Lecture Course
September-October 2007
University Groningen

    Rien van de Weygaert,

                      ZG 186,   tel. 3634086,

     Rien van de Weygaert,
                      ZG 187,   tel. 3634086,


The first lecture will be on monday morning September 3, 13.7 minutes after 9 !!!!

The tutorial lecture of thursday Sept. 20 has been shifted to tuesday Sept. 18. The regular lecture will be tuesday Sept. 9:15-11:00, ZG 161. The afternoon lecture of Sept. 18, 15:15-17:00 will involve the presentations "Early Cosmology".

The tutorial lectures of tuesday Sept. 18 and thursday Sept. 27 will involve student presentations on Early Cosmology. For the schedule look at the item "Presentation" below.

While the exam has originally been schedule on tuesday October 30, it turns out that a large number of students will be away to La Palma. At the thursday Sept. 13 lecture I would like to be informed of the alternative options, following which I will possibly decide on another date.

September 21: new exam date has been fixed.
Exam: thursday November 15, 14:00-17:15, room ZG161

The lecture book by Barbara Ryden has been ordered by yours truly at The 15 copies should arrive the end of the week of Sept. 20 or the week after. Please do not order yourself or do not go and buy it at some other place if you indicated "yes" on the circulated list. I would not like to end up with several unsold copies. You can pay me either by bank transfer or cash. The price is Euro 62, including VAT(BTW) and shipping costs.

September 25: the books have arrived !
They will be handed over at the lecture of Sept. 25. If you happen to be absent, you can collect your book from me afterwards (my office).

October 9: the lecture has been shifted from 15:15-17:00 to 9:15-11:00 in the morning, due to the lecturer's evening lecture in Arnhem (and get there in time ...).

October 10: Correction task II of the werkcollege tasks of last week (Tutorial II): there were 3 typos in the task of solving the expansion of the Universe for a general matter-dominated Universe (see below).

October 15: Correction task IV (computer task) of Tutorial II: general cosmic displacement, including shear and vorticity, contained errors in equations. Substantial upgrade and correction. (see below)

October 23: tuesday Oct. 23 yours truely has to be in the Hague. The lecture is moved to thursday October 25, from 10:15-12:00.

November 13, 15:30-17:00: cosmology exam question hour, room ZG161

Required Knowledge:

There are no real requirements (except the usual basic knowledge of first and second year mathematics, physics and astrophysics. Although some familiarity with General Relativity will facilitate insight into the Universe, the lectures in the first week will provide the necessary background.


The lecture schedule will be:

      Monday 09:15-11:00    hoorcollege     ZG 161

     Tuesday 15:15-17:00     hoorcollege     ZG 161

     Thursday 14:15-16:00    werkcollege    ZG 161


The exam will consist of three/four elements:

      written exam -- thursday November 15, 2007, 14:00-17:15

      presentation (topic historical cosmology)

      2 computer tasks

General Information:

Practical information on the course -- literature, provisional schedule, topics presentation Early Cosmology -- you may find in:

     General Lecture Information


The course will be based upon

     Lecture notes,
        to be distributed during the course
     Introduction to Cosmology
        Barbara Ryden
        Addison Wesley, 2002

        ISBN 0805389121 (hardcover)

This book entails a really fabulous introduction to the basic concepts of cosmology, nearly entirely up to date. It is one of the few textbooks really fun reading, a marvel of didactic writing. In particular for the later stages of the lecture series -- Cosmic Microwave Background, Cosmic Nucleosynthesis, Inflation -- I will assume you have the book.

In addition, there are three general cosmology books that from time to time you may wish to consult (but which are not obligatory fare for this course !!!). They are somewhat more demanding than the Ryden book, yet contain a lot of useful information,

     Cosmological Physics
        John Peacock
        Cambridge University Press, 1998

        ISBN 0521422701 (paper)

      Cosmology, The Origin and Evolution of Cosmic Structure
        P. Coles, F. Lucchin
        Wiley, 2n edition, 2002

        ISBN 0471489093

     Principles of Physical Cosmology
        P.J.E. Peebles
        Princeton Univ. Press

        ISBN 0691074283

Lecture Notes:

Below you find a listing which will gradually be updated. You may download the pdf and ppt files.

      Introduction & Overview                                     ppt
      General Relativity                                                pdf
      The Cosmological Principle: Evidence                   ppt
                  (still some modifications needed, on cosmic dipole)
      Robertson-Walker metric                                     pdf
      Cosmological Principle &                                    handout
                     Robertson-Walker metric
                     Observational Cosmology
      Cosmic Dynamics: &                                           handout
                     FRW Cosmology
      Cosmic Constituents                                            ppt
                  (still needs substantial extension on dark energy)
      FRW Universe: Solutions                                     handout
      Evolution Hubble Parameter H(t)                          handout
                   and: Cosmic Time
      Evolution Omega & Flatness Problem                   handout
                   and: Horizons & Horizon Problem
                   and: Inflationary Universe
      The Hot Big Bang                                                handout
                   & Thermal History of the Universe
                   and: Cosmic Microwave Background

Tentamen/Written Exam

The written exam is on:

      Thursday November 15, 14:00-17:15; room ZG161

The required material for the exam is the following:
   Ryden: chapter 3, 9, 10, 11
   General Relativity:    pdf file
                           metric tensor, Einstein field equation, energy-momentum tensor
                           (not more, of these the definitions and meaning)
   the Cosmological Principle:
                           Significance, Observational Evidence Isotropic & Homogeneous Universe, Implications Geometry Universe
                           content ppt file, to be downloaded from webpage (see lecture notes)
   Robertson-Walker metric: handout
   Cosmological Observables: handout
                             includes: redshift, Hubble expansion, luminosity & angular diameter distance
   Observational Cosmology: handout
                             conversion from coordinate distance to redshift, Mattig's relations, Hubble diagram (to 2nd order, with q)
   Friedmann equations: handout
                             includes: defn. Omega, acceleration parameter q, energy equation,
                             it will be expected that you will be able to manipulate and make calculations with the FRW equations !!!!!
   Cosmic constituents:
                           obligatory: the rough inventory of all ingredients,
                           including their equation of state (incl. the distinction between cosmological constant and generic dark energy),
                           and implied evolution as function of expansion factor a(t)

                           expected: having read the content of accompanying ppt file
                           (ie. you will have to be able to provide an informative text
                           on the way the properties of these constituents are measured, but need to know this by heart).
   FRW universes: evolution H(t), Omega(t), cosmic time (but not the observational constraints) : handouts
                             it will be expected that you will be able to manipulate and make calculations with the FRW equations !!!!!
   FRW Universe solutions/expansion histories: handout
                             includes: everything, except for the "historic" universes (Einstein, de Sitter, Lemaitre)
   Inflationary Universe:: handout + Ryden chapter 11
                             Flatness + Horizon problem (technically, with eqns.)
                             Monopole Problem + Structure formation (only qualitatively)
                             Basic physics (only rudimentary, inflaton field, de Sitter expansion solving flatness & horizon problems)
   Thermal History of the Big Bang:: handout + Ryden 10
                             basic physics Hot Big Bang
                             Cosmic Nucleosynthesis (Ryden 10)
   Cosmic Microwave Background: handout + Ryden 9

For reference, the exams of the years 2004 and 2005 you may find here:

     Exam cosmology 2004
     Exam cosmology 2005

Presentation: Early Cosmology

Attached you find the files with topics for your presentation on "Early Cosmology".

Chose the topic of your choice, subsequently inform me about your choice. Alternatively you may choose a topic not mentioned in the list. In that case consult lecturer. After approval you can set to work on the subject.

      Early Cosmology

You are expected to prepare a 10-15 minute presentation (with ppt or pdf notes) !

The first set of 11 early cosmology presentations will be on Sept. 18, 15:15-17:00. Given the large number of participants a second slot of presentations will follow on thursday Sept. 27, 14:15-16:00. For the schedule of the presentations see

      Early Cosmology Schedule

Werkcollege (tutorials)

Attached you find the files with the werkcollege assignments.

     Werkcollege Sept. 6-13:    General Relativity, task 1-4

     Werkcollege Oct 4:       Newtonian Cosmology, Hubble expansion, task 1-4

     Werkcollege Oct 11:       Solutions to the FRW Universe, 1-2

     Werkcollege Oct 18:       Observational Cosmology, 1-3

Important: the assignments that were not completed during the werkcollege/tutorial class, you are expected to solve yourself at home. Completed tasks should be turned in to your lecturer. Completed and approved tasks are required for completion of the course.

Thus: please turn them in to your tutor (ie. me) !

For questions and advice on the tasks you are of course welcome to contact your "werkcollegedocent", which is me ! Room 186 !

For searching the astronomical literature the two most important website to consult are those of

     ADS:       NASA Astrophysics Data System
     astro-ph:   astrophysics e-print server

Notice that ADS allows you to expand your literature search via the references of the paper under consideration, as well as the links to the papers that refer to it. While using this possibility wisely you may quickly find most relevant studies. Also notice that the links of ADS to the journals in which the papers are published may need you to use your student number + password for the University library, or you have registered with the University Library, when working from outside the university (e.g. from home). Otherwise you will not be able to use the university subscription to these journals.

Interesting Literature

During the course several papers relating to the lecture content will be handed out.
Here you may download them (will be updated during the course).

      Discovery Hubble Expansion
         Hubble E., 1929, Proc. Nat. Acad. Sci., 15 (5 pp.)
      Observational Tests World Models
         Sandage A., 1988, Ann. Rev. Astron. Astrophys. 26, 561
      Discovery Cosmic Microwave Background
         Penzias A.A. & Wilson R.W., 1965, Astrophys. J. 142, 419
      Discovery & Explanation Cosmic Microwave Background
         Dick R.H., Peebles P.J.E., Roll P.G., Wilkinson D.T., 1965, Astrophys. J. 142, 414
      SNIa discovery Lambda: High-z Supernova Search Team
         Riess et al., 1998, Astron. J., 116, 1009
      SNIa discovery Lambda: Supernova Cosmology Project
         Perlmutter et al., 1999, Astrophys. J., 517, 565
      Scale Factors & critical values Lambda in Friedmann universes
         Felten J.E., 1986, Rev. Mod. Phys. 58, 689
      Rindler: visual horizons in world models
         Rindler W., 1956, MNRAS, 116, 662
      Harrison: Hubble spheres and Particle horizons
         Harrison, E., 1991, Astrophys. J., 383, 60
      Guth: Inflationary Universe
         Guth, A.H., 1981, Phys.Rev.D., 23, 347

Lecture Schedule:
(provisional, changes possible)

Subject HoorcollegeDates
Subject Werkcollege

Sep. 3 (c)
Sep. 4 (c)
The Hot Big Bang:
a Review and Introduction

The metric Universe:
General Relativity, basics and essentials
Sep. 6 (w)Werkcollege I
2 Sep. 10 (c)
Sep. 11 (c)
The Cosmological Principle:
Cosmic Time and Weyl's Postulate

Observational Evidence Cosmological Principle
Observational Evidence Isotropic Universe
Observational Evidence Homogeneous Universe
Sep. 13 (w) Werkcollege I
3 Sep. 17 (c)
Sep. 18 (c)
Robertson-Walker metric

Cosmological Redshift
Hubble Expansion
Cosmological Observables in a Geometric Universe

Observational Cosmology
Sep. 20 (w)Presentations I:
Cosmology in History
4 Sep. 24 (c)
Sep. 25 (c)
Friedman Equations
Cosmological Parameters:
     Hubble parameter, Omega, q and curvature

Cosmic Components:
     Radiation, (Dark) Matter and Dark Energy
Sep. 28 (w)Presentations II:
Cosmology in History
5 Oct. 1 (c)
Oct. 2 (c)
Cosmological FRW Solutions:
     Radiation- and Matter-dominated Universes, Radiation-Matter Equivalence
     Dark Energy and Cosmic Acceleration
     General FRW solutions, Matter-Dominated Universes, Flat Universes, ...

Cosmic Horizons
Oct. 4(w)Werkcollege II/Computer Task I
6 Oct. 8 (c)
Oct. 9 (c)
Measuring Cosmological Parameters
The Age of the Universe
Concordance Cosmology

Thermal History of the Universe
Primordial Nucleosynthesis
Oct. 11 (w)Werkcollege III/Computer Task II
7 Oct. 15 (c)
Oct. 16 (c)
The Cosmic Microwave Background:

     Recombination, Decoupling and Freeze-out
     Thermalization and Blackbody Spectrum of the CMB
     Anisotropries of the CMB
Oct. 18 (w)Werkcollege IV
8 Oct. 22 (c)
Oct. 23 (c)
The problems of standard cosmology:
     Flatness Problem, Horizon Problem,
     Structure Problem, Monopole Problem

Inflation & the Inflationary Universe
Oct. 26 (c)Chronicle of the Universe
from Neutrino Decoupling back to the Planck Time