Cosmology. The Origin and Evolution of Cosmic Structure - Coles P., Lucchin F

Preface to First Edition

This is a book about modern cosmology. Because this is a big subject – as big as the Universe – we have had to choose one particular theme upon which to focus our treatment. Current research in cosmology ranges over fields as diverse as quantum gravity, general relativity, particle physics, statistical mechanics, nonlinear hydrodynamics and observational astronomy in all wavelength regions, from radio to gamma rays. We could not possibly do justice to all these areas in one volume, especially in a book such as this which is intended for advanced undergraduates or beginning postgraduates. Because we both have a strong research interest in theories for the origin and evolution of cosmic structure – galaxies, clusters and the like – and, in many respects, this is indeed the central problem in this field, we decided to concentrate on those elements of modern cosmology that pertain to this topic. We shall touch on many of the areas mentioned above, but only insofar as an understanding of them is necessary background for our analysis of structure formation.

Cosmology in general, and the field of structure formation in particular, has been a ‘hot’ research topic for many years. Recent spectacular observational breakthroughs, like the discovery by the COBE satellite in 1992 of fluctuations in the temperature of the cosmic microwave background, have made newspaper headlines all around the world. Both observational and theoretical sides of the subject continue to engross not only the best undergraduate and postgraduate students and more senior professional scientists, but also the general public. Part of the fascination is that cosmology lies at the crossroads of many disciplines. An introduction to this subject therefore involves an initiation into many seemingly disparate branches of physics and astrophysics; this alone makes it an ideal area in which to encourage young scientists to work.

Nevertheless, cosmology is a peculiar science. The Universe is, by definition, unique. We cannot prepare an ensemble of universes with slightly di erent parameter values and look for di erences or correlations in their behaviour. In many branches of physical science such experimentation often leads to the formulation of empirical laws which give rise to models and subsequently theories. Cosmology is di erent. We have only one Universe, and this must provide the empirical laws we try to explain by theory, as well as the experimental evidence we use to test the theories we have formulated. Though the distinction between them is, of course, not completely sharp, it is fair to say that physics is predominantly characterised by experiment and theory, and cosmology by observation and paradigm.

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(We take the word ‘paradigm’ to mean a theoretical framework, not all of whose elements have been formalised in the sense of being directly related to observational phenomena.) Subtle influences of personal philosophy, cultural and, in some cases, religious background lead to very di erent choices of paradigm in many branches of science, but this tendency is particularly noticeable in cosmology. For example, one’s choice to include or exclude the cosmological constant term in Einstein’s field equations of general relativity can have very little empirical motivation but must be made on the basis of philosophical, and perhaps aesthetic, considerations. Perhaps a better example is the fact that the expansion of the Universe could have been anticipated using Newtonian physics as early as the 17th century. The Cosmological Principle, according to which the Universe is homogeneous and isotropic on large scales, is su cient to ensure that a Newtonian universe cannot be static, but must be either expanding or contracting. A philosophical predisposition in western societies towards an unchanging, regular cosmos apparently prevented scientists from drawing this conclusion until it was forced upon them by 20th century observations. Incidentally, a notable exception to this prevailing paradigm was the writer Edgar Allan Poe, who expounded a picture of a dynamic, cyclical cosmos in his celebrated prose poem Eureka. We make these points to persuade the reader that cosmology requires not only a good knowledge of interdisciplinary physics, but also an open mind and a certain amount of self-knowledge.

One can learn much about what cosmology actually means from its history. Since prehistoric times, man has sought to make sense of his existence and that of the world around him in some kind of theoretical framework. The first such theories, not recognisable as ‘science’ in the modern sense of the word, were mythological. In western cultures, the Ptolemaic cosmology was a step towards the modern approach, but was clearly informed by Greek cultural values. The Copernican Principle, the notion that we do not inhabit a special place in the Universe and a kind of forerunner of the Cosmological Principle, was to some extent a product of the philosophical and religious changes taking place in Renaissance times. The mechanistic view of the Universe initiated by Newton and championed by Descartes, in which one views the natural world as a kind of clockwork device, was influenced not only by the beginnings of mathematical physics but also by the first stirrings of technological development. In the era of the Industrial Revolution, man’s perception of the natural world was framed in terms of heat engines and thermodynamics, and involved such concepts as the ‘Heat Death of the Universe’.

With hindsight we can say that cosmology did not really come of age as a science until the 20th century. In 1915 Einstein advanced his theory of general relativity. His field equations told him the Universe should be evolving; Einstein thought he must have made a mistake and promptly modified the equations to give a static cosmological solution, thus perpetuating the fallacy we discussed. It was not until 1929 that Hubble convinced the astronomical community that the Universe was actually expanding after all. (To put this a air into historical perspective, remember that it was only in the mid-1920s that it was demonstrated – by Hubble and

others – that faint nebulae, now known to be galaxies like our own Milky Way, were actually outside our Galaxy.) The next few decades saw considerable theoretical and observational developments. The Big Bang and steady-state cosmologies were proposed and their respective advocates began a long and acrimonious debate about which was correct, the legacy of which lingers still. For many workers this debate was resolved by the discovery in 1965 of the cosmic microwave background radiation, which was immediately seen to be good evidence in favour of an evolving Universe which was hotter and denser in the past. It is reasonable to regard this discovery as marking the beginning of ‘Physical Cosmology’. Counts of distant galaxies were also showing evidence of evolution in the properties of these objects at this time, and the first calculations had already been made, notably by Alpher and Herman in the late 1940s, of the elemental abundances expected to be produced by nuclear reactions in the early stages of the Big Bang. These, and other, considerations left the Big Bang model as the clear victor over the steady-state picture.

By the 1970s, attention was being turned to the question that forms the main focus of this book: where did the structure we observe in the Universe around us actually come from? The fact that the microwave background appeared remarkably uniform in temperature across the sky was taken as evidence that the early Universe (when it was less than a few hundred thousand years old) was very smooth. But the Universe now is clearly very clumpy, with large fluctuations in its density from place to place. How could these two observations be reconciled? A ‘standard’ picture soon emerged, based on the known physics of gravitational instability. Gravity is an attractive force, so that a region of the Universe which is slightly denser than average will gradually accrete material from its surroundings. In so doing the original, slightly denser region gets denser still and therefore accretes even more material. Eventually this region becomes a strongly bound ‘lump’ of matter surrounded by a region of comparatively low density. After two decades, gravitational instability continues to form the basis of the standard theory for structure formation. The details of how it operates to produce structures of the form we actually observe today are, however, still far from completely understood.

To resume our historical thread, the 1970s saw the emergence of two competing scenarios (a terrible word, but sadly commonplace in the cosmological literature) for structure formation. Roughly speaking, one of these was a ‘bottomup’, or hierarchical, model, in which structure formation was thought to begin with the collapse of small objects which then progressively clustered together and merged under the action of their mutual gravitational attraction to form larger objects. This model, called the isothermal model, was advocated mainly by American researchers. On the other hand, many Soviet astrophysicists of the time, led by Yakov B. Zel’dovich, favoured a model, the adiabatic model, in which the first structures to condense out of the expanding plasma were huge agglomerations of mass on the scale of giant superclusters of galaxies; smaller structures like individual galaxies were assumed to be formed by fragmentation processes within the larger structures, which are usually called ‘pancakes’. The debate

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between the isothermal and adiabatic schools never reached the level of animosity of the Big Bang versus steady-state controversy but was nevertheless healthily animated.

By the 1980s it was realised that neither of these models could be correct. The reasons for this conclusion are not important at this stage; we shall discuss them in detail during Part 3 of the book. Soon, however, alternative models were proposed which avoided many of the problems which led to the rejection of the 1970s models. The new ingredient added in the 1980s was non-baryonic matter; in other words, matter in the form of some exotic type of particle other than protons and neutrons. This matter is not directly observable because it is not luminous, but it does feel the action of gravity and can thus assist the gravitational instability process. Non-baryonic matter was thought to be one of two possible types: hot or cold. As had happened in the 1970s, the cosmological world again split into two camps, one favouring cold dark matter (CDM) and the other hot dark matter (HDM). Indeed, there are considerable similarities between the two schisms of the 1970s and 1980s, for the CDM model is a ‘bottom-up’ model like the old baryon isothermal picture, while the HDM model is a ‘topdown’ scenario like the adiabatic model. Even the geographical division was the same; Zel’dovich’s great Soviet school were the most powerful advocates of the HDM picture.

The 1980s also saw another important theoretical development: the idea that the Universe may have undergone a period of inflation, during which its expansion rate accelerated and any initial inhomogeneities were smoothed out. Inflation provides a model which can, at least in principle, explain how such homogeneity might have arisen and which does not require the introduction of the Cosmological Principle ab initio. While creating an observable patch of the Universe which is predominantly smooth and isotropic, inflation also guarantees the existence of small fluctuations in the cosmological density which may be the initial perturbations needed to feed the gravitational instability thought to be the origin of galaxies and other structures.

The history of cosmology in the 20th century is marked by an interesting interplay of opposites. For example, in the development of structure-formation theories one can see a strong tendency towards change (such as from baryonic to non-baryonic models), but also a strong element of continuity (the persistence of the hierarchical and pancake scenarios). The standard cosmological models have an expansion rate which is decelerating because of the attractive nature of gravity. In models involving inflation (or those with a cosmological constant) the expansion is accelerated by virtue of the fact that gravity e ectively becomes repulsive for some period. The Cosmological Principle asserts a kind of large-scale order, while inflation allows this to be achieved locally within a Universe characterised by large-scale disorder. The confrontation between steady-state and Big Bang models highlights the distinction between stationarity and evolution. Some variants of the Big Bang model involving inflation do, however, involve a large ‘metauniverse’ within which ‘miniuniverses’ of the size of our observable patch are continually being formed. The appearance of miniuniverses also emphasises

the contrast between whole and part: is our observable Universe all there is, or even representative of all there is? Or is it just an atypical ‘bubble’ which just happens to have the properties required for life to evolve within it? This brings into play the idea of an Anthropic Cosmological Principle which emphasises the special nature of the conditions necessary to create observers, compared with the general homogeneity implied by the Cosmological Principle in its traditional form.

Another interesting characteristic of cosmology is the distinction, which is often blurred, between what one might call cosmology and metacosmology. We take cosmology to mean the scientific study of the cosmos as a whole, an essential part of which is the testing of theoretical constructions against observations, as described above. On the other hand, metacosmology is a term which describes elements of a theoretical construction, or paradigm, which are not amenable to observational test. As the subject has developed, various aspects of cosmology have moved from the realm of metacosmology into that of cosmology proper. The cosmic microwave background, whose existence was postulated as early as the 1940s, but which was not observable by means of technology available at that time, became part of cosmology proper in 1965. It has been argued by some that the inflationary metacosmology has now become part of scientific cosmology because of the COBE discovery of fluctuations in the temperature of the microwave background across the sky. We think this claim is premature, although things are clearly moving in the right direction for this to take place some time in the future. Some metacosmological ideas may, however, remain so forever, either because of the technical di culty of observing their consequences or because they are not testable even in principle. An example of the latter di culty may be furnished by Linde’s chaotic inflationary picture of eternally creating miniuniverses which lie beyond the radius of our observable Universe.

Despite these complexities and idiosyncrasies, modern cosmology presents us with clear challenges. On the purely theoretical side, we require a full integration of particle physics into the Big Bang model, and a theory which treats gravitational physics at the quantum level. We also need a theoretical understanding of various phenomena which are probably based on well-established physical processes: nonlinearity in gravitational clustering, hydrodynamical processes, stellar formation and evolution, chemical evolution of galaxies. Many observational targets have also been set: the detection of candidate dark-matter particles in the galactic halo; gravitational waves; more detailed observations of the temperature fluctuations in the cosmic microwave background; larger samples of galaxy redshifts and peculiar motions; elucidation of the evolutionary properties of galaxies with cosmic time. Above all, we want to stress that cosmology is a field in which many fundamental questions remain unanswered and where there is plenty of scope for new ideas. The next decade promises to be at least as exciting as the last, with ongoing experiments already probing the microwave background in finer detail and powerful optical telescopes mapping the distribution of galaxies out to greater and greater distances. Who can say what theoretical ideas will be advanced in light of these new observations? Will the theoretical ideas described in this book

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turn out to be correct, or will we have to throw them all away and go back to the drawing board?

This book is intended to be an up-to-date introduction to this fascinating yet complex subject. It is intended to be accessible to advanced undergraduate and beginning postgraduate students, but contains much material which will be of interest to more established researchers in the field, and even non-specialists should find it a useful introduction to many of the important ideas in modern cosmology. Our book does not require a high level of specialisation on behalf of the reader. Only a modest use is made of general relativity. We use some concepts from statistical mechanics and particle physics, but our treatment of them is as self-contained as possible. We cover the basic material, such as the Friedmann models, one finds in all elementary cosmology texts, but we also take the reader through more advanced material normally available only in technical review articles or in the research literature. Although many cosmology books are on the market at the moment thanks, no doubt, to the high level of public and media interest in this subject, very few tackle the material we cover at this kind of ‘bridging’ level between elementary textbook and research monograph. We have also covered some material which one might regard as slightly old-fashioned. Our treatment of the adiabatic baryon picture of structure formation in Chapter 12 is an example. We have included such material primarily for pedagogical reasons, but also for the valuable historical lessons it provides. The fact that models come and go so rapidly in this field is explained partly by the vigorous interplay between observation and theory and partly by virtue of the fact that cosmology, in common with other aspects of life, is sometimes a victim of changes in fashion. We have also included more recent theory and observation alongside this pedagogical material in order to provide the reader with a firm basis for an understanding of future developments in this field. Obviously, because ours is such an exciting field, with advances being made at a rapid rate, we cannot claim to be definitive in all areas of contemporary interest. At the end of each chapter we give lists of references – which are not intended to be exhaustive but which should provide further reading on the fundamental issues – as well as more detailed technical articles for the advanced student. We have not cited articles in the body of each chapter, mainly to avoid interrupting the flow of the presentation. By doing this, it is certainly not our intention to claim that we have not leaned upon other works for much of this material; we implicitly acknowledge this for any work we list in the references. We believe that our presentation of this material is the most comprehensive and accessible available at this level amongst the published works belonging to the literature of this subject; a list of relevant general books on cosmology is given after this preface.

The book is organised into four parts. The first, Chapters 1–4, covers the basics of general relativity, the simplest cosmological models, alternative theories and introductory observational cosmology. This part can be skipped by students who have already taken introductory courses in cosmology. Part 2, Chapters 5–9, deals with physical cosmology and the thermal history of the universe in Big Bang models, including a discussion of phase transitions and inflation. Part 3, Chap-

ters 10–15, contains a detailed treatment of the theory of gravitational instability in both the linear and nonlinear regimes with comments on dark-matter theories and hydrodynamical e ects in the context of galaxy formation. The final part, Chapters 16–19, deals with methods for testing theories of structure formation using statistical properties of galaxy clustering, the fluctuations of the cosmic microwave background, galaxy-peculiar motions and observations of galaxy evolution and the extragalactic radiation backgrounds. The last part of the book is at a rather higher level than the preceding ones and is intended to be closer to the ongoing research in this field.

Some of the text is based upon an English adaptation of Introduzione alla Cosmologia (Zanichelli, Bologna, 1990), a cosmology textbook written in Italian by Francesco Lucchin, which contains material given in his lectures on cosmology to final-year undergraduates at the University of Padova over the past 15 years or so. We are very grateful to the publishers for permission to draw upon this source. We have, however, added a large amount of new material for the present book in order to cover as many of the latest developments in this field as possible. Much of this new material relates to the lecture notes given by Peter Coles for the Master of Science course on cosmology at Queen Mary and Westfield College beginning in 1992. These sources reinforce our intention that the book should be suitable for advanced undergraduates and/or beginning postgraduates.

Francesco Lucchin thanks the Astronomy Unit at Queen Mary & Westfield College for hospitality during visits when this book was in preparation. Likewise, Peter Coles thanks the Dipartimento di Astronomia of the University of Padova for hospitality during his visits there. Many colleagues and friends have helped us enormously during the preparation of this book. In particular, we thank Sabino Matarrese, Lauro Moscardini and Bepi Tormen for their careful reading of the manuscript and for many discussions on other matters related to the book. We also thank Varun Sahni and George Ellis for allowing us to draw on material cowritten by them and Peter Coles. Many sources are also to be thanked for their willingness to allow us to use various figures; appropriate acknowledgments are given in the corresponding figure captions.

Peter Coles and Francesco Lucchin

London, October 1994