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• Front Matter
• Dedication
• Preface
• Some fundamental constants
• Some conversion factors
• Comxmonly-used symbols
• Chapter 1 A Brief History of Cosmological Ideas
• Chapter 2 Observational Overview
• 2.1 In visible light
• 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.
• 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 centre, 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.
• 2.2 In other wavebands
• 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. Colour versions can be found on the book’s WWW site.
• Figure 2.4 A computer simulation showing the predicted distribution of matter in the Universe on large scales.
• Figure 2.5 The cosmic microwave background spectrum as measured by the FIRAS experiment on the COBE satellite. The error bars are so small that they have been multiplied by 400 to make them visible on this plot, and the best-fit black-body spectrum at T = 2.725 Kelvin, shown by the line, is an excellent fit.
• Figure 2.6 The cosmic microwave background intensity variations on the sky as measured by the Planck Satellite.
• 2.3 Homogeneity and isotropy
• 2.4 The expansion of the Universe
• Figure 2.7 A plot of velocity versus estimated distance for a set of 1355 galaxies. A straight-line relation implies Hubble’s law. The considerable scatter is due to observational uncertainties and random galaxy motions, but the best-fit line accurately gives Hubble’s law. (The x-axis scale assumes a particular value of H0.)
• Figure 2.8 According to Hubble’s law, the further away from us a galaxy is, the faster it is receding.
• 2.5 Particles in the Universe
• 2.5.1 What particles are there?
• Baryons
• Radiation
• Neutrinos
• Dark matter
• 2.5.2 Thermal distributions and the black-body spectrum
• Figure 2.9 The Planck function of Equation (2.7). There are far more photons with very low energy than very high energy.
• Figure 2.10 The energy density distribution of a black-body spectrum, given by Equation (2.8). Most of the energy is contributed by photons of energy hf ~ kBT.
• Problems
• Chapter 3 Newtonian Gravity
• Figure 3.1 The particle at radius r only feels gravitational attraction from the shaded region. Any gravitational attraction from the material outside cancels out, according to Newton’s theorem.
• 3.1 The Friedmann equation
• Figure 3.2 The comoving coordinate system is carried along with the expansion, so that any objects remain at fixed coordinate values.
• 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
• Figure 4.1 A sketch of a spherical surface, representing positive k. A triangle is shown which has three right angles!
• Figure 4.2 A sketch of a saddle surface, representing the hyperbolic geometry obtained when k is negative. A rather exaggerated triangle is shown with its sum of angles well below 180°.
• 4.3 Hyperbolic geometry
• Table 4.1 A summary of possible geometries
• 4.4 Infinite and observable universes
• 4.5 Where did the Big Bang happen?
• 4.6 Three values of k
• Problems
• Figure 4.3
• Chapter 5 Simple Cosmological Models
• 5.1 Hubble’s law
• 5.2 Expansion and redshift
• Figure 5.1 A photon travels a distance dr between two galaxies A and B.
• 5.3 Solving the equations
• 5.3.1 Matter
• 5.3.2 Radiation
• 5.3.3 Mixtures
• Figure 5.2 A schematic illustration of the evolution of a universe containing radiation and matter. Once matter comes to dominate the expansion rate speeds up, so the densities fall more quickly with time.
• 5.4 Particle number densities
• 5.5 Evolution including curvature
• Figure 5.3 Three possible evolutions for the Universe, corresponding to the different signs of k. The middle line corresponds to the k = 0 case where the expansion rate approaches zero in the infinite future. During the early phases of the expansion the lines are very close and so observationally it can be difficult to distinguish which path the actual Universe will follow.
• Problems
• Chapter 6 Observational Parameters
• 6.1 The expansion rate H0
• 6.2 The density parameter Ω0
• 6.3 The deceleration parameter q0
• Problems
• Chapter 7 The Cosmological Constant
• 7.1 Introducing Λ
• 7.2 Fluid description of Λ
• 7.3 Cosmological models with Λ
• Figure 7.1 Different models for the Universe can be identified by their location in the plane showing the densities of matter and Λ. This figure indicates the main properties in different regions, with the labels indicating the behaviour on each side of the dividing lines.
• Problems
• Chapter 8 The Age of the Universe
• Figure 8.1 Predicted ages as fractions of the Hubble time for open universes and for universes with a flat geometry plus a cosmological constant. The prediction H0t0 = 2/3 for critical-density models is at the right-hand edge.
• Problems
• Chapter 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
• Figure 9.1 The rotation curve of the spiral galaxy NGC3198. We see that it remains roughly constant at large radii, outside the visible disk. Faster than expected orbits require a larger central force, and so they imply the existence of extra, dark, matter.
• Figure 9.2 A schematic illustration of a galactic disk, with a few globular clusters, embedded in a spherical halo of dark matter.
• 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
• Problems
• Chapter 10 The Cosmic Microwave Background
• 10.1 Properties of the microwave background
• Figure 10.1 The evolution of the black-body spectrum as the Universe expands. The expansion reduces the number density of photons, while the redshifting reduces their frequency. In combination, these two effects map the spectrum onto a new black-body at a lower temperature.
• 10.2 The photon to baryon ratio
• 10.3 The origin of the microwave background
• Figure 10.2 Because they have travelled towards us uninterrupted since the Universe was at 3000 K, the photons making up our microwave background originated on the surface of a sphere, known as the surface of last scattering, a considerable distance away from our own galaxy. If observers exist in other galaxies, they will see microwaves coming from the surface of a different sphere centred around their location. At the last-scattering surface, the photons had a much higher frequency, which has been redshifted as the photons travel towards us.
• 10.4 The origin of the microwave background (optional advanced treatment)
• Problems
• Chapter 11 The Early Universe
• Figure 11.1 A schematic illustration of the temperature–time relation, assuming Ω0 = 0.3 and h = 0.7. When the radiation era ends the expansion rate increases and the temperature cools more quickly.
• Table 11.1 Different stages of the Universe’s evolution (taking Ω0 = 0.3 and h = 0.7). Some numbers are approximate
• Problems
• Chapter 12 Nucleosynthesis: The Origin of the Light Elements
• 12.1 Hydrogen and helium
• 12.2 Comparing with observations
• Figure 12.1 The predicted abundances of light nuclei, as a function of ΩBh2 along the top and of the baryon-to-photon number density ratio along the bottom. From top to bottom the elements are helium-4, deuterium, helium-3 and lithium-7, and the spreads in the theoretical predictions are due to uncertainties in nuclear cross-sections. The boxes show the observationally-allowed abundances and the parameter range matching them. The vertical band shows the range compatible with the deuterium abundance observations, while the narrower band within it shows the range inferred from the cosmic microwave background (Advanced Topic 6).
• Table 12.1 A comparison of nucleosynthesis and decoupling
• 12.3 Contrasting decoupling and nucleosynthesis
• Problems
• Chapter 13 The Inflationary Universe
• 13.1 Problems with the Hot Big Bang
• 13.1.1 The flatness problem
• Figure 13.1 An illustration of the horizon problem. We receive microwave radiation from points A and B on opposite sides of the sky. These points are well separated and would not have been able to interact at all since the Big Bang – the dotted lines indicate the extent of regions able to influence points A and B by the present – far less manage to interact by the time the microwave radiation was released. So in the Hot Big Bang model it is impossible to explain why they have the same temperature to such accuracy.
• 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
• Figure 13.2 Possible evolution of the density parameter Ωtot. There might or might not be a period before inflation, indicated by the dashed line. Inflation then drives log Ωtot towards zero (i.e. Ωtot towards 1), either from above or below. By the time inflation ends Ωtot is so close to one that all the evolution after inflation up to the present day is not enough to pull it away again. Only some time in the very distant future would it start to move away from one again.
• 13.3.2 The horizon problem
• Figure 13.3 A schematic illustration of the inflationary solution to the horizon problem, with a small initial thermalized region blown up to encompass our entire observable Universe.
• 13.3.3 Relic particle abundances
• 13.4 How much inflation?
• 13.5 Inflation and particle physics
• Problems
• Chapter 14 The Initial Singularity
• Figure 14.1 The solid line shows the true (decelerating) scale factor. The dotted line extrapolated back from the present shows the earliest possible time that the scale factor can have been zero.
• Problem
• Chapter 15 Overview: The Standard Cosmological Model
• Expansion
• Geometry
• Age
• Fate
• Contents
• Early history
• Outlook
• Back Matter
• Advanced Topic 1 General Relativistic Cosmology
• A1.1 The metric of space–time
• A1.2 The Einstein equations
• A1.3 Aside: Topology of the Universe
• Problems
• Advanced Topic 2 Classic Cosmology: Distances and Luminosities
• A2.1 Light propagation and redshift
• Figure A2.1 A graph of c/a(t) illustrates how the redshift law can be derived.
• A2.2 The observable Universe
• A2.3 Luminosity distance
• Figure A2.2 We receive light a distance a0r0 from the source. The surface area of the sphere at that distance is and so our detector of unit area intercepts a fraction of the total light output 4πL.
• Figure A2.3 The luminosity distance as a function of redshift is plotted for three different spatially-flat cosmologies with a cosmological constant. From bottom to top, the lines are Ω0 = 1, 0.5 and 0.3 respectively. Notice how weak the dependence on cosmology is even to high redshift. It turns out that open universe models with no cosmological constant have an even weaker dependence.
• Figure A2.4 The contours marked ‘SNe’ show observational constraints from the supernova luminosity–redshift relation from the Union2.1 data set compiled the Supernova Cosmology Project. They are displayed in the Ω0–ΩΛ plane as introduced in Section 7.3, alongside constraints from the cosmic microwave background (CMB) and from a technique known as baryon acoustic oscillations (BAO). Only a very small region, with Ω0 ≃ 0.3 and ΩΛ ≃ 0.7, matches all three data sets.
• A2.4 Angular diameter distance
• Figure A2.5 The angular diameter distance as a function of redshift is plotted for three different spatially-flat cosmologies with a cosmological constant. From bottom to top, the lines are Ω0 = 1, 0.5 and 0.3 respectively. For nearby objects ddiam and dlum are very similar, but at large redshifts the angular diameter distance begins to decrease.
• A2.5 Source counts
• Problems
• Advanced Topic 3 Neutrino Cosmology
• A3.1 The massless case
• A3.2 Massive neutrinos
• A3.2.1 Light neutrinos
• A3.2.2 Heavy neutrinos
• A3.3 Neutrinos and structure formation
• Problems
• Advanced Topic 4 Baryogenesis
• Figure A4.1 The favourite way to make a matter–anti-matter asymmetry is to do so very early, when the Universe was full of baryons and anti-baryons, by making a small excess of baryons. (I’ve contented myself with drawing fifteen rather than a billion!) Later, when the baryons and anti-baryons annihilate, the small excess is left over.
• Advanced Topic 5 Structures in the Universe
• A5.1 The observed structures
• Figure A5.1 Gravity pulls material towards the denser regions, enhancing any initial irregularities.
• A5.2 Gravitational instability
• A5.3 The clustering of galaxies
• Figure A5.2 The completed 2dF galaxy redshift survey, with our galaxy located at the centre. The three-dimensional survey volume has been flattened to make this image, and the sudden angular variations indicate regions which were not surveyed. The number of galaxies is so large that projection effects make it difficult to see the structures. The radial distance indicates the redshift to the galaxy, which is independent of the underlying cosmological model, while the scale indicating distance makes particular assumptions about the cosmological model.
• A5.4 Cosmic microwave background anisotropies
• A5.4.1 Statistical description of anisotropies
• A5.4.2 Computing the Cℓ
• A5.4.3 Microwave background observations
• Figure A5.3 A typical prediction of cosmic microwave anisotropies, in this case for the Standard Cosmological Model. The predicted curve is calculated to better than 1 per cent accuracy.
• Figure A5.4 The radiation angular power spectrum as measured by the Planck satellite, shown as the dots. The line shows a theoretical prediction from the best-fit cosmological model, which fits the data extremely well. They define Cℓ using the multipoles of ΔT itself rather than ΔT/T, so their scale is times that of Figure A5.3. Note that while Figure A5.3 uses a logarithmic ℓ-axis, this plot uses a non-standard scaling along the ℓ-axis chosen to display the observations evenly.
• A5.4.4 Spatial geometry
• A5.5 The origin of structure
• Problems
• Advanced Topic 6 Constraining cosmological models
• A6.1 Cosmological models and parameters
• A6.2 Key cosmological observations
• A6.3 Cosmological data analysis
• Figure A6.1 An example of joint constraints on two pairs of parameters, obtained from an MCMC calculation using data from the WMAP satellite. The filled contours, showing 68% and 95% confidence limits, are from the combined five-year dataset, while the unfilled contours show the results from the first thee years for comparison. The choice of variables on the axes of these plots is discussed in Advanced Topic 6.4; Ωc is the density parameter for cold dark matter alone.
• A6.4 The Standard Cosmological Model: 2014 edition
• Table 6.1 Parameter values for the Standard Cosmological Model 2014. The model allows six parameters to vary as shown in the upper part of the table. The lower part of the table shows other parameters of interest that can be derived from this basic set. (Results, with some additional rounding, from the Planck 2013 data release, published as Ade et al. (Planck Collaboration Paper XVI, 2014))
• Figure A6.2 The three dominant constituents of the present Universe. The present densities of photons and of neutrinos are too small to appear in this figure.
• A6.5 The future
• Bibliography
• Background
• Introductory undergraduate
• Advanced undergraduate
• Postgraduate
• Numerical Answers and Hints to Problems
• Index
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