.
A dictionary of terms in general relativity and cosmology from English to Finnish.
Last updated: September 2, 2025