One of the fundamental problems in cosmology is to compile a census of the contents of the universe. Material at a range of different densities and temperatures can be detected by emission or absorption somewhere in the electromagnetic spectrum. Gravity, however, detects mass quite independently of its equation of state. In an ideal world, these two routes to the total density would coincide; in practice, the gravitational route is able to detect more mass by a factor of up to ten than can be detected in any other way. This chapter, and the two that follow, summarize some of the methods that have been used to learn about the gas, radiation, dark matter and galaxies that together make up the observed universe.

Background radiation

We start with the constraints on any large-scale distribution of matter. A near-uniform intergalactic medium (IGM) will manifest itself in ‘background’ radiation that is isotropic on the sky. In many wavebands, the background radiation originates at sufficiently large distances that we are seeing back to a time when there were no discrete objects in existence. However, in other wavebands, the background may consist of the contribution of a large number of discrete sources, which are too faint to be detected individually. Studying backgrounds of this type tells us about the integrated properties of galaxy populations at more recent times, which can also provide crucial cosmological information.

The temperatures and densities of the nucleosynthesis era are remote from everyday experience, but the picture of the big bang up to T ∼ 1010 K stands a fair chance of being correct, since it is based on well-established nuclear physics. The next two chapters will be much more speculative. The frontier of cosmology from the 1980s onwards consisted of looking at exotic physics and asking whether the state of the universe at very high redshift could have differed radically from a simple radiation-dominated plasma. Chapters 10 and 11 look at different aspects of such high-energy phase changes.

Phase transitions in cosmology

There are several phase transitions of potential importance in cosmology that may have left observable signatures in the present. In descending order of energy, these are:

1. (1) The GUT transition, E ∼ 1015 GeV. Above this temperature, all interactions except gravity had equal strength and the universe had no net baryon number. Below this temperature, the symmetry is broken via the Higgs mechanism so that the gauge group of particle physics degenerates from the grand-unified G to the usual SU(3) ⊗ SU(2) ⊗ U(1) of the standard model. Baryon non-conserving processes can now operate; this may have generated the present-day excess of matter over antimatter.

2. (2) The electroweak transition, E ≃ 300 GeV. At this energy scale, the Higgs mechanism again breaks the SU(2)⊗U(1) part of the theory to yield the apparently distinct electromagnetic and weak interactions.

3. […]

The galaxy population

galaxy types For the optical astronomer, the most striking feature of the universe is the fact that stars appear in the discrete groups known as galaxies. There is no danger that the identification of galaxies is a subjective process akin to the grouping of stars in the Milky Way into constellations: the typical distances between galaxies are of order Mpc, and yet their characteristic sizes are a few kpc. Galaxies are thus concentrations of ≳ 108 times the mean stellar density. Why matter in the universe should be organised around such clear characteristic units is one of the most outstanding cosmological questions.

Galaxies come in several clear types, and it is a challenge to account for their distinct properties. At the crudest level, galaxies form a two-parameter family in which the characteristics that vary are the total amount of light and how this is divided between two components, the bulge and the disk.

1. (1) The bulge. This dominates the central portions of galaxies and is distinguished by its stellar populations and dynamics. The component is close to spherically symmetric and, although it rotates in general, it is supported against gravity primarily through stellar ‘pressure’: the bulge stars have a large radial component to their orbital velocities. The stars are population II: a set of stars that have aged sufficiently that short-lifetime stars more massive than the Sun have departed from the main sequence, leaving light that is dominated by the contribution of the giant branch.

2. […]

Having given an overview of the relevant parts of particle physics, this section of the book now discusses in some detail the application of some of these fundamental processes in the early universe. The next three chapters increase in energy, starting here with ‘normal’ physics at temperatures up to about 1010 K, and moving on to more exotic processes in chapters 10 and 11.

Thermodynamics in the big bang

adiabatic expansion What was the state of matter in the early phases of the big bang? Since the present-day expansion will cause the density to decline in the future, conditions in the past must have corresponded to high density – and thus to high temperature. We can deal with this quantitatively by looking at the thermodynamics of the fluids that make up a uniform cosmological model.

The expansion is clearly adiathermal, since the symmetry means that there can be no net heat flow through any surface. If the expansion is also reversible, then we can go one step further, because entropy change is defined in terms of the heat that flows during a reversible change. If no heat flows during a reversible change, then entropy must be conserved, and the expansion will be adiabatic. This can only be an approximation, since there will exist irreversible microscopic processes.

This is a textbook on cosmology – a subject that has the modest aim of understanding the entire universe and all its contents. While it can hardly be claimed that this task is complete, it is a fact that recent years have seen astonishing progress towards answering many of the most fundamental questions about the constitution of the universe. The intention of this book is to make these developments accessible to someone who has studied an undergraduate course in physics. I hope that the book will be useful in preparing new Ph.D. students to grapple with the research literature and with more challenging graduate-level texts. I also hope that a good deal of the material will be suitable for use in advanced undergraduate courses.

Cosmology is a demanding subject, not only because of the vast scales with which it deals, but also because of the range of knowledge required on the part of a researcher. The subject draws on just about every branch of physics, which makes it a uniquely stimulating discipline. However, this breadth is undeniably intimidating for the beginner in the subject. As a fresh Ph.D. student, 20 years ago, I was dismayed to discover that even a good undergraduate training had covered only a fraction of the areas of physics that were important in cosmology. Worse still, I learned that cosmologists need a familiarity with astronomy, with all its peculiar historical baggage of arcane terminology.

Overview

The overall properties of the universe are very close to being homogeneous; and yet telescopes reveal a wealth of detail on scales varying from single galaxies to large-scale structures of size exceeding 100 Mpc (see figure 15.1). The existence of these cosmological structures tells us something important about the initial conditions of the big bang, and about the physical processes that have operated subsequently. This chapter deals with the gravitational and hydrodynamical processes that are relevant to structure formation; the following chapters apply these ideas to large-scale structure, galaxy formation and the microwave background. We will now outline the main issues to be covered.

origin and growth of inhomogeneities The aim of studying cosmological inhomogeneities is to understand the processes that caused the universe to depart from uniform density. Chapters 10 and 11 have discussed at some length the two most promising existing ideas for how this could have happened: either through the amplification of quantum zero-point fluctuations during an inflationary era, or through the effect of topological defects formed in a cosmological phase transition. Neither of these ideas can yet be regarded as established, but it is astonishing that we are able to contemplate the observational consequences of physical processes that occurred at such remote energies.

Mechanisms for primary fluctuations

At the last-scattering redshift (z ≃ 1000), gravitational instability theory says that fractional density perturbations δ ≳ 10−3 must have existed in order for galaxies and clusters to have formed by the present. A long-standing challenge in cosmology has been to detect the corresponding fluctuations in brightness temperature of the cosmic microwave background (CMB) radiation, and it took over 25 years of ever more stringent upper limits before the first detections were obtained, in 1992. The study of CMB fluctuations has subsequently blossomed into a critical tool for pinning down cosmological models.

This can be a difficult subject; the treatment given here is intended to be the simplest possible. For technical details see e.g. Bond (1997), Efstathiou (1990), Hu & Sugiyama (1995), Seljak & Zaldarriaga (1996); for a more general overview, see White, Scott & Silk (1994) or Partridge (1995). The exact calculation of CMB anisotropies is complicated because of the increasing photon mean free path at recombination: a fluid treatment is no longer fully adequate. For full accuracy, the Boltzmann equation must be solved to follow the evolution of the photon distribution function. A convenient means for achieving this is provided by the public domain CMBFAST code (Seljak & Zaldarriaga 1996). Fortunately, these exact results can usually be understood via a more intuitive treatment, which is quantitatively correct on large and intermediate scales.

The concepts of general relativity

special relativity To understand the issues involved in general relativity, it is helpful to begin with a brief summary of the way space and time are treated in special relativity. The latter theory is an elaboration of the intuitive point of view that the properties of empty space should be the same throughout the universe. This is just a generalization of everyday experience: the world in our vicinity looks much the same whether we are stationary or in motion (leaving aside the inertial forces experienced by accelerated observers, to which we will return shortly).

The immediate consequence of this assumption is that any process that depends only on the properties of empty space must appear the same to all observers: the velocity of light or gravitational radiation should be a constant. The development of special relativity can of course proceed from the experimental constancy of c, as revealed by the Michelson-Morley experiment, but it is worth noting that Einstein considered the result of this experiment to be inevitable on intuitive grounds (see Pais 1982 for a detailed account of the conceptual development of relativity). Despite the mathematical complexity that can result, general relativity is at heart a highly intuitive theory; the way in which our everyday experience can be generalized to deduce the large-scale structure of the universe is one of the most magical parts of physics.

The Robertson–Walker metric

To the relativist, cosmology is the task of finding solutions to Einstein's field equations that are consistent with the large-scale matter distribution in the universe. Modern observational cosmology has demonstrated that the real universe is highly symmetric in its large-scale properties, but the evidence for this was not known at the time when Friedmann and Lemaître began their pioneering investigations. Just as Einstein aimed to write down the simplest possible relativistic generalization of the laws of gravity, so cosmological investigation began by considering the simplest possible mass distribution: one whose properties are homogeneous (constant density) and isotropic (the same in all directions).

isotropy implies homogeneity At first sight, one might think that these two terms mean the same thing, but it is possible to construct universes that are homogeneous but anisotropic; the reverse, however, is not possible. Consider an observer who is surrounded by a matter distribution that is perceived to be isotropic; this means not only that the mass density is a function of radius only, but that there can be no preferred axis for other physical attributes such as the velocity field. This has an important consequence if we take the velocity strain tensor ∂vi/∂xj and decompose it into symmetric and antisymmetric parts.