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1. Course title

Kosmologinen häiriöteoria

Cosmological Perturbation Theory

2. Course code


3. Course status: compulsory or optional

-Which degree programme is responsible for the course?

Master's programme in Particle 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 and Doctoral level
-Does the course belong to basic, intermediate or advanced studies (cf. Government Decree
on University Degrees)?,


5. Recommended time/stage of studies for completion

After PAP326 Cosmology II and PAP335 General relativity.

Second year of Master’s level studies

(Note, however, that the course is only lectured every second year)

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

Lectured every second year, even years. The course will be offered in the spring term, in III and IV period.

7. Scope of the course in credits

 10 cr

8. Teacher coordinating the course

Hannu Kurki-Suonio

9. Course learning outcomes

You will understand how perturbations in the spacetime geometry and energy distribution are described in different gauges.

You will learn to convert these quantities from one gauge to another You will learn how the perturbations evolve in time You know how to use a public numerical code (CAMB or CLASS) for numerical evolution of pertubations You will understand how perturbations are generated during inflation You understand the difference between isocurvature and adiabatic perturbations and their evolution You are familiar with phenomenological descriptions of dark energy and modified gravity models and their effect on cosmological perturbations

10. Course completion methods

Lectures and homework problems

11. Prerequisites

FYS2081 Cosmology I, PAP326 Cosmology II, PAP335 General relativity, FYS1010 Matemaattiset apuneuvot I (calculus), FYS1011 Matemaattiset apuneuvot II (differential equations), FYS1012 (vector calculus), FYS2010 Mathematical Methods Ia (complex analysis, Euler functions), FYS2011 Mathematical Methods Ib (Fourier series), FYS2012 Mathematical Methods IIa (special functions), or similar background

12. Recommended optional studies

PAP342 Galaxy Survey Cosmology  can be taken either before or after this course

13. Course content

Perturbative general relativity: background and perturbations Pertrubations in the metric and in the energy-momentum tensor Gauges and gauge transformations Scalar, vector, and tensor perturbations Adiabatic and isocurvature perturbations Neutrino perturbations The real universe Evolution of superhorizon and subhorizon perturbations Evolution of perturbations from the early radiation-dominated era to the present Gaussian initial conditions Sachs-Wolfe effect Phenomenological descriptions of dark energy and modified gravity models and their effect on cosmological perturbations Perturbations during inflation: single-field and many-field Primordial power spectrum to first and second order in slow roll Double inflation Curvaton

14. Recommended and required literature

Lecture notes on the course homepage

15. Activities and teaching methods in support of learning

Lectures and exercises (homework problems), individual study

16. Assessment practices and criteria, grading scale

Final grade is based on graded exercises.

There will be no exam.

17 Teaching language


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