Lecturer:

Assistant:

Lectures: Mo 14-16 and Th 12-14 (Physicum A315)

Exercises: Fr 10-12 (D106 in period I, D114 in period II)

The grades were reported to the office on Dec 23rd, 2015.

The first lecture is on Thursday, Sep 3rd. The last lecture on Thursday, Dec 10th.

This is an advanced course on cosmological perturbation theory.
Cosmological perturbation theory is the tool to study and understand the origin and
evolution of structure (like galaxies and their clustering) in the universe, and lies at the heart of modern cosmology. If you plan to do research in cosmology, you should learn it.

**Prerequisites** (recommended):
Cosmology I+II, General Relativity. Knowledge of general relavity is
essential for being able to understand the course. If you haven't taken
Cosmology I+II, you could read Chapters 2, 3, 4 (luminosity distance
not needed), 10 and 11
of my Cosmology lecture notes,
available at the bottom of this page.
(We'll be redoing Chapter 11 material at a deeper level in this course.)
Alternatively, you can read the more recent Cosmology I+II lecture notes by Syksy Räsänen; note that he has different chapter numbering.

**Tentative contents: **Cosmological perturbation theory.
Scalar, vector, and tensor perturbations. Gauges. Newtonian gauge and synchronous gauge. Adiabatic and isocurvature perturbations.
Initial conditions. Primordial power spectra. Transfer functions. Generation and evolution of perturbations during inflation. Multi-field inflation. Observables. Dependence of cosmological parameters. CAMB and CosmoMC.

The course does not follow any textbook. Lecture notes (in English) will be made available.

**Exams and grades: ** The grade is based entirely on the homework. There is
no other way to pass the course than doing the homework in time. Instead of an exam there will
an additional homework to problem set to be done after the lectures have ended.

** Some literature:**

[1] V.F. Mukhanov, H.A. Feldman, and R.H. Brandenberger: Theory of Cosmological
Perturbations, Phys. Rep. 215, 203 (1992).

[2] A.R. Liddle
and D.H. Lyth:
Cosmological Inflation and Large-Scale Structure
(Cambridge University Press 2000), Chapters 14 and 15. Check the
errata!

[3] C.-P. Ma and E. Bertschinger: Cosmological Perturbation Theory in the
Synchronous and Conformal Newtonian Gauges, ApJ 455, 7 (1995). You can get it
from NASA
ADS.

[4] A.R. Liddle and D.H.Lyth: The Cold Dark Matter Density Perturbation, Phys. Rep. 231, 1 (1993).

[5] C. Gordon: Adiabatic and entropy perturbations in cosmology, Ph.D.
thesis, Univ. of Portsmouth, astro-ph/0112523.

[6]
S. Dodelson:
Modern Cosmology (Academic Press 2003).
Errata. (In the reference
library)

In Chapter 21 I take some results from my 2007 CMB Physics course.

My old notes about the late-time evolution of the small scale
perturbations (based on the book by S. Dodelson, Chapter 7)
from my 2004 CMB Physics course are below. This material is now included in the above,
but not yet the figures; so look at the figures here:

M1. Prelude
(hand, 7 pages, 154 KB pdf)

M2. Large Scales
(hand, 4 pages, 83 KB pdf)

M3. Small Scales
(hand, 7 pages, 139 KB pdf)

M4. Transfer Function
(hand, 2 pages, 44 KB pdf)

This year we did not have time to discuss tensor perturbation, but I attach my hand-written
notes on them from 2007:

T1. Einstein Equations

T2. Evolution in a Matter-Dominated Universe

T3. Evolution in the Radiation-Dominated Universe

T4. Radiation+Matter Universe and the Transfer Function

T5. Power Spectrum

T6. The Effect of Late-Time Acceleration (Vacuum Energy)

Cosmological Perturbation Theory, part 2, 31.12.2015 version

Homework problem sets:

Homework 1 due Wed, Sep 16th

Homework 2 due Wed, Sep 23rd

Homework 3 due Wed, Oct 7th

Homework 4 due Wed, Oct 14th

Homework 5 due Wed, Oct 28th

Homework 6 due Wed, Nov 4th

Homework 7 due Wed, Nov 11th

Homework 8 due Wed, Nov 25th

Homework 9 due Wed, Nov 25th

Homework 10 due Wed, Dec 2nd

Homework 11 due Wed, Dec 9th

Homework 12 (the last one!) due Wed, Dec 16th

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Return your solutions to Anna-Stiina by Wednesday evening. Put them in her mailbox, at the front end of the 3rd floor C corridor.

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Last updated: December 31st, 2015.