An Introduction to Modern Cosmology E-Book

Andrew Liddle

• Herausgeber: John Wiley & Sons
• Kategorie: Lebensstil
• Sprache: Englisch
• Veröffentlichungsjahr: 2015

Seitenzahl: 318

Beschreibung

An Introduction to Modern Cosmology Third Edition is an accessible account of modern cosmological ideas. The Big Bang Cosmology is explored, looking at its observational successes in explaining the expansion of the Universe, the existence and properties of the cosmic microwave background, and the origin of light elements in the universe. Properties of the very early Universe are also covered, including the motivation for a rapid period of expansion known as cosmological inflation. The third edition brings this established undergraduate textbook up-to-date with the rapidly evolving observational situation. This fully revised edition of a bestseller takes an approach which is grounded in physics with a logical flow of chapters leading the reader from basic ideas of the expansion described by the Friedman equations to some of the more advanced ideas about the early universe. It also incorporates up-to-date results from the Planck mission, which imaged the anisotropies of the Cosmic Microwave Background radiation over the whole sky. The Advanced Topic sections present subjects with more detailed mathematical approaches to give greater depth to discussions. Student problems with hints for solving them and numerical answers are embedded in the chapters to facilitate the reader's understanding and learning. Cosmology is now part of the core in many degree programs. This current, clear and concise introductory text is relevant to a wide range of astronomy programs worldwide and is essential reading for undergraduates and Masters students, as well as anyone starting research in cosmology. The accompanying website for this text, http://booksupport.wiley.com, provides additional material designed to enhance your learning, as well as errata within the text.

Leseprobe

An Introduction to Modern Cosmology

Third Edition

Andrew Liddle

Institute for Astronomy, University of Edinburgh, UK

This edition first published 2015

© 2015 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Liddle, Andrew R.

An introduction to modern cosmology / Andrew Liddle, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill. – Third edition.

pages cm

Includes bibliographical references and index.

ISBN 978-1-118-50209-9 (hardback) – ISBN 978-1-118-50214-3 (paper)

1. Cosmology. I. Title.

QB981.L567 2015

523.1–dc23

2015001070

A catalogue record for this book is available from the British Library.

To my grandmothers

Contents

Cover

Title Page

Copyright

Dedication

Preface

Constants, conversion factors and symbols

1 A (Very) Brief History of Cosmological Ideas

2 Observational Overview

2.1 In visible light

2.2 In other wavebands

2.3 Homogeneity and isotropy

2.4 The expansion of the Universe

2.5 Particles in the Universe

2.5.1 What particles are there?

2.5.2 Thermal distributions and the black-body spectrum

3 Newtonian Gravity

3.1 The Friedmann equation

3.2 On the meaning of the expansion

3.3 Things that go faster than light

3.4 The fluid equation

3.5 The acceleration equation

3.6 On mass, energy and vanishing factors of

c

2

4 The Geometry of the Universe

4.1 Flat geometry

4.2 Spherical geometry

4.3 Hyperbolic geometry

4.4 Infinite and observable universes

4.5 Where did the Big Bang happen?

4.6 Three values of

k

5 Simple Cosmological Models

5.1 Hubble’s law

5.2 Expansion and redshift

5.3 Solving the equations

5.3.1 Matter

5.3.2 Radiation

5.3.3 Mixtures

5.4 Particle number densities

5.5 Evolution including curvature

6 Observational Parameters

6.1 The expansion rate

H

0

6.2 The density parameter Ω

0

6.3 The deceleration parameter

q

0

7 The Cosmological Constant

7.1 Introducing Λ

7.2 Fluid description of Λ

7.3 Cosmological models with Λ

8 The Age of the Universe

9 The Density of the Universe and Dark Matter

9.1 Weighing the Universe

9.1.1 Counting stars

9.1.2 Nucleosynthesis foreshadowed

9.1.3 Galaxy rotation curves

9.1.4 Galaxy cluster composition

9.1.5 The formation of structure

9.1.6 The geometry of the Universe and the brightness of supernovae

9.1.7 Overview

9.2 What might the dark matter be?

9.2.1 Fundamental particles

9.2.2 Compact objects

9.3 Dark matter searches

10 The Cosmic Microwave Background

10.1 Properties of the microwave background

10.2 The photon to baryon ratio

10.3 The origin of the microwave background

10.4 The origin of the microwave background (advanced)

11 The Early Universe

12 Nucleosynthesis: The Origin of the Light Elements

12.1 Hydrogen and helium

12.2 Comparing with observations

12.3 Contrasting decoupling and nucleosynthesis

13 The Inflationary Universe

13.1 Problems with the Hot Big Bang

13.1.1 The flatness problem

13.1.2 The horizon problem

13.1.3 Relic particle abundances

13.2 Inflationary expansion

13.3 Solving the Big Bang problems

13.3.1 The flatness problem

13.3.2 The horizon problem

13.3.3 Relic particle abundances

13.4 How much inflation?

13.5 Inflation and particle physics

14 The Initial Singularity

15 Overview: The Standard Cosmological Model

Advanced Topic 1 General Relativistic Cosmology

1.1 The metric of space–time

1.2 The Einstein equations

1.3 Aside: Topology of the Universe

Advanced Topic 2 Classic Cosmology: Distances and Luminosities

2.1 Light propagation and redshift

2.2 The observable Universe

2.3 Luminosity distance

2.4 Angular diameter distance

2.5 Source counts

Advanced Topic 3 Neutrino Cosmology

3.1 The massless case

3.2 Massive neutrinos

3.2.1 Light neutrinos

3.2.2 Heavy neutrinos

3.3 Neutrinos and structure formation

Advanced Topic 4 Baryogenesis

Advanced Topic 5 Structures in the Universe

5.1 The observed structures

5.2 Gravitational instability

5.3 The clustering of galaxies

5.4 Cosmic microwave background anisotropies

5.4.1 Statistical description of anisotropies

5.4.2 Computing the

C

ℓ

5.4.3 Microwave background observations

5.4.4 Spatial geometry

5.5 The origin of structure

Advanced Topic 6 Constraining cosmological models

6.1 Cosmological models and parameters

6.2 Key cosmological observations

6.3 Cosmological data analysis

6.4 The Standard Cosmological Model: 2014 edition

6.5 The future

Bibliography

Numerical Answers and Hints to Problems

Index

End User License Agreement

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Guide

Cover

Contents

Begin Reading

List of Illustrations

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

Figure 3.1

Figure 3.2

Figure 4.1

Figure 4.2

Figure 4.3

Figure 5.1

Figure 5.2

Figure 5.3

Figure 7.1

Figure 8.1

Figure 9.1

Figure 9.2

Figure 10.1

Figure 10.2

Figure 11.1

Figure 12.1

Figure 13.1

Figure 13.2

Figure 13.3

Figure 14.1

Figure A2.1

Figure A2.2

Figure A2.3

Figure A2.4

Figure A2.5

Figure A4.1

Figure A5.1

Figure A5.2

Figure A5.3

Figure A5.4

Figure A6.1

Figure A6.2

List of Tables

Table 4.1

Table 11.1

Table 12.1

Table 6.1

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, and its material composition is accurately determined.

We are now in an era where understanding of cosmology has shifted from the qualitative to the quantitative. 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 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, was a short lecture course at the University of Sussex, around 20 lectures, taught to students in the final year of a bachelor’s degree or the penultimate year of a master’s degree. The prerequisites are all very standard physics, and the emphasis is aimed at physical intuition rather than mathematical rigour. It has been further developed through my experiences of teaching cosmology at Imperial College London, the University of Hawai‘i, and at the University of Edinburgh, plus much useful feedback from readers.

The structure of the book is a central ‘spine’, the main chapters from 1 to 15, which provide a self-contained introduction to modern cosmology. In addition there are six 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.

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. Each successive edition of this book has introduced new discoveries, and lecturers can expect opportunities to crop up during their course to discuss new results which impact on cosmologists’ views of the Universe.

You can follow my own evolving views by checking out this book’s WWW Home Page at

http://www.roe.ac.uk/~arl/cosbook.html

There you may 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. Full-colour versions of many of the images can also be found there.

Andrew R. Liddle Edinburgh September 2014

Supplementary material, including full-colour images, updates and links for students and instructors, are available on the author's website:

http://www.roe.ac.uk/~arl/cosbook.html

Some fundamental constants

Newton’s constant

G

6.672 × 10

−11

m

3

kg

−1

sec

−2

Speed of light

c

2.998 × 10

8

msec

−1

or 3.076 × 10 Mpc yr