Lecture Course
Large Scale Structure of the Universe
April-June 2009
University Groningen

    Rien van de Weygaert,

                      ZG 186,   tel. 3634086,

     Jakob van Bethlehem,
                      ZG 153,   tel. 3634063,


The lecture schedule will be:

      Monday    13:45-15:30       hoorcollege/lecture               ZG 161     
                                                                                            (April 27, May 4)
         Monday    09:15-11:00       hoorcollege/lecture               ZG161     
                                                                                            (June 8, June 22)
         Monday    09:15-11:00       hoorcollege/lecture               Bernoulliborg, 5161.0273     
                                                                                            (May 18, May 25, June 15)

      Thursday   09:15-11:00      werkcollege/tutorials             ZG 257

      Friday       09:15-11:00       hoorcollege/lecture               ZG 257


At 4 occasions (May 18, May 25, June 8, June 15) this lecture series will be part of the Osaka lecture program: as a result, on these mondays the monday lectures will take place from 09:15-11:00, in the large lecture hall of Bernoulliborg.
On thursday April 30 there will no tutorial lecture, due to Queen's Day.
In the week of May 11-17 there will be no lectures, due to the absence of lecturer (conference Granada). Of course the tutorials/werkcollege will continue.
On thursday May 21 there will no tutorial lecture, due to Ascension Day holidays.
On monday May 25 Osaka Lecture: surveys of large scale structure.
On monday June 1 there will no lecture, because of Pentecost holidays.
On monday June 8 From 11:15-13:00. Tutorial lecture (instead of the one on thursday June 11)
On thursday June 11 Extra lecture instead of tutorial lecture.
On monday June 15 Osaka Lecture: measures of large scale structure.
On thursday June 18 Extra lecture instead of tutorial lecture. The tutorial will be in the week of June 22-25.
On friday June 26 there will be no lecture, due to the absence of lecturer (conference Copenhagen).
On tuesday June 30 Osaka Lecture: cosmic microwave background.

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 exam will consist of three/four elements:

      written exam -- July 7, 2009: 14:00-17:30

      report special topic

      3 computer tasks (point processes & correlation function, Gaussian random fields, N-body simulations)


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

No specific book will be followed. Nonetheless, two books are recommended for the purpose
of the necessary backup information, overlapping substantially with parts of the lecture material:

     Cosmological Physics
        John Peacock
        Cambridge University Press, 1998

        ISBN 0521422701 (paper)

The most up-to-date book is:

     Galaxy Formation
        Malcolm Longair
        Astronomy & Astrophysics Library, 2nd ed., Springer

        ISBN 9783540734772 (hb)

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 & Exam Material:

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

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 of the notes, and I will notify you when they become available. Subsequently, they will be available for downloading.
Please check the notes you have. When you are missing one or more items contact me.

      FRW cosmology                     pdf
         reference (basic knowledge, not part of exam)

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

         read thoroughly: while not necessary to know all details, you may be asked to reproduce general facts (cosmic web, clusters, voids, simulations, ...)

      Galaxy Redshift Surveys                 ppt
         Galaxy Redshift Surveys, h2pdf      handout, pdf, colour

         read thoroughly: while not necessary to know all details, you may be asked to reproduce general facts on e.g. SDSS survey. Necessary to know in detail: listing of "cosmic fossils" (and what they mean), galaxy luminosity function, Schechter function, survey depths, survey strategies, photometric redshifts, magnitude- and volume-limited surveys, ...

      Gravitational Instability Theory Handout
         Overview & Outline gravitational instability theory (& course)

      Linear Perturbation Theory       pdf

         Key chapter !!!!!! You must be able to follow all equations (and work with them).
          Know by heart: comoving vs. physical perturbation quantities (eqn. 2,3,10,15,16,18), full and linear fluid equations (particularly: eqns. sect. 6.1), linear perturbation eqn.(eqn. 4), general solution (eqn. 43), solution for EdS universe (eqn. 48), solution empty Universe (eqn. 54), structure freeze-out time open Universe (eqn. 61, 62), general growth factor (eqn. 87, 88), relation matter and radiation density fluctuation adiabatic regime (eqn. 106), gravitational potential fluctuation (eqn. 111), potential growth factor (eqn. 115), peculiar gravity (eqn. 120), peculiar gravity growth factor (eqn. 121), peculiar velocity (eqn. 142), definition Peebles factor (eqn. 143, 144), peculiar velocity growth factor (eqn. 148), peculiar velocity (eqn. 153, 158), definition bias (eqn. 157), beta factor (eqn. 159)
         Skip: section 7.3.5, 7.3.6

         Use the next item, the cosmic flows draft, as illustration of linear velocity fields.

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

          Read thoroughly. Know by heart: definition dipole.

      Random Field Theory              Handout
         "Starting Conditions"

         Important for exam !!!! Know by heart Fourier definitions, definition power spectrum, relation power spectrum and correlation function, definition Gaussian distribution (in real space and Fourier space), velocity and potential power spectrum. Important to be able to explain the influence of power spectrum on development structure. Different contributions to power spectrum (primordial power spectrum: Harrison-Zeldovich spectrum; transfer functions), normalization power spectrum, be able to explain features (slopes, maximum) in CDM power spectrum).

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

         Important for exam !!!! Know by heart: fluid eqns. of motion including pressure, definition Jean instability, Jeans mass, sound velocity in pre- and post-recombination era, perturbation evolution during radiation- and mass-domination in pre-recombination era (both sub- and super Jeans mass scale), development horizon, Jeans and Silk damping mass as function of time.

      Going nonlinear                      pdf

         Exam material:
         Zel'dovich approximation, Spherical Model, Ellipsoidal Model
         Not exam material: Lagrangian Perturbation Theory (sect. 3: but good to read); also skip sect. 4.2, 4.3
         Know by heart: Zel'dovich, eqn. 31, 36, 49, 50, 52, 54, 63, 64, 71.
         Know by heart: Spherical model, eqn. 79, 82, 83, 95, 96, 97, 98, 99
         Know by heart: Ellipsoidal model, eqn. 110, 111, 116, 123
         Also see handout "Systems of High Symmetry"

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

         Exam material: study thoroughly. You will be expected to be able to follow all equations in detail, and reproduce the line of reasoning.

      Clusters and the Theory of the Cosmic Web                    pdf
         van de Weygaert & Bond 2008a;
         A Pan-Chromatic View of Clusters and the Large-Scale Structure;
         Lecture notes in Physics 740; eds. M. Plionis, O. Lopez-Cruz, D. Hughes

         Exam: read thoroughly; you will be expected to understand the overall picture (but not the details); you may e.g. be asked to summarize the essential points of the cosmic web theory.

      Observations and Morphology of the Cosmic Web           pdf
         van de Weygaert & Bond 2008b;
         A Pan-Chromatic View of Clusters and the Large-Scale Structure;
         Lecture notes in Physics 740; eds. M. Plionis, O. Lopez-Cruz, D. Hughes

         Exam: read thoroughly; you will be expected to understand the overall picture (but not the details); you may e.g. be asked to write a summary on major components of the cosmic web and the role of voids.

      Statistical Measures of Large Scale Structure      ppt
         Statistical Measures of Large Scale Structure, h2pdf            handout, pdf, colour

         Exam: study thoroughly and in detail. Necessary to know the definition of two-point correlation function, n-point correlation functions, ergodic theorem, ways to measure the correlation functions, influence boundary and selection effects, power-law 2pt correlation function (parameters and values), power spectrum analysis, Minkowski functionals;

      CMB                                      ppt
         CMB, h2pdf                           handout, pdf, colour
         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)

         Exam: study thoroughly and in detail. Necessary to know the description of CMB temperature fluctuations in spherical harmonics, power spectrum in spherical harmonics, Sachs-Wolfe effect (eqn.), primary and secondary CMB anisotropies, sensitivity angular power spectrum to curvature, baryonic matter, matter and dark energy. Rest: read thoroughly.

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


Werkcollege (tutorials)

Attached you find the files with the werkcollege assignments.

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. Jakob) !

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 !).

A list of 19 topics will be 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 Jakob

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.

Lecture Schedule:
(provisional, changes possible)

Subject HoorcollegeDates
Subject Werkcollege

Apr. 27 (c)

May 1 (c)
Introduction: Cosmic Inventory:
Large Scale Structure & Cosmic Structure Formation
Galaxies, Groups, Clusters, Superclusters, IGM
Primordial Fluctuations & the Cosmic Microwave Background
Cosmic Structure Formation

Basic Cosmology:
Einstein Field Equation,
Cosmological Principle, Robertson-Walker metric,
Redshift, Cosmic Distances
Friedman Equations
Cosmic Epochs
Apr. 30 (w)no werkcollege/tutorial (queen's day)
2 May 4 (c)

May 8 (c)
Gravitational Instability:
(Linear) Perturbation Theory,
Structure Growth
Cosmic Flows

Cosmic Components &
Influence on Cosmic Structure Formation:
   Matter: Baryonic Matter & Dark Matter
   Dark Energy
May 7 (w)

FRW Cosmology
FRW universe solutions
Observational Cosmology
3 May 11 (c)
May 15 (c)
no lectures

(Granada conference, NAC conference)
May 14 (w)

Linear Perturbation Equations
(Physical & Comoving Coordinates)

4 May 18 (c)
(Osaka lecture)

May 22 (c)
Mapping the Universe
Galaxy sky surveys
Galaxy redshift Surveys
Lensing Surveys
The Cosmic Web Observed
Cosmic Web: Filaments, Sheets and Voids
Clusters of Galaxies

Random Density & Velocity Fields
Multidimensional Gaussian distributions
Power Spectrum
May 21 (w)

(Ascension Day,
other date will
be announced)
Point Processes
(computer task)
5 May 25 (c)
(Osaka lecture)

May 29 (c)
Analysis of the Large Scale Structure
Correlation functions
Counts in Cells
Power spectrum
Minkowski functionals
Higher-order statistics
Morphology & Topology
Watersheds, Cosmic Spine, Morse Complex

Origin Primordial Perturbations: Inflation
Superhorizon and subhorizon perturbations
Perturbation Evolution
Radiation & Matter Perturbations
Baryonic (Acoustic) Oscillations
May 28(w) Random Gaussian Fields
(computer task)
6 June 4 (c)

June 5 (c)
Matter Scales
Jeans Mass, Silk damping
Cosmic Scenarios:
Power spectra Cold Dark Matter, Hot Dark Matter
non-Gaussian perturbations

Nonlinear Clustering & Structure Formation
Hierarchical Clustering,
Anisotropic Collapse and the Formation of Voids
Spherical Model, Ellipsoidal Model
June 5 (w)
(will be on
other date,
to be announced)
Two-point correlation function
(computer task)
7 June 8 (c)
(Osaka lecture)

June 12 (c)
Nonlinear Structure Formation: N-body models
N-body simulation techniques
Cosmological Hydro simulation techniques
Cosmological Computer Simulations:
Cluster Simulations
Large Scale Structure simulations

Zel'dovich formalism
Adhesion approximation
Cosmic Tidal Fields &
Cosmic Web Theory
June 11 (w)Power Spectrum &
Spherical Model
8 June 15 (c)
(Osaka lecture)

June 19 (c)

Cosmic Microwave Background Anisotropies
CMB anisotropies, temperature perturbations
CMB anisotropies, experiments & satellites
CMB anisotropies, analysis & maps

CMB anisotropies, secondary perturbations
CMB anisotropies, polarization

June 18 (w)N-body Simulations
(computer task)
9 June 22 (c)

June 26 (c)
Hierarchical clustering:
Press-Schechter and Excursion set formalism
Peak-patch formalism
Halo Model

Intergalactic Medium: Lya forest & WHIM
Gravitational Lensing, Cosmic Shear
Dark Ages, First Stars & Reionization
June 25 (w)Press-Schechter Formalism
& Halo Mass Functions