1. Course title

Gravitational Lensing

2. Course code


3. Course status: compulsory or optional

-Which degree programme is responsible for the course?

Master’s Programme in Particle Physics and Astrophysical Sciences

-Which module does the course belong to?

PAP3002 Advanced Studies in Particle Physics and Cosmology
optional for

  • Study Track in Particle Physics and Cosmology

-Is the course available to students from other degree programmes?


4. Course level (first-, second-, third-cycle/EQF levels 6, 7 and 8)

-Master’s level, degree programmes in medicine, dentistry and veterinary medicine = secondcycle
degree/EQF level 7
-Doctoral level = third-cycle (doctoral) degree/EQF level 8
-Does the course belong to basic, intermediate or advanced studies (cf. Government Decree
on University Degrees)?,

5. Recommended time/stage of studies for completion

-The recommended time for completion may be, e.g., after certain relevant courses have
been completed.

6. Term/teaching period when the course will be offered

-The course may be offered in the autumn or spring term or both.
-If the course is not offered every year, this must be indicated here.
-Specification of the teaching period when the course will be offered

7. Scope of the course in credits

5 cr

8. Teacher coordinating the course

Elina Keihänen

9. Course learning outcomes

The course gives you the theoretical basis to understand gravitational lensing as a physical phenomenon. You will understand the relation between lensing theory and observations, and how lensing can be used to extract cosmological information.  You will have the conceptual basis that allows you to deepen your knowledge by reading further literature or publications.

10. Course completion methods

The course program consists of 4 hours of lectures/week, and weekly homework problems.  The grading will be based on the homework. There is no exam.

11. Prerequisites

- Fymm 1-2a (vector fields, complex analysis, Fourier analysis, special functions)

- Cosmology I

- General relativity

Or equivalent knowledge

Possibly helpful but not required:  

Cosmology II, Cosmological Perturbation Theory

12. Recommended optional studies

13. Course content

Gravitational lensing is a powerful cosmological probe. This course is an introduction to the theory of gravitational lensing in the context of cosmology. The theory is built on the theory of general relativity, and on the FRW model of the universe.  The focus is on cosmology, thus we will mainly be working at the weak-lensing limit, strong lensing is touched only briefly.

The course is motivated by Euclid, the European Space Agency’s satellite mission to probe the large scale structure and expansion history of the universe.  The course forms a natural continuation to the course of Galaxy Survey Cosmology, but can also be taken individually.


- Propagation of light in general relativity

 -Lensing geometry and basic concepts

- Weak and strong lensing

- Magnification and distortion

- Relation to observations

- Lensing as a cosmological probe

- Shear field

- Lensing spectrum and correlation function

- Shear as a spin-2 field

14. Recommended and required literature

Lecture notes will be made available as the course progresses.

15. Activities and teaching methods in support of learning

16. Assessment practices and criteria, grading scale

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