
An Introduction to Modern Cosmology
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Updated edition of a popular introduction to cosmology, now with new observational data, supporting web material, and problems with solutions
An Introduction to Modern Cosmology is an accessible account of modern cosmological ideas that enables readers to understand cosmology without resorting to the mathematical apparatus of general relativity. This fully revised Fourth Edition of the 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.
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 readers' understanding and learning.
The new edition contains updated observational data, more detailed explanations and examples of the central-to-cosmology Friedman equations, and references to extensive online supporting material. It also incorporates up-to-date results from the Planck mission, which imaged the anisotropies of cosmic microwave background radiation over the whole sky.
Sample topics explored in An Introduction to Modern Cosmology include:
- The geometry of the universe, covering flat, spherical, and hyperbolic geometry, infinite and observable universes, and the three values of k
- Simple cosmological models, covering Hubble's law, expansion and redshift, particle number densities, and evolution including curvature
- The density of the universe and dark matter, covering galaxy cluster composition and brightness of the supernovae
- The origin of light elements in the universe, covering hydrogen and helium, problems with the Hot Big Bang, and flatness and horizon problems
Written in a clear, concise format with short, accessible chapters, An Introduction to Modern Cosmology is an essential textbook resource on the subject for advanced undergraduate and graduate students of astronomy, astrophysics, and physics.
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Persons
Marina Cortês is Research Faculty at the Institute of Astrophysics and Space Science of the University of Lisbon, Portugal. She previously held positions at Lawrence Berkeley National Laboratory in the United States, Perimeter Institute for Theoretical Physics in Canada, and the Royal Observatory of Edinburgh in the United Kingdom. Her research spans observational and theoretical cosmology, including work on large-scale surveys such as SDSS-III's BOSS and DESI, and on fundamental questions about the nature of time and the Universe. She won the inaugural Buchalter Cosmology Prize in 2014.
Andrew Liddle is Research Faculty at the Institute of Astrophysics and Space Science of the University of Lisbon, Portugal. He held previous positions as Professor at the Universities of Edinburgh and Sussex, United Kingdom, where he was also Head of Faculty. He is interested in understanding the properties of the Universe and is best known for his work on cosmological models, in particular early Universe inflation.
Content
Preface xi
About the Companion Website xv
1 A Brief History of Cosmological Ideas 1
2 Observational Overview 3
2.1 In visible light 4
2.2 In other wavebands 8
2.3 Homogeneity and isotropy 11
2.4 The expansion of the Universe 11
2.5 Particles in the Universe 14
3 Newtonian Gravity 21
3.1 The Friedmann equation 22
3.2 On the meaning of the expansion 25
3.3 Things that go faster than light 25
3.4 The fluid equation 26
3.5 The acceleration equation 27
3.6 On mass, energy, and vanishing factors of c2 28
4 The Geometry of the Universe 31
4.1 Flat geometry 31
4.2 Spherical geometry 32
4.3 Hyperbolic geometry 35
4.4 Infinite and observable universes 36
4.5 Where did the Big Bang happen? 36
4.6 Three values of k 37
5 Simple Cosmological Models 39
5.1 Hubble's law 39
5.2 Expansion and redshift 40
5.3 Solving the equations 41
5.4 Particle number densities 46
5.5 Evolution including curvature 47
6 Observational Parameters 51
6.1 The expansion rate H0 51
6.2 The density parameter O0 53
6.3 The deceleration parameter q0 55
7 The Cosmological Constant 57
7.1 Introducing ¿ 57
7.2 Fluid description of ¿ 58
7.3 Cosmological models with ¿ 60
8 The Age of the Universe 63
9 The Density of the Universe and Dark Matter 69
9.1 Weighing the Universe 69
9.2 What might the dark matter be? 76
9.3 Dark matter searches 78
10 The Cosmic Microwave Background 81
10.1 Properties of the microwave background 81
10.2 The photon to baryon ratio 83
10.3 The origin of the microwave background 84
10.4 The origin of the microwave background (optional advanced treatment) 87
11 The Early Universe 91
12 Nucleosynthesis: The Origin of the Light Elements 99
12.1 Hydrogen and helium 100
12.2 Comparing with observations 103
12.3 Contrasting decoupling and nucleosynthesis 105
13 The Inflationary Universe 107
13.1 Problems with the Hot Big Bang 107
13.2 Inflationary expansion 111
13.3 Solving the Big Bang problems 113
13.4 How much inflation? 115
13.5 Inflation and particle physics 116
14 The Initial Singularity 121
15 Overview: The Standard Cosmological Model 125
15.1 Expansion 126
15.2 Geometry 126
15.3 Age 126
15.4 Fate 126
15.5 Contents 127
15.6 Early history 128
15.7 Outlook 128
Advanced Topic 1 General Relativistic Cosmology 129
A1.1 The metric of space-time 129
A1.2 The Einstein equations 131
A1.3 Aside: Topology of the Universe 132
Advanced Topic 2 Classic Cosmology: Distances and Luminosities 135
A2.1 Light propagation and redshift 135
A2.2 The observable Universe 138
A2.3 Luminosity distance 138
A2.4 Angular diameter distance 143
A2.5 Source counts 145
Advanced Topic 3 Neutrino Cosmology 149
A3.1 The massless case 149
A3.2 Massive neutrinos 151
A3.3 Neutrinos and structure formation 153
Advanced Topic 4 Baryogenesis 157
Advanced Topic 5 Structures in the Universe 161
A5.1 The observed structures 161
A5.2 Gravitational instability 163
A5.3 The clustering of galaxies 165
A5.4 Cosmic microwave background anisotropies 167
A5.5 The origin of structure 173
Advanced Topic 6 Constraining Cosmological Models 177
A6.1 Cosmological models and parameters 177
A6.2 Key cosmological observations 178
A6.3 Cosmological data analysis 179
A6.4 The Standard Cosmological Model: 2025 edition 181
A6.5 Tensions and hints of new physics 184
A6.6 The future 185
Bibliography 187
Numerical Answers and Hints to Problems 191
Index 197
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 twentieth 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 have also entered 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 the 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, most excitingly of all, in 2015, the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) made the first direct detection of gravitational waves, ripples in space-time itself, which has become a technique to observe astronomical events such as colliding stars and black hole mergers.
The advent of large ground- and satellite-based telescopes operating in all parts of the electromagnetic spectrum has revolutionized our picture of the Universe. While there are probably gaps in our knowledge, some of which may be important for all we know, we do seem to have a consistent picture, based on the cosmological principle, of how material is distributed in the Universe. Our discussion here is brief; for a more detailed discussion of the observed Universe, see some of the more advanced textbooks listed in the Bibliography. A huge array of images can be found online; the ones shown here are just a taster for what you can find for yourself.
2.1 In visible light
Historically, our picture of the Universe was built up through ever more careful observations using visible light.
- Stars: The main source of visible light in the Universe is nuclear fusion within stars. The Sun is a fairly typical star, with a mass of about 2 × 1030 kg. This is known as a solar mass, indicated , and is a convenient unit for measuring masses. The nearest stars to us are a few light years away, a light year being the distance (about 1016 m) that light can travel in a year. For historical reasons, an alternative unit, known as the parsec and denoted "pc,"1 is more commonly used in cosmology. A parsec equals 3.261 light years. In cosmology, one seldom considers individual stars, instead preferring to adopt as the smallest considered unit the conglomerations of stars known as .
- Galaxies: Our Solar System lies some way off-center in a giant disk structure known as the Milky Way galaxy. It contains a staggering hundred thousand million (1011) or so stars, with masses ranging from about a tenth that of our Sun to tens of times larger. It consists of a central bulge, plus a disk of radius 12.5 kiloparsecs (kpc, equal to 103 pc), and a thickness of only about 0.3 kpc. We are located in the disk about 8 kpc from the center. The disk rotates slowly (and also differentially, with the outer edges moving more slowly, just as more distant planets in the Solar System orbit more slowly). At our radius, the galaxy rotates over a period of 200 million years. Because we are within it, we can't get an image of our own galaxy, but it probably looks not unlike the M100 galaxy shown in Figure 2.1.
Figure 2.1 If viewed from above the disk, our own Milky Way galaxy would probably resemble the M100 galaxy, imaged here by the Hubble Space telescope. (Courtesy of NASA.)
Our galaxy is surrounded by smaller collections of stars, known as globular clusters. These are distributed more or less symmetrically about the bulge, at distances of 5-30 kpc. Typically, they each contain a million stars, and are thought to be remnants of the formation of the galaxy. As we shall discuss later, it is believed that the entire disk and globular cluster system are embedded in a larger spherical structure known as the Galactic halo.
Galaxies are the most visually striking and beautiful astronomical objects in the Universe, exhibiting a wide range of properties. However, in cosmology, the detailed structure of a galaxy is usually irrelevant, and galaxies are normally thought of as point-like objects emitting light, often broken into subclasses according to colors, luminosities, and morphologies.
- The Local Group: Our galaxy resides within a small concentrated group of galaxies known as the local group. The nearest galaxy is a small irregular galaxy known as the Large Magellanic Cloud (LMC), which is 50 kpc away from the Sun. The nearest galaxy of similar size to our own is the Andromeda Galaxy, at a distance of 770 kpc. The Milky Way is one of the largest galaxies in the local group. A typical galaxy group occupies a volume of a few cubic megaparsecs. The megaparsec, denoted Mpc and equal to a million parsecs, is the cosmologist's favorite unit for measuring distances, because it is roughly the separation between neighboring galaxies. It equals 3.086 × 1022 m.
- Clusters of Galaxies, Superclusters, and Voids: Surveying larger regions of the Universe, say on a scale of hundreds of Mpc, one sees a variety of large-scale structures, as shown in Figure 2.2. This figure is not a photograph, but rather a carefully constructed map of the nearby region of our Universe, on a scale of about 1:1027! In some places, galaxies are clearly grouped into clusters of galaxies.
Figure 2.2 A map of galaxy positions in a narrow slice of the Universe, as measured by the Sloan Digital Sky Survey. Our galaxy is located at the center, and the survey radius is around 600 Mpc. The galaxy positions were obtained by measurement of the shift of spectral lines, as described in Section 2.4. (Figure courtesy M. Blanton and the Sloan Digital Sky Survey, www.sdss3.org.)
A famous example of a cluster of galaxies is the Coma cluster, which is about 100 Mpc away from our own Galaxy. The upper panel of Figure 2.3 shows a combined optical/infrared image of Coma; although the image resembles a star field, almost every source is a distinct galaxy (the main exception being two bright stars in the upper right quadrant). Coma contains perhaps 10 000 galaxies, mostly too faint to show in this image, orbiting in their common gravitational field.
Figure 2.3 Images of the Coma cluster of galaxies in visible/infrared light (top) and in X-rays (bottom), the latter being on a larger angular scale. (Courtesy of NASA/Spitzer satellite and ESA/U. Briel/MPE Garching/XMM-Newton satellite.)
However, most galaxies, sometimes called field galaxies, are not part of a cluster. Galaxy clusters are the largest gravitationally collapsed objects in the Universe, and they themselves are grouped into superclusters, joined by filaments and walls of galaxies. In between this "foamlike" structure lie large voids, some as large as 50 Mpc across. Structures in the Universe will be further described in Advanced Topic 5. Figure 2.4 shows an example of a computer simulation aiming to model the distribution of material within the Universe.
Figure 2.4 A computer simulation showing the predicted distribution of matter in the Universe on large scales. (Courtesy of V. Springel and the Virgo Consortium.)
- Large-scale Smoothness: Only once we get to scales of hundreds of megaparsecs or more does the Universe begin to appear smooth, as revealed by extremely large galaxy surveys such as the 2dF galaxy redshift survey and the Sloan Digital Sky Survey. Such surveys do not find any huge structures on scales greater than those described above; the galaxy superclusters and voids are believed to be the biggest structures in the present Universe. The observation that the Universe does indeed become smooth on the largest scales, the cosmological principle, is the underpinning of modern cosmology. It is interesting that, while the smoothness of the matter distribution on large scales has been a key assumption of cosmology for decades, it is only fairly recently that a convincing observational demonstration has become possible.
2.2 In other wavebands
Observations using visible light provide us with a good picture of what's going on in the present-day Universe. However, many other wavebands make vital contributions to our understanding, and in particular our best knowledge of cosmology comes not from visible light but from microwaves.
- Microwaves: For cosmology, this is by far the most important waveband. Penzias & Wilson's accidental discovery in 1965 that the Earth is bathed in microwave radiation, with a blackbody spectrum at a temperature of around 3 K, was and is one of the most powerful pieces of information in support of the Big Bang theory, around which cosmology is based. This is now known as the cosmic microwave background or simply CMB. Observations by the Far InfraRed Absolute Spectrometer (FIRAS) experiment on board the COsmic Background Explorer (COBE) satellite have confirmed that the radiation is extremely close to the blackbody form at a temperature 2.725 ± 0.001 K. This data is shown in...
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