(Cosmological Perturbation Theory)

Lecturer: **Hannu Kurki-Suonio**, office hour We 10-11, C328

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

Starting on February 21st, the lectures will be in A315. The first
lecture is on Monday, January 20th. The last
lecture will be on Friday, May 23rd.

Exercises:
the nature of exercises is to be determined later

Exam:
Wednesday, June 18th, in the large auditorium D101, at 12.00-16.00.
I will give out a
collection of central equations, so that you don't have to memorize
the perturbation equations in general gauge etc. See course news June
11th, 12th below

This is a research-oriented graduate level course on the physics related to
the cosmic microwave background (CMB) anisotropy.
If you don't think you
will be doing research related to the CMB and/or cosmology,
it might be a good idea to
contact the lecturer beforehand to find out whether the course is useful
for you.

Language of instruction (English and/or Finnish) depends on the audience.

First lecture on Monday, January 20th.
Background expected: Cosmology and general relativity

Note added 10.9.04:

I have now prepared a typed set of
lecture notes
(with
figures), that covers
about a third of this course, and replaces the chapters G1 to G14 of my
handwritten notes, and are better organized.

Course news:

Feb 11: Starting on Friday, February 21st, the lectures will be held in
the HIP seminar room A315.

Feb 11: The course binder with my lecture notes is now in the library.
On each topic, I have put first my "organized" notes, that you should
study, followed by my "disorganized" notes, where you may find some
details worked out, but the notation may not be consistent.

Feb 17: Todays lecture notes are now in the library. The second
homework problem set is due on Monday, Feb 24th.

Feb 21: Todays lecture notes (G8.7--8, G10.1 -- G13.3), as well as
some older notes (full versions of G-1.1 and G-1.2; and G6.1--3), are
now in the library. Missing H-factors added on page G8.6.
I also added a "Contents" page for Chapter G, giving titles for the
sections G.1--13.

Feb 21: I am now using Riotto [5] as a reference too. There seem to
be some sign errors in his formulae.

Feb 25: Yesterday's and part of next Friday's lecture notes, G14.1--8,
are now in the library. There are also two summary pages: "Gauge
transformations" and "The Gauge-Invariant Equations" (the lecture notes
don't yet go quite far enough to get all of these). Pages G8.1--6
are also now complete. No homework problems this week.

Feb 28: New and beautiful lecture notes, numbered G14-1..10,
covering Monday's and the first
part of today's lectures, replacing G14.1--8, except some of the details
are still to be found there.

March 3: New lecture notes G14.12,13, G15-1..10, G15.1--7,11, and G15*. Error
on page G14*2 corrected (v_N = v-E'). Homework 3 due Monday, March
10th.

March 17: New lecture notes G15.12, G16-4, and Chapter G17.

March 24: New lecture notes in the library: G17-2a, G17-5a,b,
G17-7..10, G17.6--16 (old G17.6,7 thrown away). This ends the second
part of this course, which discussed cosmological perturbation theory
with a fluid description of the energy-momentum, and applies to the
universe after inflation and reheating. The next part will
be cosmological parturbation theory with scalar field sources, which
applies to inflation.

March 28: I have now begun discussing scalar fields, using Mukhanov et
al [2] and Gordon [3] as references. Today's lecture notes
S1.1--4, S2.1--4 are in the library.

April 22:
I spent the Easter time cleaning up my lecture notes,
so now is a good time to go to the library to make copies of them:
Error on p. S2-5 corrected ( "`)" must be ")'" ).
New pages S6-1..4, and S6.5,6 (I threw away the pages S6.1--3, since
that treatment, in the Newtonian gauge spirit, was replaced by a simpler
treatment in the spatially flat gauge spirit). Error on p. S7-2
corrected (epsilon_S has 1/16piG = M^2/2). New pages S8.5--11
(I threw out old page 8.5, which was rather schematic.)
I have updated star page S2*1, and added new star pages S2*2, S6*1.

April 25:
I am now following Gordon's thesis. Note the differences in notation
conventions listed on page S8.9. New pages in the library, S9-1..10
and S9.1--4.

April 29:
New pages S9-11,12. Errors on p. S9-2, eq. (3), and p. S9-7 corrected.
Equation numbering added to pp. S9-9,10. Note that my eqs. (40-42) do
not agree with Gordon's eqs. (2.42) and (2.43). I believe mine are
correct. Note the new homework problem set, number 4---I have extended
the deadline to Friday noon, May 9th. Since several lectures were cancelled due
to travel/illness, I am planning to keep lecturing beyond the end of the
spring term, possibly up to May 23rd, so that I could cover the Sachs--Wolfe
effect.

May 5:
Today's lecture notes, pages S10.1--6, are now in the library.

May 15:
New pages S4.2--5 (more about Bardeen's potential, stuff that we need
now), S9.5--9 (my calculations related to Homework 4),
S11-1..11 (taking you halfway into last Monday's lectures).

May 15, later:
The rest of this week's lecture notes, pages S11-12..19 and S11-20.1--5,
taking us finally till the end of Gordon's Chapter 2. (The last five
pages are my unpolished original notes, but should be readable). Minor
error on p. S11-8 corrected. I am not going to cover Gordon's Chapter
3. I will say something about Gordon's Chapter 4 on Monday, as it
relates to the WMAP paper #11 (Peiris et al) and Väliviita &
Muhonen, astro-ph/0304175. That will be enough on Gordon's thesis.
I am still planning to do the Sachs-Wolfe effect in the end.

May 22:
Because of the Cosmology Summer School (for children) in Kiljava next
week, I won't have time to clean up my notes for this week's lectures
until after the Summer School. For those who can't wait to see some
notes, I have put my raw notes in the library. Pages S12.1--15 are for
Monday' lecture. The rest are for Friday's lecture which is about
the Sachs-Wolfe effect. Pages SW-1..2 are my old Oslo lectures on the
topic (they give a short summary, without derivations, include only the
case of adiabatic modes, and use L&L notation, with the symbols for the
Bardeen potentials interchanged from the MFB [2] convention, which I
use). Pages SW2.1--5 and SW3.1--4 are my new notes.

June 9:
My set of lecture notes in the library are finally complete!
I have added now the "cleaned-up" notes of the last week's lectures:
New pages S11-20..25 (threw out the "dot" pages S11-20.1--5).
New pages S12-1..7 (threw out all S12.pages, except S12.3,4, which
actually relate now tho chapter S11).
Sachs-Wolfe effect: SW1-1, SW2-1..4, SW3-1, SW4-1..5, SW5-1..4 (threw
out the SW "dot" pages, except SW3.pages which renamed to SW4.pages).
Corrected errors on pages S11-1,8,16. Updated page S8.5 (solution to
homework 4.1).

June 11: I am preparing the
collection of central formulae which you will have available in the exam.
It will contain the "star pages", G14*1, G14*2, G14*3, G15*, S2*1, S2*2,
S6*1, page G17-5b (about relating derivatives wrt different time
coordinates to each other), a page with the perturbations of the
Einstein tensor and the energy-momentum tensor (fluid and scalar field)
in general gauge, plus one or two more pages, with Bardeen and
Kodama-Sasaki eqs and equations about the comoving curvature and
entropy perturbations.

June 11, later:
See below about the logical order of my lecture notes.

June 12:
I have put in the library the collection of equations
available in the exam, so that you can familiarize yourself with it
beforehand (section * in the course binder).
Please tell me of any errors you may find. The official
version will be given out in the exam.

** Note about my page numbering scheme:**

The "dot" pages, e.g., G15.1, are what I write first, while figuring out
things. Then, if I have time, I try to write a more clean and organized
set of notes, the "dash" pages, e.g. G15-1. I don't usually copy all
the details of calculations onto the "dash" pages. Thus, if the "dash"
pages seem to form a rather complete set, you may not need to study
the "dot" pages, except maybe for some detail you were not able to
figure out yourself. However, I usually don't have enough time to
make a complete set of the "dash" pages, and then you have to live by
the "dot" pages. The "star" pages, e.g., G14*2, are collections of
important formulae. You should paste these up on your wall for
ready reference.

The logical order of my lecture
notes:
(chapters G8 to G17 and S1 to S12)

G8.1--8, G9.1--4, G10.1, G11.1--2, G12.1--4, G13.1--3, G14-1..10,
G15-1..10, G15.6--12, G16-1..4, G16.1--7, G17-1, G17.1, G17-2, G17-2a,
G17-3..10, G17.12--16

(Thus the dash pages of G15 and G17 go only half-way, you have to go to
the dot pages for the rest of the subject.
G16 is not very organized, the dash pages contain only a summary
of the equations, so I give also the full set of dot pages)

S1.1--4, S2.1--5, S3.1--2, S4-1, S4.2--5, S5-1..2, S6-1..4, S6.6,
S7-1..2, S7-2b, S7-3..6, S8.1--11, S9.1, S9-1..12, S10.1--6, S11-1..25,
S12-1..7

I recommend you put your copies of the notes in this order, and move the
rest of the dot pages to an appendix (they have been replaced by dash
pages, but may still contain some calculations that were not copied onto
the dash pages).

** What to do to prepare for the first lectures:**

1. I am assuming you have a cosmology background at least corresponding
to Liddle & Lyth [1] pp. 1--75. If you do not know that material well,
you could start by reading these pages.

2. During the first lecture I started discussing "Vacuum fluctuations
and how they generate the primordial perturbations in inflation".
This is in Liddle & Lyth [1] chapter 7, so you could next read this
chapter.

3. The next topic is
"General relativistic perturbation theory", and I start by
following Mukhanov et al [2] together with Liddle & Lyth [1] chapter 14, trying
to bring these two standard references into contact, overcoming their
notational differences. If you find them too tough reading at first
sight, you can first look at my General Relativity lecture notes (fall 2002),
Chapter 7, in the library, which presents a bare-bones version.

**The final list of contents:**

Vacuum fluctuations and how they generate the primordial perturbations in
inflation

General relativistic perturbation theory

Scalar, vector, and tensor perturbations

Gauges

Adiabatic and isocurvature perturbations

Some inflation models

Sachs-Wolfe effect

Foregrounds (by Mika Juvela)

WMAP results

**Some literature that may be used in the course:**

I will start with the first two.

[1] A.R. Liddle and D.H. Lyth: Cosmological Inflation and Large-Scale Structure
(Cambridge University Press 2000). (In the reference library)

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

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

[4] R. Durrer: The theory of CMB Anisotropies, astro-ph/0109522.

[5] A. Riotto: Inflation and the Theory of Cosmological Perturbations,
hep-ph/0210162.

[6] A.R. Liddle and D.H. Lyth: The Cold Dark Matter Density Perturbation,
Phys. Rep. 231, 1 (1992).
(In the reference library)

[7] D.H. Lyth and A. Riotto: Particle Physics Models of Inflation and the
Cosmological Density Perturbation, Phys. Rep. 314, 1 (1999).

The WMAP first year results are in: The scientific papers and the data.

Homework problem sets (assistants):

Homework 1 (Janne Högdahl)

Homework 2 (Jussi Väliviita)

Homework 3 (Asko Jokinen)

Homework 4 (Antti Väihkönen)

Last updated: June 12th, 2003.