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Course content

This course examines the history of our universe from the Big Bang, through the formation of the cosmic microwave background; to the universe we see today, with all its large scale structures. To be able to understand this whole evolution, a combination of a wide range of physics is needed: perturbation theory, Einstein's General Theory of Relativity, statistical physics, thermodynamics, and a little bit of quantum field theory. You will first learn the theory, then implement and numerically solve the equations we derive in order to obtain theoretical predictions that will in the end be compared to actual observations.

Learning outcome

After completing this course, you:

  • are familiar with the principles and equations of Einstein General Relativity, and be able to solve them in some specific cases.
  • are familiar with the basics of thermodynamics and statistical mechanics in an expanding universe.
  • are able to describe, qualitatively, and quantitatively important epochs in the early universe, such as inflation, recombination (both for hydrogen and helium), reionisation and the formation of cosmic microwave background radiation.
  • know how to obtain equations from the linearly perturbed Einstein Equations and Boltzmann Equations that describe the formation of structures in the universe and be able to solve them numerically.
  • understand what the main statistical observables are, which can be applied to large scale structure datasets, and from them obtain the main properties of our universe, and the laws that describe it.
  • understand the physical mechanisms that generates polarisation in the cosmic microwave background and can describe this mathematically.
  • have developed an individual Einstein-Boltzmann solver that computes the theoretical predictions for these main observables - including polarization - that can be compared to observations of the cosmic microwave background and observations of the large scale structure of the universe from galaxy surveys.
  • are able to present the results of the numerical analysis together with a summary of the theory written up as a scientific article.

Admission to the course

PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Courses AST3220 – Cosmology I/ AST4220 – Cosmology I (discontinued) and FYS4160 – The General Theory of Relativity are useful.

At the beginning of the semester we will review what the student needs to know from the courses AST3220 – Cosmology I and FYS4160 – The General Theory of Relativity. In particular, a basic knowledge of doing calculations with tensors will be especially useful. The student can easily follow this course without having taken AST3220 – Cosmology I and FYS4160 – The General Theory of Relativity if the student has a good theoretical background.

The student does not have to be an expert, but basic knowledge of programming is to be expected, otherwise the student will find it quite challenging to complete the numerical project assignment. There is a free choice of programming language in this course, but code templates are offered in C + + and Fortran to make it easier to get started with the assignment.

Overlapping courses


Teaching extends over one semester. There will be 4 hours of lectures/tutorials each week.


This course has a final written exam which counts 70 % in the grade assessment, and a written numerical project assignment given in the form of a home exam, which counts for 30 % in the grade assessment.

The final grade is determined after an overall assessment of the two parts.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: AST5220 – Cosmology II

Examination support material

No examination support material is allowed during the final exam.

Language of examination

Subjects taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Sep. 28, 2022 12:10:24 PM

Facts about this course

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