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.

The sequence of galaxy formation

The discussion of galaxy evolution in chapter 13 raised many basic questions about the process of galaxy formation: did bulges form first, and did they accrete disks later? What is the importance of galaxy mergers? What sets the form of the galaxy luminosity function? In addition, we have seen in chapters 12 and 16 that an Ω = 1 universe requires galaxy formation to be biased in favour of high-density environments; how could such a bias have arisen? The purpose of this chapter is to present some of the theoretical tools with which these questions may be tackled. We start with a simple overview of two contrasting ways in which collapsed objects like galaxies could form.

dissipationless collapse What will be the final state of an object that breaks away from the background and undergoes gravitational collapse? If the matter of the object is collisionless (either purely dark matter, or stars), this is a relatively well-posed problem, which should be capable of a clear solution.

The analytical approach has concentrated on gravitational thermodynamics, and sought an equilibrium solution. This has turned out to be a subtle and paradoxical problem, whose main analysis goes back to a classic paper by Lynden-Bell (1967). Imagine initially that the self-gravitating body consists of gas, so that it is reasonable to look for an equilibrium solution in the form of a configuration of constant temperature.