The first edition of this book was based on my lecture notes for an upper-level undergraduate cosmology course at The Ohio State University. The students taking the course were primarily juniors and seniors majoring in physics and astronomy. In my lectures, I assumed that my students, having triumphantly survived freshman and sophomore physics, had a basic understanding of electrodynamics, statistical mechanics, classical dynamics, and quantum physics. As far as mathematics was concerned, I assumed that, like modern major-generals, they were very good at integral and differential calculus. Readers of this book are assumed to have a similar background in physics and mathematics. In particular, no prior knowledge of general relativity is assumed; the (relatively) small amounts of general relativity needed to understand basic cosmology are introduced as needed.

The second edition that you are reading now is updated with observational and theoretical developments during the 14 years that have elapsed since the first edition. It has been improved by many comments by readers. (My thanks go to the eagle-eyed readers who caught the typographical errors that snuck into the first edition.) The second edition also contains an extended discussion of structure formation in the final two chapters. For a brief course on cosmology, the first ten chapters can stand on their own.

Unfortunately, the National Bureau of Standards has not gotten around to establishing a standard notation for cosmological equations. It seems that every cosmology book has its own notation; this book is no exception. My main motivation was to make the notation as clear as possible for the cosmological novice.

Many of the illustrations in this book were adapted from figures in published scientific papers; my thanks go to the authors of those papers for granting permission to use their figures or to replot their hard-won data. Particular thanks go to Avishai Dekel (Figure 2.2), Wendy Freedman (Figure 2.5), David Leisawitz (Figure 8.1), Alain Coc (Figure 9.4), Richard Cyburt (Figure 9.5), Rien van de Weygaert (Figure 11.1), Ashley Ross (Figure 11.6), Xiaohui Fan (Figure 12.3), and John Beacom (Figure 12.4).

Some of the observations on which modern cosmology is based are highly complex, requiring elaborate apparatus and sophisticated data analysis. However, other observations are surprisingly simple. Let's start with an observation that is deceptive in its extreme simplicity.

The Night Sky is Dark

Step outside on a clear, moonless night, far from city lights, and look upward. You will see a dark sky, with roughly two thousand stars scattered across it. The fact that the night sky is dark at visible wavelengths, instead of being uniformly bright with starlight, is known as Olbers’ paradox, after the astronomer Heinrich Olbers, who wrote a scientific paper on the subject in 1823. As it happens, Olbers was not the first person to think about Olbers’ paradox. As early as 1576, Thomas Digges mentioned how strange it is that the night sky is dark, with only a few pinpoints of light to mark the location of stars.

Why should it be paradoxical that the night sky is dark? Most of us simply take for granted the fact that daytime is bright and nighttime is dark. The darkness of the night sky certainly posed no problems to the ancient Egyptians or Greeks, to whom stars were lights stuck to a dome or sphere. However, the cosmological model of Copernicus required that the distance to stars be very much larger than an astronomical unit; otherwise, the parallax of the stars, as the Earth goes around on its orbit, would be large enough to see with the naked eye. Moreover, since the Copernican system no longer requires that the stars be attached to a rotating celestial sphere, the stars can be at different distances from the Sun. These liberating realizations led Thomas Digges, and other post-Copernican astronomers, to embrace a model in which stars are large, opaque, glowing spheres like the Sun, scattered throughout infinite space.

Cosmology is the study of the universe, or cosmos, regarded as a whole. Attempting to cover the study of the entire universe in a single volume may seem like a megalomaniac's dream. The universe, after all, is richly textured, with structures on a vast range of scales; planets orbit stars, stars are collected into galaxies, galaxies are gravitationally bound into clusters, and even clusters of galaxies are found within larger superclusters. Given the complexity of the universe, the only way to condense its history into a single book is by a process of ruthless simplification. For much of this book, therefore, we will be considering the properties of an idealized, perfectly smooth, model universe. Only near the end of the book will we consider how relatively small objects, such as galaxies, clusters, and superclusters, are formed as the universe evolves. It is amusing to note in this context that the words cosmology and cosmetology come from the same Greek root: the word kosmos, meaning harmony or order. Just as cosmetologists try to make a human face more harmonious by smoothing over small blemishes such as pimples and wrinkles, cosmologists sometimes must smooth over small “blemishes” such as galaxies.

A science that regards entire galaxies as being small objects might seem, at first glance, very remote from the concerns of humanity. Nevertheless, cosmology deals with questions that are fundamental to the human condition. The questions that vex humanity are given in the title of a painting by Paul Gauguin (Figure 1.1): “Where do we come from? What are we? Where are we going?” Cosmology grapples with these questions by describing the past, explaining the present, and predicting the future of the universe. Cosmologists ask questions such as “What is the universe made of? Is it finite or infinite in spatial extent? Did it have a beginning some time in the past? Will it come to an end some time in the future?”

Cosmology deals with distances that are very large, objects that are very big, and timescales that are very long.

On cosmological scales (that is, on scales greater than 100 Mpc or so), the dominant force determining the evolution of the universe is gravity. The weak and strong nuclear forces are short-range forces; the weak force is effective only on scales of or less, and the strong force on scales of or less. Both gravity and electromagnetism are long-range forces. On small scales, gravity is negligibly small compared to electromagnetic forces; for instance, the electrostatic repulsion between a pair of protons is larger by a factor than the gravitational attraction between them. However, on large scales, the universe is electrically neutral, so there are no electrostatic forces on large scales. Moreover, intergalactic magnetic fields are sufficiently small that magnetic forces are also negligibly tiny on cosmological scales.

In referring to gravity as a force, we are implicitly adopting a Newtonian viewpoint. In physics, the two useful ways of looking at gravity are the Newtonian (classical) viewpoint and the Einsteinian (general relativistic) viewpoint. In Isaac Newton's view, as formulated by his laws of motion and law of gravity, gravity is a force that causes massive bodies to be accelerated. By contrast, in Einstein's view, gravity is a manifestation of the curvature of spacetime. Although Newton's view and Einstein's view are conceptually very different, in most contexts they yield the same predictions. The Newtonian predictions differ significantly from the predictions of general relativity only in the limit of deep potential minima (to use Newtonian language) or strong spatial curvature (to use general relativistic language). In these limits, general relativity yields the correct result.

In the limit of shallow potential minima and weak spatial curvature, it is permissible to switch back and forth between a Newtonian and a general relativistic viewpoint, adopting whichever one is more convenient. I will frequently adopt the Newtonian view of gravity in this book because, in many contexts, it is mathematically simpler and conceptually more familiar.

The universe can be approximated as being homogeneous and isotropic only if we smooth it with a filter across. On smaller scales, the universe contains density fluctuations ranging from subatomic quantum fluctuations up to the large superclusters and voids, across, which characterize the distribution of galaxies in space. If we relax the strict assumption of homogeneity and isotropy that underlies the Robertson–Walker metric and the Friedmann equation, we can ask (and, to some extent, answer) the question, “How do density fluctuations in the universe evolve with time?”

The formation of relatively small objects, such as planets, stars, or even galaxies, involves fairly complicated physics. Because of the greater complexity when baryons are involved in structure formation, we will postpone the discussion of galaxies and stars until the next chapter. In this chapter, we will focus on the formation of structures larger than galaxies – clusters, superclusters, and voids. Cosmologists use the term large scale structure of the universe to refer to all structures bigger than individual galaxies. A map of the large scale structure of the universe, as traced by the positions of galaxies, can be made by measuring the redshifts of a sample of galaxies and using the Hubble relation, to estimate their distances. For instance, Figure 11.1 shows two slices through the universe based on data from the 2dF Galaxy Redshift Survey (2dFGRS). From our location near the midplane of our galaxy's dusty disk, we get our best view of distant galaxies when we look perpendicular to the disk, toward what are conventionally called the “north galactic pole” (in the constellation Coma Berenices) and the antipodal “south galactic pole” (in the constellation Sculptor). The 2dFGRS selected two long narrow stripes on the sky, one near the north galactic pole and the other near the south galactic pole. In each stripe, the redshift was measured for galaxies. By plotting the redshift of each galaxy as a function of its angular position along the stripe, a pair of two-dimensional slices through the universe were mapped out.