Published in Observational and Physical Cosmology, eds, F. Sánchez, M. Collados and R. Rebolo, 1992.

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The Large Scale Structure of the Universe

Bernard J.T. Jones

Astronomy Center, Sussex University, UK
Niels Bohr Institute, University of Copenhagen DK

Reality is a question of perspective; the further you
get from the past the more concrete and plausible
it seems - but as you approach the present, it
inevitably seems more and more incredible.
Midnight's Children (All-India Radio)
Salman Rushdie

This is an interesting time for cosmology since it seems that our theories for the large scale structure of the Universe are being seriously challenged by the growing amount of data. The goal of these lectures is to introduce and explain the current debate on this issue. By its very nature the problem of the large scale structure is one that mixes both observational and the theoretical aspects of cosmology. The plan of the lectures is first to discuss the general theoretical framework for cosmology, and then go on to discuss the impact of key data. In this article, I shall try to build up the essential concepts from simple starting points. More details can be found in a number of books and review articles.

There are many fine books on cosmology. There are the two great "classics" Physical Cosmology by Peebles (1971) and Gravitation and Cosmology by Weinberg (1972). The 1980's brought The Large Scale Structure of the Universe by Peebles (1980, referred to hereafter as "LSSU"), volume 2 of Relativistic Astrophysics by Zel'dovich and Novikov (1980), and The Isotropic Universe by Raine (1981). These are becoming somewhat outdated owing to the rapid progress in cosmology in recent years, but they do discuss the fundamentals of the subject. At a pedagogical level, the book by Berry (1976), Principles of Cosmology and Gravitation is highly recommended.

In recent years we have The Early Universe, Facts and Fiction by Borner (1988), The Early Universe by Kolb and Turner (1990), and Physics of the Early Universe edited by Peacock, Heavens, and Davies (1990). This last book contains a fine review article by White (1990) on Physical Cosmology and another on inhomogeneities in the universe and in particular their contribution to microwave background anisotropy, by Efstathiou (1990).

There are numerous conference proceedings and reviews on the subject. An outstanding conference book is the "Vatican Study Week: Large Scale Motions in the Universe" (Rubin and Coyne, 1988). There is also a recent review on the large scale structure by Kashlinsky and Jones (1991).

It is of course impossible to discuss everything about the large scale structure of the universe, and even less possible to cite all the appropriate references. My strategy has therefore been to provide a background against which some of the major issues can be addressed, and to give enough recent references to enable the reader to get into the bibliography on those issues.

I have tried to stick to the question of the large scale structure and not get drawn into issues of galaxy formation or even galaxy cluster formation. There is no doubt that these have an important bearing on large scale structure, but they have not as yet played a decisive role. For example, the question of the biasing of galaxy formation has so far been tackled in a rather simplistic way and there may now be a need to go into the details of the process by looking more carefully at the galaxy formation process. On the other hand I have gone a little way into the question of inflationary universes and the origin of the fluctuation spectrum since this is a major issue as regards the scale of the largest structures.

Throughout this article I shall use a distance scale corresponding to a present value of the Hubble constant H0 = 100h km s-1 Mpc-1 and the reader can substitute her/his own favourite value for h. I shall endeavour to use "Universe" whenever I mean the place where we live, and "universe" for a model of the Universe. Similarly, "the Galaxy" is the "galaxy" where we are situated. I shall try to avoid abbreviations, but the following bits of jargon are frequently encountered and may slip into the text: "CDM" for "Cold Dark Matter", "HDM" for "Hot Dark Matter", "LSSU" for Peebles' book "The Large Scale Structure of the Universe", "MWB" for "Microwave Background" and "CBR" for the "Cosmic Background Radiation". Generally MWB and CBR are used interchangeably, despite the fact that there are many background radiations that are not in the microwave band (such as the X-ray background, but that would be an "XRB"!). I will studiously avoid "GA" for "Great Attractor" and but I will use the shortened form "S7" for the names of the people involved in its discovery (Burstein, Davies, Dressler, Faber, Lynden-Bell, Terlevich and Wegner, in alphabetic order).

Table of Contents

The Universe at Large
Homogeneity and Isotropy
Scale Factors, Redshifts and all that
Important quantities: H0, Omega0, rhoc
The Hubble Parameter h
The Cosmological Constant Lambda
Expansion with Lambda
The lambda parameter
Why introduce Lambda?
The Value of Omega0
The Deceleration Parameter q0
The classical approach again
Cosmic Nucleosynthesis
Omega0 from Hubble flow deviations
Omega = 1, Dark Matter and Inflation
Flatness and Inflation

2-Point Correlation Functions
The Power Spectrum
Projected Surveys
Redshift Surveys
Optical Galaxy Samples
Surveys based on the IRAS catalogue
Pencil Beam Surveys
Surveys with Independent Distance Estimates
The Rubin-Ford Effect
Samples of Elliptical Galaxies
Samples of spiral galaxies
The "Real" 3-Dimensional Distribution
Clusters and Voids
Galaxy Clusters
The Cluster-Cluster Correlation Function
Great Attractors, Dipoles and all that
The Great Attractor and Others
Dipole Convergence
Large Scale Flows and CBR Anisotropy
Velocity Correlations

Two-Point Correlation Functions
Higher Order Correlation Functions
Counts in cells

The Origin of the Fluctuation Spectrum
Modelling the Evolution of Large Scale Structure
CDM models
CDM with "gas"
Adhesion Model
Classical Pancakes
Decaying WIMPS
Formation of Galaxy Clusters
Understanding Large Scale Structure