Lecture Course
Large Scale Structure of the Universe
Feb.-April 2007
University Groningen

    Rien van de Weygaert,

                      ZG 186,   tel. 3634086,

     Erwin Platen,
                      ZG 187,   tel. 3634087,


The lecture of tuesday Feb. 13 is postponed to the 2nd lecture week.
This because of the exam ISM on Feb. 13.
Instead, the lecture will take place on wednesday Feb. 21, from 13:15-15:00.

As of thursday February 22, room ZG 257 has been reserved for the tutorial/ "werkcollege".

On wednesday February 21 the list with 19 report topic suggestions has been distributed. Students are invited to select a topic and to write a report of around 20 pages. Reports may be written alone or in groups of two (see section below)

Wednesday February 28, room ZG 257 (!!!!): for those of you who are interested, there will be a "question" lecture in which you may ask any question/problem you have with respect to FRW cosmology and Big Bang cosmology. In the first set of lectures undoubtedly various issues could not be treated in depth, here is your chance to find out !

As of wednesday March 7 the "question lectures" are repeated each week, 13:15-15:00, room ZG 161.

Werkcollege/tutorial March 8: Virgo computercluster, ZG 291

Thursday April 5: last werkcollege is transformed into round-off lecture (crucial topic)

Friday April 20, 10:00, ZG161: question hour

Required Knowledge:

Although it will be helpful to have followed the basic lecture course "Cosmology", this is not a requisite.

A recapitulation, overview and summary of the necessary knowledge of basic Cosmology (including some General Relativity), will be the subject of the first week's lectures.


The lecture schedule will be:

      Monday 09:15-11:00    hoorcollege     ZG 161

     Tuesday 11:15-13:00     hoorcollege     ZG 161

     Thursday 09:15-11:00    werkcollege    ZG 257


The exam will consist of three/four elements:

      written exam -- April 24, 2007: 09:15-12:30

      report special topic

      3 computer tasks (point processes, correlation function, Gaussian random fields)


The course will be based upon the lecture notes, to be distributed during the course.

No specific book will be followed,
for the purpose of the necessary backup information and context the following book is recommended:

     Cosmological Physics
        John Peacock
        Cambridge University Press, 1998

        ISBN 0521422701 (paper)

In addition, THE book on basic cosmology that I will always warmly recommend (but which you are not required to have) - one of the few textbooks really fun reading and a marvel of didactic writing -- is:

     Introduction to Cosmology
        Barbara Ryden
        Addison Wesley, 2002

        ISBN 0805389121 (hardcover)

Lecture Notes:

The course is based upon the lecture notes. Below you find a listing of the notes.

Part of the notes you can download in 3 forms:
* ppt file, a colour pdf (handout, 2 slices/page) and a greyscale pdf (handout, 2 slices/page)
* pdf file texed notes
* xerox copy, distributed during the course

Below you find a listing. You may download the pdf and ppt files.
Please check the hotes you have. When you are missing one or more items contact me.

      General Relativity                   pdf
         Not exam material: for your information only

      FRW cosmology                     pdf

      The Cosmic Web                     ppt
         The Cosmic Web, h2pdf          handout, pdf, colour
         The Cosmic Web, gh2pdf        handout, pdf, greyscale

      Gravitational Instability Theory Handout
         Overview & Outline gravitational instability theory (& course)
         Important for exam !!!!

      Linear Perturbation Theory       pdf
         Key chapter !!!!!!
         Use the next item, the cosmic flows draft, as illustration of linear velocity fields.

      Cosmic Flows                         ppt
         Cosmic Flows, h2pdf               handout, pdf, colour
         Cosmic Flows, gh2pdf             handout, pdf, greyscale

      Random Field Theory              Handout
         "Starting Conditions"
         Important for exam !!!!

      Power spectra & Correlation functions                    
                                                       pdf + handout
         CDM power spectra
         SDSS & 2dFGRS power spectra
         SDSS & 2dFGRS 2pt correlation function
         REFLEX cluster power spectrum & 2pt correlation function

      Statistical Measures                 Handout
         Ergodic theorem
         Two-point correlation function (spatial and sky)
         not exam: redshift space correlations, higher order correlations, other measures

      Fluctuation Modes/Mass Scales Handout
         Fluctations modes (adiabatic, isocurvature, isothermal)
         Jeans Instability, Jeans Mass, Silk Damping, Silk Mass, Meszaros effect
         Important for exam !!!!

      Going nonlinear                      pdf
         Exam material:
         Zel'dovich approximation, Spherical Model, Ellipsoidal Model
         Not exam material: Lagrangian Perturbation Theory
         Also see handout "Systems of High Symmetry"

      Systems of High Symmetry     Handout
         Includes exam material:
         Spherical Model,
         Ellipsoidal Model,
         Press-Schechter Formalism

      CMB                                      ppt
         CMB, h2pdf                           handout, pdf, colour
         CMB, gh2pdf                         handout, pdf, greyscale
         For exam:     Sachs-Wolfe effect; the rest: read thoroughly
         (ie. you are supposed to know to answer a general question, without equations, on the CMB)

Large Scale Structure movies

It is highly instructive to study the following movies:

Galaxy Distribution:

      SDSS3 galaxy redshift survey, zoom-out
      SDSS3 galaxy redshift survey, rotate

Computer Simulations Structure Formation:

      Virgo LCDM simulation
         Courtesy: Volker Springel & Virgo consortium
      Millennium simulation, zoom-in
         Courtesy: Volker Springel & Virgo consortium
      Millennium simulation, flythrough
         Courtesy: Volker Springel & Virgo consortium


Attached you find the file with tentamen Large Scale Structure 2002 (2004 was an oral exam)

      Tentamen LSS2002

Werkcollege (tutorials)

Attached you find the files with the werkcollege assignments.

  Feb. 19    Werkcollege I/Tutorial I

  Feb. 22    Werkcollege II/Tutorial II  

  Mar. 29    Werkcollege III/Tutorial III  

  Mar 8      Computer Task I   

                    the Soneira-Peebles Model
                    explanatory manuscript, Schaap & van de Weygaert

  Mar 15    Computer Task II   

  Mar 22    Computer Task III   

You are expected to solve the assignments yourself that were not completed during the werkcollege/tutorial class. Please turn them in to your tutor (ie. Erwin) !

Report Topics:

The report is part of the final exam. The intention is to investigate in some detail and to some depth one particular topic related to the formation of structure in the Universe. You are expected to acquaint yourself with a few of the essential literature references and to critically assess them (do not always take statements for granted, the field is moving quickly, knowledge may get outdated, viewpoints may change or be proven wrong).

Write a report of around 20 pages (of course this may vary, anything from 15-30 will probably be acceptable). Include some essential equations, calculations, results and figures, whenever applicable. You are more than welcome to include your own discussions, equations, viewpoints, calculations (also computer calculations), plots if you would like to do so ! In other words, the content is entirely up to your own preference ! Evidently, include a reference list, as unbiased as possible (not easy !).

      Large Scale Structure Report Topics

A list of 19 topics has been distributed during the 4th lecture (see above). You are invited to choose a topic and write the report in groups of two. Given that none of the topics is really trivial and may involve working through some tough material (front research !) it is usually beneficial to be able to discuss about the involved issues and problems with a collaborator. In fact, these days it is rare to write papers and work on a project all by yourself: also astrophysics and cosmology has entered the era of cooperate and consortium science ! Evidently, you are also welcome to work on a topic by yourself.

Each topic has been accompanied by a list of relevant literature references. These are intended to provide a guideline. You are welcome to stroll around all by yourself through the literature and find yourself (better) references. You do not need to exhaustively read everything ! Usually the best thing to do is to start with a recent up-to-date review paper, it often provides a reasonable idea of what is going on in the field.

Please select a topic and establish a collaboration, subsequently inform me (Rien) about your project choice and collaborator.

We are looking forward to some illuminating and interesting papers ! Recall this may be deep stuff and we need to learn far more ourselves about most issues too. So please educate us !

Rien and Erwin

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.

      Hamilton A.J.S., 2001
        Formulae for growth factors in expanding universes containing matter and a cosmological constant
        MNRAS 322, 419

      Soneira R.A., Peebles P.J.E., 1978
        A computer model Universe: simulation of the nature of the galaxy distribution in the Lick catalog
        Astron. J. 83, 845

Lecture Schedule:
(provisional, changes possible)

Subject HoorcollegeDates
Subject Werkcollege

Feb. 12 (c)
Feb. 15 (c)
The Cosmic Web, an Inventory:
from Galaxies, Groups, Clusters, Superclusters to the CMB

General Relativity,

Basic Cosmology:
Cosmological Principle, Robertson-Walker metric,
Redshift, Cosmic Distances
Friedman Equations
Cosmic Components:
Radiation, Matter - Baryonic & Dark - and Dark Energy
Cosmic Epochs
Feb. 15 (w)no werkcollege
2 Feb. 20 (c)
Feb. 21 (c)
Basic Cosmology:
Cosmological Principle, Robertson-Walker metric,
Redshift, Cosmic Distances
Friedman Equations
Cosmic Components:
Radiation, Matter - Baryonic & Dark - and Dark Energy
Cosmic Epochs
Feb. 19 (w)

Feb. 22 (w)
Robertson-Walker metric
FRW universe solutions

Observational Cosmology:
Number counts & Luminosity distance
3 Feb. 26 (c)
Feb. 27 (c)
Gravitational Instability:
(Linear) Perturbation Theory,
Structure Growth
Cosmic Flows

Random Density & Velocity Fields
Multidimensional Gaussian distributions
Power Spectrum
Mar. 1 (w)Linear Perturbation Equations:
Physical & Comoving Coordinates
4 Mar. 5 (c)
Mar 6 (c)
(Spatial) Statistical Analysis of the LSS:
Correlation functions
Counts in Cells
Power spectrum
Minkowski functionals
Higher-order statistics

Galaxy sky surveys,
Galaxy redshift Surveys
Clusters of Galaxies
Mar. 8 (w) Point Processes
(computer task)
5 Mar. 12 (c)
Mar. 13 (c)
Origin Primordial Perturbations: Inflation
Superhorizon and subhorizon perturbations
Perturbation Evolution
Radiation & Matter Perturbations
Baryonic Oscillations

Matter Scales
Jeans Mass, Silk damping
Power Spectra: Cold Dark Matter, Hot Dark Matter
non-Gaussian perturbations
Mar. 15(w) Two-point correlation function
(computer task)
6 Mar. 19 (c)
Mar. 20 (c)
Nonlinear Clustering & Structure Formation
Hierarchical Clustering, Anisotropic Collapse and the Formation of Voids
Spherical Model, Ellipsoidal Model
Zel'dovich formalism

Hierarchical clustering:
Press-Schechter and Excursion set formalism
Peak-patch formalism
Halo Model
Mar. 22 (w)Gaussian Random Fields
(computer task)
7 Mar. 26 (c)
Mar. 27 (c)
Cosmic Microwave Background
CMB anisotropies, theory
CMB anisotropies, analysis
Mar. 29 (w)Power Spectrum &
Spherical Model
8 Apr. 2 (c)
Apr. 3 (c)
Intergalactic Medium: Lya forest & WHIM
Gravitational Lensing, Cosmic Shear
Dark Ages, First Stars & Reionization
Apr. 5 (w)Press-Schechter Formalism
& Halo Mass Functions