An Introduction to Modern Cosmology E-Book

Andrew Liddle

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

Seitenzahl: 310

Veröffentlichungsjahr: 2013

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.

Leseprobe

Contents

Preface

Some fundamental constants

Chapter 1 A (Very) Brief History of Cosmological Ideas

Chapter 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

Chapter 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 c2

Chapter 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

Chapter 5 Simple Cosmological Models

5.1 Hubble’s law

5.2 Expansion and redshift

5.3 Solving the equations

5.4 Particle number densities

5.5 Evolution including curvature

Chapter 6 Observational Parameters

6.1 The expansion rate H0

6.2 The density parameter Ω0

6.3 The deceleration parameter q0

Chapter 7 The Cosmological Constant

7.1 Introducing Λ

7.2 Fluid description of Λ

7.3 Cosmological models with Λ

Chapter 8 The Age of the Universe

Chapter 9 The Density of the Universe and Dark Matter

9.1 Weighing the Universe

9.2 What might the dark matter be?

9.3 Dark matter searches

Chapter 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)

Chapter 11 The Early Universe

Chapter 12 Nucleosynthesis: The Origin of the Light Elements

12.1 Hydrogen and Helium

12.2 Comparing with observations

12.3 Contrasting decoupling and nucleosynthesis

Chapter 13 The Inflationary Universe

13.1 Problems with the Hot Big Bang

13.2 Inflationary expansion

13.3 Solving the Big Bang problems

13.4 How much inflation?

13.5 Inflation and particle physics

Chapter 14 The Initial Singularity

Chapter 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

3.3 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

5.5 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: 2008 edition

6.5 The future

Bibliography

Numerical answers and hints to problems

Index

Copyright 2003

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Reprinted April and December 2004, December 2005, October 2007, July 2009, February 2010

Reprinted with corrections February 2007, December 2008

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Produced from author’s LaTeX files

To my grandmothers

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 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. 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 broad-brush 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 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.

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 and Michael Turner provided two of the figures, and Martin Hendry, Martin Kunz and Franz Schunck helped with three others, while two figures were generated from NASA’s Sky View facility (http://skyview.gsfc.nasa.gov) located at the NASA God-dard 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 LiddleBrightonFebruary 2003

Some fundamental constants

Some conversion factors

Commonly-used symbols

Chapter 1

A Brief History of Cosmological Ideas

The cornerstone of modern cosmology is the belief that the place which we occupy in the Universe is in no way special. This is known as the cosmological principle, and it is an idea which is both powerful and simple. It is intriguing, then, that for the bulk of the history of civilization it was believed that we occupy a very special location, usually the centre, in the scheme of things.

The ancient Greeks, in a model further developed by the Alexandrian Ptolemy, believed that the Earth must lie at the centre of the cosmos. It would be circled by the Moon, the Sun and the planets, and then the ‘fixed’ stars would be yet further away. A complex combination of circular motions, Ptolemy’s Epicycles, was devised in order to explain the motions of the planets, especially the phenomenon of retrograde motion where planets appear to temporarily reverse their direction of motion. It was not until the early 1500s that Copernicus stated forcefully the view, initiated nearly two thousand years before by Aristarchus, that one should regard the Earth, and the other planets, as going around the Sun. By ensuring that the planets moved at different speeds, retrograde motion could easily be explained by this theory. However, although Copernicus is credited with removing the anthropocentric view of the Universe, which placed the Earth at its centre, he in fact believed that the Sun was at the centre.

Newton’s theory of gravity put what had been an empirical science (Kepler’s discovery that the planets moved on elliptical orbits) on a solid footing, and it appears that Newton believed that the stars were also suns pretty much like our own, distributed evenly throughout infinite space, in a static configuration. However it seems that Newton was aware that such a static configuration is unstable.

Over the next two hundred years, it became increasingly understood that the nearby stars are not evenly distributed, but rather are located in a disk-shaped assembly which we now know as the Milky Way galaxy. The Herschels were able to identify the disk structure in the late 1700s, but their observations were not perfect and they wrongly concluded that the solar system lay at its centre. Only in the early 1900s was this convincingly overturned, by Shapley, who realized that we are some two-thirds of the radius away from the centre of the galaxy. Even then, he apparently still believed our galaxy to be at the centre of the Universe. Only in 1952 was it finally demonstrated, by Baade, that the Milky Way is a fairly typical galaxy, leading to the modern view, known as the cosmological principle (or sometimes the Copernican principle) that the Universe looks the same whoever and wherever you are.

It is important to stress that the cosmological principle isn’t exact. For example, no one thinks that sitting in a lecture theatre is exactly the same as sitting in a bar, and the interior of the Sun is a very different environment from the interstellar regions. Rather, it is an approximation which we believe holds better and better the larger the length scales we consider. Even on the scale of individual galaxies it is not very good, but once we take very large regions (though still much smaller than the Universe itself), containing say a million galaxies, we expect every such region to look more or less like every other one. The cosmological principle is therefore a property of the global Universe, breaking down if one looks at local phenomena.

The cosmological principle is the basis of the Big Bang Cosmology. The Big Bang is the best description we have of our Universe, and the aim of this book is to explain why. The Big Bang is a picture of our Universe as an evolving entity, which was very different in the past as compared to the present. Originally, it was forced to compete with a rival idea, the Steady State Universe, which holds that the Universe does not evolve but rather has looked the same forever, with new material being created to fill the gaps as the Universe expands. However, the observations I will describe now support the Big Bang so strongly that the Steady State theory is almost never considered.

Chapter 2

Observational Overview

For most of history, astronomers have had to rely on light in the visible part of the spectrum in order to study the Universe. One of the great astronomical achievements of the 20th century was the exploitation of the full electromagnetic spectrum for astronomical measurements. We now have instruments capable of making observations of radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays and gamma rays, which all correspond to light waves of different (in this case increasing) frequency. We are even entering an epoch where we can go beyond the electromagnetic spectrum and receive information of other types. A remarkable feature of observations of a nearby supernova in 1987 was that it was also seen through detection of neutrinos, an extraordinarily weakly interacting type of particle normally associated with radioactive decay. Very high energy cosmic rays, consisting of highly-relativistic elementary particles, are now routinely detected, though as yet there is no clear understanding of their astronomical origin. And as I write, experiments are starting up with the aim of detecting gravitational waves, ripples in space-time itself, and ultimately of using them to observe astronomical events such as colliding stars.