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Contents
Preface xi
Constants, conversion factors and symbols xiv
1 A (Very) Brief History of Cosmological Ideas 1
2 Observational Overview 3
2.1 In visible light 3
2.2 In other wavebands 7
2.3 Homogeneity and isotropy 8
2.4 The expansion of the Universe 9
2.5 Particles in the Universe 11
2.5.1 What particles are there? 11
2.5.2 Thermal distributions and the black-body spectrum 13
3 Newtonian Gravity 17
3.1 The Friedmann equation 18
3.2 On the meaning of the expansion 21
3.3 Things that go faster than light 21
3.4 The fluid equation 22
3.5 The acceleration equation 23
3.6 On mass, energy and vanishing factors of c2 24
4 The Geometry of the Universe 25
4.1 Flat geometry 25
4.2 Spherical geometry 26
4.3 Hyperbolic geometry 28
4.4 Infinite and observable Universes 29
4.5 Where did the Big Bang happen? 29
4.6 Three values of k 30
5 Simple Cosmological Models 33
5.1 Hubble'slaw 33
5.2 Expansion and redshift 34
5.3 Solving the equations 35
5.3.1 Matter 36
5.3.2 Radiation 37
5.3.3 Mixtures 38
5.4 Particle number densities 39
5.5 Evolution including curvature 40
6 Observational Parameters 45
6.1 The expansion rate HO 45
6.2 The density parameter Q0 47
6.3 The deceleration parameter QQ 48
7 The Cosmological Constant 51
7.1 Introducing A 51
7.2 Fluid description of A 52
7.3 Cosmological models with A 53
8 The Age of the Universe 57
9 The Density of the Universe and Dark Matter 63
9.1 Weighing the Universe 63
9.1.1 Counting stars 63
9.1.2 Nucleosynthesis foreshadowed 64
9.1.3 Galaxy rotation curves 64
9.1.4 Galaxy cluster composition 66
9.1.5 Bulk motions in the Universe 67
9.1.6 The formation of structure 68
9.1.7 The geometry of the Universe and the brightness of supernovae . 68
9.1.8 Overview 69
9.2 What might the dark matter be? 69
9.3 Dark matter searches 72
10 The Cosmic Microwave Background 75
10.1 Properties of the microwave background 75
10.2 The photon to baryon ratio 77
10.3 The origin of the microwave background 78
10.4 The origin of the microwave background (advanced) 81
11 The Early Universe 85
12 Nucleosynthesis: The Origin of the Light Elements 91
12.1 Hydrogen and Helium 91
12.2 Comparing with observations 94
12.3 Contrasting decoupling and nucleosynthesis 96
13 The Inflationary Universe 99
13.1 Problems with the Hot Big Bang 99
13.1.1 The flatness problem 99
13.1.2 The horizon problem 101
13.1.3 Relic particle abundances 102
13.2 Inflationary expansion 103
13.3 Solving the Big Bang problems 104
13.3.1 The flatness problem 104
13.3.2 The horizon problem 105
13.3.3 Relic particle abundances 106
13.4 How much inflation? 106
13.5 Inflation and particle physics 107
14 The Initial Singularity 111
15 Overview: The Standard Cosmological Model 115
Advanced Topic 1 General Relativistic Cosmology 119
1.1 The metric of space-time 119
1.2 The Einstein equations 120
1.3 Aside: Topology of the Universe 122
Advanced Topic 2 Classic Cosmology: Distances and Luminosities 125
2.1 Light propagation and redshift 125
2.2 The observable Universe 128
2.3 Luminosity distance 128
2.4 Angular diameter distance 132
2.5 Source counts 134
Advanced Topic 3 Neutrino Cosmology 137
3.1 The massless case 137
3.2 Massive neutrinos 139
3.2.1 Light neutrinos 139
3.2.2 Heavy neutrinos 140
3.3 Neutrinos and structure formation 140
Advanced Topic 4 Baryogenesis 143
Advanced Topic 5 Structures in the Universe 147
5.1 The observed structures 147
5.2 Gravitational instability 149
5.3 The clustering of galaxies 150
5.4 Cosmic microwave background anisotropies 152
5.4.1 Statistical description of anisotropies 152
5.4.2 Computing the Ct 154
5.4.3 Microwave background observations 155
5.4.4 Spatial geometry 156
5.5 The origin of structure 157
Bibliography 161
Numerical answers and hints to problems 163
Index 167
Preface
The development of cosmology will no doubt be seen as one of the scientific triumphs of
the twentieth century. At its beginning, cosmology hardly existed as a scientific discipline.
By its end, the Hot Big Bang cosmology stood secure as the accepted description of the
Universe as a whole. Telescopes such as the Hubble Space Telescope are capable of seeing
light from galaxies so distant that the light has been travelling towards us for most of the
lifetime of the Universe. The cosmic microwave background, a fossil relic of a time when
the Universe was both denser and hotter, is routinely detected and its properties examined.
That our Universe is presently expanding is established without doubt.
We are presently in an era where understanding of cosmology is shifting from the
qualitative to the quantitative, as rapidly-improving observational technology drives our
knowledge forward. The turn of the millennium saw the establishment of what has come
to be known as the Standard Cosmological Model, representing an almost universal consensus
amongst cosmologists as to the best description of our Universe. Nevertheless, it is
a model with a major surprise — the belief that our Universe is presently experiencing accelerated
expansion. Add to that ongoing mysteries such as the properties of the so-called
dark matter, which is believed to be the dominant form of matter in the Universe, and it is
clear that we have some way to go before we can say that a full picture of the physics of
the Universe is in our grasp.
Such a bold endeavour as cosmology easily captures the imagination, and over recent
years there has been increasing demand for cosmology to be taught at university in an
accessible manner. Traditionally, cosmology was taught, as it was to me, as the tail end of
a general relativity course, with a derivation of the metric for an expanding Universe and
a few solutions. Such a course fails to capture the flavour of modern cosmology, which
takes classic physical sciences like thermodynamics, atomic physics and gravitation and
applies them on a grand scale.
In fact, introductory modern cosmology can be tackled in a different way, by avoiding
general relativity altogether. By a lucky chance, and a subtle bit of cheating, the correct
equations describing an expanding Universe can be obtained from Newtonian gravity.
From this basis, one can study all the triumphs of the Hot Big Bang cosmology — the expansion
of the Universe, the prediction of its age, the existence of the cosmic microwave
background, and the abundances of light elements such as helium and deuterium — and
even go on to discuss more speculative ideas such as the inflationary cosmology.
The origin of this book, first published in 1998, is a short lecture course at the University
degree or the penultimate year of a master's degree. The prerequisites are all very standard
of Sussex, around 20 lectures, taught to students in the final year of a bachelor's
physics, and the emphasis is aimed at physical intuition rather than mathematical rigour.
Since the book's publication cosmology has moved on apace, and I have also become
aware of the need for a somewhat more extensive range of material, hence this second edition.
To summarize the differences from the first edition, there is more stuff than before,
and the stuff that was already there is now less out-of-date.
Cosmology is an interesting course to teach, as it is not like most of the other subjects
taught in undergraduate physics courses. There is no perceived wisdom, built up over a
century or more, which provides an unquestionable foundation, as in thermodynamics,
electromagnetism, and even quantum mechanics and general relativity. Within our broadbrush
picture the details often remain rather blurred, changing as we learn more about the
Universe in which we live. Opportunities crop up during the course to discuss new results
which impact on cosmologists' views of the Universe, and for the lecturer to impose their
own prejudices on the interpretation of the ever-changing observational situation. Unless
I've changed jobs (in which case I'm sure www. google. com will hunt me down), you
can follow my own current prejudices by checking out this book's WWW Home Page at
http://astronomy.susx.ac.uk/~andrewl/cosbook.html
There you can find some updates on observations, and also a list of any errors in the book
that I am aware of. If you are confident you've found one yourself, and it's not on the list.
I'd be very pleased to hear of it.
The structure of the book is a central 'spine', the main chapters from one to fifteen,
which provide a self-contained introduction to modern cosmology more or less reproducing
the coverage of my Sussex course. In addition there are five Advanced Topic chapters,
each with prerequisites, which can be added to extend the course as desired. Ordinarily
the best time to tackle those Advanced Topics is immediately after their prerequisites have
been attained, though they could also be included at any later stage.
I'm extremely grateful to the reviewers of the original draft manuscript, namely Steve
Eales, Coel Hellier and Linda Smith, for numerous detailed comments which led to the
first edition being much better than it would have otherwise been. Thanks also to those
who sent me useful comments on the first edition, in particular Paddy Leahy and Michael
Rowan-Robinson, and of course to all the Wiley staff who contributed. Matthew Colless.
Brian Schmidt and Michael Turner provided three of the figures, and Martin Hendry, Martin
Kunz and Franz Schunck helped with three others, while two figures were generated
from NASA's SkyView facility (http: / /skyview. gsfc.nasa. gov) located at the
NASA Goddard Space Flight Center. A library of images, including full-colour versions
of several images reproduced here in black and white to keep production costs down, can
be found via the book's Home Page as given above.
Andrew R Liddle
Brighton
February 2003
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