CMB Physics, fall 2004
What does CMB stand for?
Lecturer: Hannu Kurki-Suonio, office hour We 10-11, C328
Lectures: Mo 14-16 and Fr 12-14 (Physicum A315)
lecture is on Monday, Sep 6th. The last
lecture will be on Friday Dec 10th. Note:
Because I have had to cancel some lectures,
I shall give a couple of extra lectures at the beginning
of spring term 2005. The last of these is on Tuesday, March 15th at
There will be occasional homework problems, but there will be no
This is a research-oriented graduate-level course on the physics related to
the cosmic microwave background (CMB) anisotropy,
and on methods to extract cosmological information from the CMB.
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
Language of instruction (English and/or Finnish) depends on the audience.
Background expected: Cosmology and general relativity
What to do to prepare for the first lectures:Review my notes on
Cosmological Perturbation Theory (expanded from my 2004 GR course).
Modern Cosmology (Academic Press 2003).
Errata. (In the reference
 A.R. Liddle
and D.H. Lyth:
Cosmological Inflation and Large-Scale Structure
(Cambridge University Press 2000), Chapters 14 and 15. Check the
W. Hu: Wandering in the Background: A CMB Explorer,
PhD Thesis (UC Berkeley 1995),
 J. Väliviita:
An analytic approach to cosmic microwave background radiation,
Master's thesis (Univ. Helsinki 1999)
 C.-P. Ma and E. Bertschinger: Cosmological Perturbation Theory in the
Synchronous and Conformal Newtonian Gauges, ApJ 455, 7 (1995). You can get it
 M. Bucher, K. Moodley, and N. Turok: General primordial cosmic
PRD 62, 083508 (2000) ,
Constraining Isocurvature Perturbations with
Cosmic Microwave Background Polarization,
PRL 87, 191301 (2001)
 W. Hu and N. Sugiyama: Anisotropies in the Cosmic Microwave Background:
An Analytic Approach, ApJ 444, 489 (1995). Get it from NASA
 W. Hu, M. Fukugita, M. Zaldarriaga, and M. Tegmark: CMB Observables and
Their Cosmological Implications,
ApJ 549, 669 (2001)
 U. Seljak and M. Zaldarriaga: A Line-of-Sight Integration Approach to
Cosmic Microwave Background Anisotropies, ApJ 469, 437 (1996).
Get it from NASA
 H. Kurki-Suonio, V. Muhonen, and J. Väliviita: Correlated
Primordial Perturbations in Light of CMB and LSS Data,
 SDSS Collaboration, M. Tegmark et al.:
Cosmological parameters from SDSS and WMAP,
PRD 69, 103501 (2004)
Codes to calculate the CMB spectra:
In terms of contents, this course is a logical continuation of my
originally named "CMB Physics" also, but which I now prefer to call
"Cosmological Perturbation Theory", since most of the time was spent on that.
The 2003 course is, however, not a necessary prerequisite for taking this
course. A sufficient background in cosmological perturbation theory is
provided by my 2004 General Relativity course.
As with the previous course, the actual content is not known beforehand, as
I am creating the course while lecturing it. I plan to start
with a short review of perturbation theory to
cover needed material beyond the GR course. Then I plan to follow
Chapter 4 of Dodelson's book: on the Boltzmann's equations for the
cosmological plasma in the perturbed spacetime. This is the first major
topic, and provides the foundation for CMB theory.
Sep 17: I have now started a course binder for lecture notes.
It is located in room A314. It now contains the LaTeX'ed lecture notes on
Cosmological Perturbation Theory, now continuing to page 33.
It also contains
six pages of handwritten notes, starting us on the road to Boltzmann equations.
The first of them was covered in class today; the rest are for Monday.
From here on you will be getting handwritten notes. You can either make copies
of them from the course binder, or print them from the Web, once I get
around to scanning them (hopefully early next week).
Sep 21: Pages 30, 33, B3.1, B3.3 in the course binder replaced with corrected
ones. New pages up to B7.2. I have now also scanned the handwritten pages,
so everything in the course binder is also available below.
(I do not know why pages B6.1 and B6.2 came upside down.)
Oct 6: Rescanned sections B1 to B7: Some trivial errors corrected
on page B1.1; new pages B6.3, B6.4.
Oct 25: Section B15 replaced with a corrected version. Section B16
finishes the discussion of Boltzmann Equations (B), and we move to a new
chapter: Initial Conditions (I). If you have fallen off the tracks
after section B6, now is a good point to get back on: from sections B7
to B15 we will basically just use the collision terms derived;
so if you are willing to accept those, just read section B16 and
you are ready for the Intial Conditions.
No lecture on Friday, Oct 29th, because of the
Particle Physics Day
Dec 10: With today's lecture (notes A4) we have reached the final results
of this course: the line-of-sight formula for the present-day multipoles
of the Fourier components of the brightness function, Eqs (8) and (10);
and the CMB angular power spectrum C_l in terms of these multipoles, or the
corresponding transfer functions and the
primordial power spectra, Eqs (11) and (16). Finally we obtained a
helpful approximate version, Eq (19), of the line-of-sight integral.
I plan to give an extra lecture at the beginning of the spring term, to
wrap up the course with a discussion on how the C_l depend on the
cosmological parameters, and how that can be understood in terms of the
physics we have learned. I shall also tell you about the exam then.
There remain two important topics that we did not
have time to cover in this course, tensor perturbations and polarization.
Maybe I can return to them some day.
March 11th, 2005: My Cosmological Perturbation Theory notes
had a serious sign error in the unnnumbered equation in Section 15.
(With my sign conventions the comoving curvature perturbation cal R
has the opposite sign to the metric perturbation psi of
the comoving gauge.) This is now fixed in the 26.2.05 version of these
April 12th, 2005: I finally scanned the remaining pages of my lecture notes
(Sections A5 and A6, as well as some plots for A2) here.
G. Cosmological Perturbation Theory, 26.2.05 version
(LaTeX, 2+33 pages, 560 KB PostScript)
continuity (handwritten, 1 page,
225 KB pdf)
B. Boltzmann Equations
Boltzmann Equations, sections B1 to B7
(handwritten, 15 pages, 3491 KB pdf, updated 6.10.04)
B8. From Thomson Cross Section to the Collision Term
(handwritten, 8 pages, 2191 KB pdf)
B9. Lorentz Invariance of Integration Elements
(handwritten, 9 pages, 2111 KB pdf)
B10. The Collision Term for Photons
(handwritten, 6 pages, 1363 KB pdf)
B11. Boltzmann Equation for Photons, Optical Depth
(hand, 7 pages, 1465 KB pdf)
B12. Angular Integrals
(hand, 3 pages, 538 KB pdf)
(hand, 8 pages, 175 KB pdf)
B14. Cold Dark Matter
(hand, 3 pages, 63 KB pdf)
B15. Baryonic Matter
(hand, 6 pages, 108 KB pdf)
B16. Fourier Transform and Legendre Expansion
(hand, 7 pages, 157 KB pdf)
I. Initial Conditions
I1. Curvature Perturbations Deep in the Radiation-Dominated
Era (hand, 10 pages, 249 KB pdf)
I2. Entropy Perturbations
(hand, 2 pages, 46 KB pdf)
I3. General Observations
(hand, 3 pages, 82 KB pdf)
I4. Gaussian Initial Conditions
(hand, 5 pages, 107 KB pdf)
I5. Transfer Functions for Scales that Enter During
(hand, 7 pages, 151 KB pdf)
X1. The Einstein and Fluid Equations (Newtonian Gauge)
(hand, 1 page, 14 KB pdf)
(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)
A. Anisotropy of the CMB
A2. Acoustic Oscillations
(hand, 4 pages, 77 KB pdf)
A2.4x Some plots for Section A2
(scanned, 11 pages, 136 KB pdf)
A3. Diffusion Damping
(hand, 5 pages, 102 KB pdf)
A4. From Inhomogeneities to Anisotropies
(hand, 10 pages, 184 KB pdf)
A5. The C_ell spectrum at Large and Small Scales
(hand, 9 pages, 168 KB pdf)
A6. Cosmological Parameters
A6 and A6.1 Curvature
(hand, 6 pages, 133 KB pdf)
A6.2 Sound Horizon Angle and the Acoustic Peaks
(hand, 13 pages, 225 KB pdf)
A6.3 to A6.7
(hand, 14 pages, 222 KB pdf)
Homework problem sets (assistants):
Homework 1 (Torsti Poutanen)
Homework 2 (Vesa Muhonen)
Homework 3 (Ville Heikkilä)
The WMAP first year results:
scientific papers and the
4th NorFA Network Meeting on Particle Physics and Cosmology
Last updated: April 12th, 2005.