Principles of Cosmology and Gravitation
Berry (Michael V.)
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Cover Blurb

  1. General relativity and quantum mechanics1 have become the two central pillars of theoretical physics, with general relativity having important applications in astrophysics and high-energy physics. In the study of cosmology, where gravitation is the dominant force over the large scales considered, general relativity is the basic component.
  2. Principles of Cosmology and Gravitation, covering the fundamentals of the subject, is a well-known book first published by Cambridge University Press and is now reissued with corrections to meet a continuing demand for it as a course text.
  3. Principles of Cosmology and Gravitation is an ideal text for undergraduates studying cosmology as it develops the general theory of relativity by considering symmetrical situations and without recourse to tensor calculations. The book provides a theoretical framework from which the important cosmological formulae can be derived and numerical calculations performed. Different evolutionary models are considered, as are the gravitational effects of massive bodies.
  4. Principles of Cosmology and Gravitation is also a useful introduction for research students and physicists wishing to learn more about the subject.

Amazon Product Description
    General relativity and quantum mechanics2 have become the two central pillars of theoretical physics. Moreover, general relativity has important applications in astrophysics and high-energy particle physics. Covering the fundamentals of the subject, Principles of Cosmology and Gravitation describes the universe as revealed by observations and presents a theoretical framework to enable important cosmological formulae to be derived and numerical calculations performed. Avoiding elaborate formal discussions, the book presents a practical approach that focuses on the general theory of relativity. It examines different evolutionary models and the gravitational effects of massive bodies. The book also includes a large number of worked examples and problems, half with solutions.

Amazon Customer Review
  1. Berry's book is definately one of the more accessible yet rigorous treatments of this fascinating subject.
  2. It assumes a sound knowledge of Special Relativity and a good command of Calculus, Differential Equations and Vector Algebra, but without the onerous use of tensors and as such it is a serious book for the Physics student rather than a popular presentation of science.
  3. All of the fundamentals are covered here: an outline of cosmography, distance and velocity measurements, the rationale for General Relativity based on a critical assessment of the shortcomings of both the Newtonian model and Special Relativity, the Principle of Equivalence, Curved Space-time, geodesics, Gravitational Waves, Black holes, and Cosmic models.
  4. The author makes excellent use of diagrams and the discussion of the physical principles is balanced by a careful presentation of the mathematics.
  5. A highly recommended book!

Amazon Customer Review
  1. This book doesn't seem as well known as it should be. I think it gets lost between some famous special relativity books on the one side and standard advanced texts on the other. But it's really a uniquely tight, transparent, thoughtful piece of teaching.
  2. The unique position of this book is it succeeds as an introduction to general relativity and cosmology that is *fully honest*-- eg, quantitative-- and at the same time understandable at the undergraduate level. The typical drill of a standard text is to first inculcate you with very general (and abstract) tensor math power tools, and then to clothe ("hide"?) the physics in that. This book, on the other hand, demonstrates the surprising amount of low hanging fruit that you can satisfyingly consume before or without all that. Put the general case aside for the moment, and look at some basic cases, straight-on. It is satisfying because those simple models apply to some systems you will probably care about. Eg, the fabric of the entire universe as a whole, for one-- that's the "cosmology" part. There is a lot of fundamental intuition that becomes transparent, and which you will probably retain because it is simple and specific.
  3. The only minuses: I wish it were cheaper (not that the teaching isn't worth it). I also wish for an update: It would make a really interesting read to apply the basics to recent observations, like the "accelerating universe" problem (or is it just a layer of cosmological smog between us and them dim supernovas?...). However, the cosmological constant: it's there. So this book is absolutely the straightest, shortest path to bringing any curious reader up to speed on fully enjoying cosmological sightings in the news.


Institute of Physics Publishing, Bristol and Philadelphia; 2nd Revised edition edition (1 Jan 1989)

"Berry (Michael V.) - Principles of Cosmology and Gravitation"

Source: Berry (Michael V.) - Principles of Cosmology and Gravitation

    Preface to the 1989 reprint – ix
    Preface to the first edition – x
  1. Introduction – 1
  2. Cosmography – 3
    … 2.1 What the universe contains – 3
    … 2.2 The cosmic distance hierarchy, and the determination of galactic densities – 5
    … … 2.2.1 Parallax – 6
    … … 2.2.2 Distance from velocity measurements – 8
    … … 2.2.3 Distance from apparent luminosity – 9
    … … 2.2.4 Weighing galaxies – 15
    … 2.3 The red shift and the expansion of the universe – 17
  3. Physical basis of general relativity – 23
    … 3.1 The need for relativistic ideas and a theory of gravitation – 23
    … 3.2 Difficulties with Newtonian mechanics: gravity – 26
    … 3.3 Difficulties with Newtonian mechanics: inertial frames and absolute space – 30
    … 3.4 Inadequacy of special relativity – 34
    … 3.5 Mach's principle, and gravitational waves – 37
    … 3.6 Einstein's principle of equivalence – 41
  4. Curved spacetime and the physical mathematics of general relativity – 47
    … 4.1 Particle paths and the separation between events – 47
    … 4.2 Geodesics – 55
    … 4.3 Curved spaces – 60
    … 4.4 Curvature and gravitation – 70
  5. General relativity near massive objects – 74
    … 5.1 Spacetime near an isolated mass – 74
    … 5.2 Around the world with clocks – 76
    … 5.3 Precession of the perihelion of Mercury – 79
    … 5.4 Deflection of light – 85
    … 5.5 Radar echoes from planets – 88
    … 5.6 Black holes – 91
  6. Cosmic kinematics – 103
    … 6.1 Spacetime for the smoothed-out universe – 103
    … 6.2 Red shifts and horizons – 107
    … 6.3 Apparent luminosity – 111
    … 6.4 Galactic densities and the darkness of the night sky – 113
    … 6.5 Number counts – 115
  7. Cosmic dynamics – 119
    … 7.1 Gravitation and the cosmic fluid – 119
    … 7.2 Histories of model universes – 123
    … 7.3 The steady state theory – 133
    … 7.4 Cosmologies in which the strength of gravity varies – 136
  8. In the beginning – 140
    … 8.1 Cosmic black-body radiation – 140
    … 8.2 Condensation of galaxies – 145
    … 8.3 Ylem – 153
    Appendix A: Labelling astronomical objects – 159
    Appendix B: Theorema egregium – 160
    Problems – 165
    Solutions to odd-numbered problems – 168
    Useful numbers – 175
    Bibliography – 176
    Index – 177

Preface to the 1989 reprint
  1. The decision to make this book available again, after it has been out of print for several years, was prompted by continuing requests from students and teachers. I have taken the opportunity to make many minor corrections, most of which were kindly supplied by readers.
  2. Several new themes have entered the subject in the fifteen years since the original writing. The link between cosmology and particle physics has been strengthened by the development of inflationary theories, which provide an explanation for the high degree of uniformity of the early universe. Large-scale structure in the present universe has received extensive attention, partly because of the discovery of giant voids in which there are no galaxies and partly because of the application of fractal mathematics to describe hierarchical galaxy clustering. And the enthusiasm (in my view misplaced) for the anthropic principle reflects the revival of the idea that the evolution of the universe as a whole, and of us as a cosmologising species, are inevitably connected.
  3. These are important developments, but I have not revised the book to incorporate them because I would not be able to do them justice. I hope that the original material will still serve as a useful introduction at the undergraduate level to gravitational relativity applied to the expanding universe — subjects that continue to form the backbone of cosmology.
    … Bristol 1988, Michael Berry

Preface to the first edition
  1. Modern scientific cosmology is one of our grandest intellectual adventures. It is also physics, uninhibited, applied on the largest scale. Indeed, many people are first ‘turned on' to physics by popular books or films about cosmology. What a pity, then, that the subject is rarely taught in universities. Perhaps this is because a suitable textbook is lacking. There are many advanced treatises for the specialist, and many elementary expositions for the lay reader, but at the undergraduate level there is a gap.
  2. This book is designed to fill that gap, and so promote teaching of cosmology in universities. The aim is to describe the universe as revealed by observation, and to present a theoretical framework powerful enough to enable important cosmological formulae to be derived and numerical calculations performed.
  3. Any serious treatment must grasp the nettle of Einstein's general theory of relativity, because this gives the best description of the behaviour of matter and light under the influence of gravity; it forms the basis of current ‘standard cosmology', and is employed constantly in the interpretation of observations. Here we avoid an elaborate and formal discussion based on the tensor calculus. Of course it is necessary to introduce the general expression for the separation (or interval) between two events, and this involves the metric tensor of spacetime. However, it is possible in the case of the highly symmetrical spacetimes of elementary general relativity and cosmology to determine the metric tensor by employing Gauss's formula for the curvature of an ordinary two-dimensional surface instead of using the general Einstein field equations. The curvature of a surface is a concept that makes no demands on the credulity of a student, so that this approach is a convenient way to introduce the geometrical interpretation of gravity.
  4. A previous exposure to the ideas of special relativity is assumed, as is a knowledge of calculus, including partial differentiation. This book is, therefore, a suitable text for the final year of an undergraduate physics course. Experience shows that the material can be covered comfortably in twenty-four lectures. Problems of varying difficulty are included, together with solutions.
  5. In writing this book [… snip …].
    … Bristol 1974, Michael Berry

  1. It is customary to start with definitions, which are often all too glib and rob a subject of its richness. Nevertheless it can help to fix our ideas if we do have a definition, providing we do not take it too seriously. According to Chambers's Dictionary, cosmology is ‘the science of the universe as a whole'. Again, it is customary to divide a subject into neatly-separated sections, even though this can obscure the richness of their interconnections. Nevertheless, it does help to distinguish three main aspects of cosmology.
  2. Firstly, we have cosmography: cataloguing the objects in the universe and charting their positions and motions. Unlike geographers, we are restricted to one vantage-point — the Earth — where we sit and receive electromagnetic radiation. All our information about the universe is contained in the directional distribution of this radiation (a star here, a galaxy there) and in its spectral composition (light, X-ray, radio, etc.). By comparison, we have learned very little from the analysis of cosmic rays and meteorites (objects falling in from space), or from our first toddling steps outside the Earth.
  3. Secondly, there is theoretical cosmology, where we search for a frame-work within which to comprehend the information from cosmography. Even here the tidy scheme breaks down, because it is not possible to discuss even the simplest observations without a theoretical framework — for example, ‘the distance of an object' can have at least five different meanings, depending on how it is measured. Theoretical cosmology employs the physical laws established on and near the Earth, and makes the outrageous extrapolation that they apply throughout the universe. But physics, even extrapolated, is not enough; to escape from the prison of our single vantage-point we need something more: a ‘cosmological principle'. This is essentially philosophical in nature; it does not follow from the laws of physics. In simple terms, the cosmological principle says: ‘There is nothing special, cosmologically, about the Earth; therefore our large-scale observations are the same as those which would be made by observers anywhere else in the universe'. How fickle our intellect is! To mediaeval man it was completely natural to consider the Earth as being at the centre of the universe, yet here we are, a mere few centuries later, elevating anti-anthropocentrism to the level of a basic principle. The cosmological principle is immensely powerful: it enables us to select from all the complicated solutions of the equations of physics those which have certain simple symmetries.
  4. What kind of physics does cosmology require? I am afraid it is a pretty rich stew, whose basic ingredient is a theory of gravitation, since that is the dominant force on the cosmic scale. The best description of gravity that we have is Einstein's ‘general theory of relativity', and this will form the core of our account of cosmology. To flavour the stew there will be a bit of electromagnetism, some thermodynamics, and even a dash of particle physics. The proof of any stew lies in the eating, which in this case means comparison with observation. We shall see that theoretical cosmology based on general relativity is capable of explaining the observations. However, these are not yet precise enough or extensive enough to indicate which of a range of ‘universe models' applies to our actual world.
  5. The third aspect of cosmology is cosmogony; this is the study of the origin (or perhaps the infinitely distant past) of the universe. Here our arrogance will be extreme, for we shall extrapolate the laws of physics to the most distant times as well as places. We shall find ourselves interpreting the most modern radio-astronomical observations as giving detailed information about conditions in the chaos of a ‘big bang' ten thousand million years ago. Distinguishing the distant past from the distant future involves the nature of time itself, especially its reversibility, and this leads to connections — still mysterious — between cosmology and laboratory physics.

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