PART TWO:
The Stuff of the Universe
101
FOUR: The Particle Zoo 103
Sizing Up Neutrinos; Missing Links; The Axion; Supersymmetric Partners; Making the Most of Monopoles; Quark Nuggets; A Black Hole Bonanza; Do Black Holes Explode?; Great Dark Hopes
FIVE: Halo Stuff 132
Dusky Dwarfs; Black Hole Beasts; Baryons May Be Cool; Making Mountains Out of Molehills; More Answers Than Questions
SIX: Core Stuff 152
A Brief History of Black Holes; The Quasar Connection; Black Hole Powerhouses; Weighing the Evidence; At the Heart of the Milky Way; A Flare for Black Holes
SEVEN: Cosmic String 175
A Theory of Everything?; Breaking Up Is Not So Hard to Do; Out of the Shadows?; Strings and Things; Trapping the Vacuum; Making Galaxies; Seeking Strings
EIGHT: Gravity's Telescopes 202
Making Waves; Measuring Waves; Gravitational Lenses; Luminous Arcs; Shedding Light on Dark Matter; Dark Galaxies
NINE: The Lyman Forest:
Emergence and Evolution of Galaxies 223
Quasars and Lyman Alpha; Into the Forest; Large Scale Lessons; Heavy Signs of a Galaxy Wall; Into the Past
PART THREE:
The Bespoke Universe
239
TEN: Tailor-Made for Man? 241
The Beryllium Bottleneck; Hoyle's Anthropic Insight; The Stellar Pressure Cooker; The Supernova Connection; A Cosmic Connection; Space, Time, and the Universe; An Alternative Universe
ELEVEN: Or Off the Peg? 270
The Quantum Realities; Inflation in a Nutshell; Bubbles on the River of Time; Cosmic Dragons; The Philosophy of Cosmology; The End of Physics?
INTRODUCTION
•
Why Are We Here?
THERE ARE three motives for studying the Universe. The first is discovery: to learn what's out there, whether in our own Solar System or in the extragalactic realm. This vicarious exploration—of the surface of Mars, or the patterns of spiral galaxies—is something a wide public can share.
For the astrophysicist, this exploration is preliminary to a second goal: to understand and interpret what we see, in terms of the laws of physics established here on Earth, and to place our entire Solar System in an evolutionary context that can be traced back to the birth of the Milky Way Galaxy, and beyond—right back, indeed, to the initial instants of the so-called Big Bang with which our Universe began.
To the physicist, there is a third motive: The cosmos is a "laboratory" offering more extreme conditions than can be simulated on Earth. Known laws can be tested, perhaps to the breaking point, by applying them, for instance, to the amazing densities of neutron stars; and a better understanding of the astounding temperatures and energies of the Big Bang could reveal new laws. Essentially all that we know about gravity—one of the four fundamental forces, and the one that controls the motions of stars, gal-
axies, and the entire expanding Universe—comes from astronomy.
Astronomy is, of course, an old pursuit—perhaps it was the first science to become professionalised—but it has greatly enlarged its scope during the past two decades. Recent progress has been largely "driven" by experimental and observational advances. No armchair theorist, even equipped with current physical knowledge, could have envisaged the extraordinary phenomena and objects that have been discovered. This burgeoning is due partly to technical improvements in optical astronomy, but even more to the new windows on the Universe opened up by radio astronomy and by observations from space. Valuable data are also obtained in other ways—from underground neutrino detectors and gravitational-wave experiments. There are few branches of terrestrial physics, indeed, that do not find application somewhere in astronomy.
In this book, we have (especially in the middle section) described those recent developments that we have found (from our experience of lecturing and writing) that seem to fascinate nonspecialists most. We aim to answer the questions that we most often are asked. Few of these topics—quasar spectra, protogalaxies, gravitational lenses, gravitational waves, and cosmic strings—have yet been given due prominence in nontechnical publications. On the other hand, stories such as that of black holes are not emphasised here because such exotic objects have become so familiar from the many excellent books that already exist.
All these topics relate to a single overall conclusion— something that has as much right to be called a paradigm shift as anything in twentieth-century astronomy. This is the realisation that the dynamics of our Universe, and of all the galaxies in it, are controlled not by what we see but by dark matter. Only 10 percent (at most) of the Universe shines; what we see is a biased
and incomplete sample of the Universe's overall contents. Without the dark matter, our Universe would be a very different place: Dark matter controls the structure and eventual fate of the Universe. Discovering what the "dark stuff" is surely rates as the number-one problem confronting cosmologists today.
The search for a solution to this puzzle is a natural development from recent discoveries in cosmology that have been reported in earlier books. A fuller description of Big Bang cosmology and the expanding Universe can be found in In Search of the Big Bang; the ultimate fate of the Universe, and evidence that dark matter does indeed exist, are discussed in detail in The Omega Point. Here, moving on from such discoveries, we are more concerned with the exact nature of the dark matter, the stuff of the Universe, than with the detailed proof that there is some sort of dark matter around.
It is no exaggeration to say that we would not be here to wonder at the Universe if the dark stuff were not around. We can imagine ways in which the Universe might have emerged from the Big Bang without this background sea of stuff, so that stars, galaxies, and creatures like us would never have been produced. And yet we are here, and this relates to the second main theme of our book.
Science deals mostly with complex manifestations of laws that in essence are well known—the real scientific challenge lies in understanding the rich complexity inherent in these phenomena. Cosmology and particle physics are, however, the two frontier areas, where even the basic laws are still mysterious. iMoreover, deep interconnections are becoming apparent between these two endeavours—the study of the cosmos and of the microworld. For example, the dark matter that dominates the Universe is probably in the form of myriads of tiny particles whose individual properties can be understood only in microphysical terms.
The study of the Universe, and our place in it, evolves in a piecemeal way. We can make progress only by tackling problems in "bite-sized" pieces, and specialists are perforce concerned with technical details. But the occupational risk of astrophysicists, and indeed of all scientists, is to forget that one is wearing blinkers— that there are broader questions at issue, and that a main goal of our piecemeal efforts is eventually to elucidate them.
Why is our Universe the way it is? What is our place in it? Could things have been otherwise, and could alternative universes exist? Why, above all, does the Universe have the symmetry and simplicity that have allowed us to make any progress in understanding it? These issues, where even the specialists are still groping for clues, are the ones that come up most frequently in general discussions. Their investigation sometimes goes by the name of anthropic cosmology —but giving the investigation a name doesn't mean that we yet have all, or any, of the answers.
As the frontier of cosmological knowledge has advanced, its periphery has expanded, and issues that were once purely conjectural have come within the scope of serious investigation. Questions about how the Universe began and how it may end can now be addressed scientifically, and not just in our nonprofessional moments. Such debates have been the subjects of previous books; here, we have not shied away from more speculative issues, coming just within the periphery of respectable science, and we try to give the flavour of current debates that are on (but not beyond) the frontiers of the subject.
The unifying theme of this book can be stated in nontechnical terms—indeed, there is no other way to express it, since the specialists are as perplexed about the answer as anyone else: What features of the Universe were essential for the emergence of creatures such as
ourselves, and is it through coincidence, or for some deeper reason, that our Universe has these features? We hope our discussion of these issues will answer some of the questions in your mind.
John Gribbin Martin Rees October 1988
PART ONE
•
Cosmic Coincidences
CHAPTER ONE
How Special Is the Universe?
science is not simply the accumulation of more and more facts about the natural world. If that were the case, science would long since have ground to a halt, clogged up by the accumulation of vast amounts of data. Instead, science proceeds because of our ability to discern patterns and regularities in the natural world. As we come to see how previously unconnected facts hang together, we fit more data into laws of greater scope and generality, and we need to remember fewer independent basic facts, from which all the rest can be deduced. The astonishing triumph of modern science, especially physics and astronomy, is its ability to describe so many of the bewildering complexities of the natural world in terms of a few underlying principles. But this success seems to rest upon the fact that our Universe is "constructed" along very simple lines. The laws of physics are straightforward enough to be understood by human minds, and the laws we deduce from experiments here on Earth seem to apply across the Universe, at all places and at all times. Is such simplicity an inevitable feature of the Universe? Is it
merely a coincidence that creatures intelligent enough to understand a few simple physical laws exist in a world where only those physical laws are needed to explain how everything works? Or is there some deeper plan that ensures that the Universe is tailor-made for humankind?
These questions, which relate to our place in the Universe, and are concerned with the issues of what has been dubbed anthropic cosmology, are addressed in this book. The success of science in explaining complex patterns of behaviour by simple laws can be seen by a few examples. The regular courses of the Moon and planets across the sky had been known since ancient times, but were explained only when Newton realised that they were governed by the same gravitational force that holds us down on the Earth. And the complexity of chemistry, which so baffled the alchemists, began to be understood when Mendeleev, in the nineteenth century, found regularities in the way the properties of elements related to one another; these regularities are now attributed to the fact that atoms are made from just three basic types of component, the protons and neutrons (together making up the nucleus) and the electrons (which are distributed outside the nucleus in accordance with the laws of quantum mechanics).
Physicists have now reduced nature still further. They believe that the basic structure of the entire physical world—not just atoms but stars and people as well—is in principle determined by a few basic "constants." These are the masses of a few so-called elementary particles, and the strengths of the forces—electric, nuclear, and gravitational—that bind those particles together and govern their motions.
In terms of these simple rules, some natural phenomena are more easily explained than others. Biological processes, for example, are much harder to understand than the fall of an apple from a tree or the orbit of a
How Special Is the Universe? 5
planet around the Sun. But it is complexity, not sheer size, that makes a process hard to comprehend. We already understand the inside of the Sun better than we do the interior of the Earth. The Earth is harder to understand because the temperatures and pressures inside it are less extreme, and therefore more subtle, than those inside the Sun. Complex structures—chemical compounds containing many atoms joined together—exist inside the Earth; inside the Sun, however, everything is reduced by the heat and pressure to the constituent atomic nuclei and electrons, and their behaviour is governed by the basic rules.
Our Universe contains thousands of millions of galaxies, and each of those galaxies may, like our Milky Way, contain thousands of millions of stars, more or less like our Sun. Observations show that the Universe is expanding, with groups of galaxies moving apart from one another as time goes by. Cosmologists infer that there was a time, roughly 15 billion years ago, when all of the matter and energy of the Universe, and space and time as well, were concentrated in a superhot region, a fireball known as the Big Bang. In the earliest stages of the primordial fireball, matter would surely have been reduced, or broken down, into its most primitive constituents—a "thermal soup" at a temperature of 10 billion degrees Celsius, initially expanding at such a rate that it doubled in size every second. In this sense, conditions in the Big Bang were even simpler than those inside the Sun today. So we can realistically hope to explain why the Universe is expanding the way it is—it isn't presumptuous to try to understand the physics involved. Perhaps we can also understand how stars and galaxies came into existence in the expanding Universe, and therefore begin to appreciate the nature of our own origins. But as soon as we begin to gain an understanding of these processes, we immediately run into the puzzle of the cosmic coincidences.
The Anthropic Universe
The Universe is a simple place, but we are complex creatures. One reason for this is that we do not inhabit a typical place in the Universe. Most of the Universe is empty space, filled with a weak background sea of electromagnetic radiation, with a temperature only 3 degrees above the absolute zero of temperature, which lies at -273 degrees C. But we live on a planet, which orbits around a simple, stable star. Conditions inside that star—our Sun—provide the energy that life, including human life, needs; conditions on the surface of that planet—the Earth—allow for the complexity that seems essential to life as we know it. Clearly, our home represents a special place in the Universe (although not necessarily a unique place). Slightly more subtly, we can see that we also exist at a special time in the Universe. In the Big Bang itself, conditions were too extreme for the complexity that represents human life to exist; today, they are just right (at least on one planet, orbiting one star in one galaxy). In the future, perhaps conditions will once again be unsuitable for life as we know it. We exist here and now because of the exact relationships between the basic forces and particles. And this raises many questions.
Why, for example, are stars so big? The strength of the electrical force between two protons (in, say, a hydrogen molecule) can be compared with the gravitational force between the same two particles. Electrical forces are 10 36 (a 1 followed by 36 zeroes) times stronger than gravitational forces, and on the scale of an atom gravity can be completely ignored. But when large numbers of atoms are grouped together, the force of gravity increases as the total mass increases. Each atom has zero net electrical charge, because the positive charge on each proton is exactly balanced by the negative charge on an electron in the atom (some people, inci-
dentally, see this exact balance between the charge on an electron and the charge on a proton as a remarkable coincidence in its own right). So, a large mass carries no net electrical charge and exerts no net electrical force. When an apple falls from a tree, it does so not because of the electrical forces pulling it towards the Earth, but because of the accumulated gravitational force of the enormous numbers of atoms that together make up the Earth. In fact, the apple is held together by electrical forces, acting between its constituent atoms and molecules. The same forces hold together the atoms and molecules of the stem that attaches the apple to the tree. The apple falls if, and when, the gravity of the whole Earth is strong enough to overcome the electrical forces in the stem and break the apple free from its parent tree. The gravity of the whole Earth is needed to break the electrical forces involving the relatively few atoms in the stem of the apple.
Theoretical studies of stars and their life cycles were stimulated by the challenge of observations— people saw the stars and wondered what they were made of. It is interesting, though, that the properties of stars could have been deduced by a physicist who lived on a perpetually cloud-bound planet. Such a physicist could have posed the question: Can one have a gravitationally bound fusion reactor, and what would it be like? He or she might then have reasoned like this: Because gravity is never cancelled out in the way electrical charges cancel, it must win out over electrical forces on a sufficiently large scale. But how large?
Imagine that we assemble a set of objects containing successively 10, 100, 1,000 atoms, and so on. The 24th object would be the size of a sugar lump—about 1 cubic centimetre. The 39th would be like a rock 1 kilometre across. Gravity starts off with a "handicap" of 10 36 , but it gains on electrical forces as a two-thirds
power.* So when we get to our 54th object, because 36 is two-thirds of 54, it will have caught up. Our 54th object will have the mass of Jupiter; anything bigger than Jupiter will start to get crushed by gravity. So, to be squeezed by gravity and heated to the point where nuclear fusion could ignite, an object must contain well over 10 54 atoms.
Gravitationally bound fusion reactors—stars—must be massive because gravity is so weak. Having inferred this, our hypothetical physicist could in principle calculate the entire life cycle of a star. Sir Arthur Edding-ton was the first person to express this line of argument clearly, in the 1920s; he went on to conclude that "when we draw aside the veil of clouds beneath which our physicist is working and let him look up at the sky, there he will find a thousand million globes of gas, nearly all with masses [in this calculated range]."
Gravity dominates the electrical forces, and crushes atoms out of existence, when the total mass of a collection of atoms approaches 10 57 times the mass of a proton. Even the interior of the Earth can resist the inward pressure of gravity and maintain atoms as distinct entities. But when the total mass nears that critical value, the structure of atoms is destroyed. What remains is a sea of freely mingling nuclei and electrons. Stars do indeed have masses around 10 57 times the mass of a proton. They are held together by gravity, and gravity initiates the process of nuclear fusion, when atomic nuclei are squeezed together to make new nuclei, which provides the energy that keeps stars hot. If gravity were even weaker, stars would be bigger still; if gravity were stronger, stars would be smaller and would
*The reason is simple: the force involved depends on mass M and radius R and is proportional to MIR; for uniform density, mass is proportional to the cube of radius, that is, radius is the one-third power of the mass, and MIR goes as the two-thirds power of mass.
run through their life cycles more quickly—perhaps so quickly that there would be no time for intelligent life to evolve on any planets orbiting those stars.
The basic forces also determine how big a human being can be. Our bodies, like all chemical structures, are held together by electrical forces. These forces are fixed by the basic laws of nature. But because the gravitational force acting on our bodies—our weight— depends on how many atoms the bodies contain, the force is bigger if people (or other creatures) are bigger. The bigger they come, the harder they fall. A simple calculation shows that any creatures much bigger than a human being, inhabiting the surface of a planet the size of the Earth, will simply break apart when they fall over. We are as big as we can be, given our lifestyle—or rather, the lifestyle of our recent ancestors. Whales can be big, because their mass is supported by the sea; but our ancestors, who were tree-dwelling primates, couldn't be so big that an occasional fall would inevitably prove fatal.
We shall look in more detail at these, and other cosmic coincidences in part 3 of the book. But it is worth spelling out now just how delicate the balances between the basic forces that permit our existence really are. For example, if the nuclear forces, which control the behaviour of protons and neutrons within the nucleus of an atom, were slightly stronger than they actually are, compared with electrical forces, then the di-proton (an atomic nucleus composed of two protons) would be stable. In our Universe, the electrical force of repulsion between two positively charged protons overwhelms the nuclear force of attraction between them, and di-protons do not exist. Two protons can be held in a stable atomic nucleus only if there is a neutron or two there as well; these uncharged particles add to the attractive force but do not affect the repul-
sive force. Now, stars gain their energy by fusing protons and neutrons together into such nuclei; if, instead, they could fuse pairs of protons together into di-protons, stars would evolve quite differently and the Universe would be a very different place. If, on the other hand, nuclear forces were slightly weaker than they are in our Universe, no complex nuclei could form at all. The entire Universe would be composed of hydrogen, the simplest element, whose atoms consist of a single proton and a single electron.
All the familiar chemical elements except hydrogen and primordial helium were, in fact, built up by nuclear transmutations inside stars that exploded long before our Solar System formed. Iron, carbon, oxygen, and the rest are all products of stellar nucleosynthesis, a process that is sensitive to several apparent accidents of physics, as Fred Hoyle pointed out in the 1950s. We shall look in detail at those coincidences later; what matters here is that the Universe seems to have been set up in such a way that interesting things can happen in it. It is very easy to imagine other kinds of universes, which would have been stillborn because the laws of physics in them would not have allowed anything interesting to evolve.
Imagine, for instance, tinkering with the Universe by varying the strength of gravity. Suppose that it were only 10 26 , rather than about 10 36 , times weaker than the electrical force. We would then have a smaller Universe, in which stellar processes would occur more rapidly. Stars, which are fusion reactors bound together by gravity, would each have only about 10~ 15 (one-millionth of a billionth) of the Sun's mass. Although each one would have a mass of a trillion tons, it would take 10 million of them to add up to the mass of our Moon; and each would last for just about a year before burning out. Very probably, this would not provide time for life forms as complex as ourselves to evolve; in
any case, complex structures could not grow very large before being crushed by gravity.
So the fact that we exist tells us, in a sense, what conditions are like inside stars and in the Universe at large. This is the mildest form of what is now known as anthropic reasoning, or anthropic cosmology. Given the brute fact that we are a carbon-based form of life, which evolved slowly on a planet orbiting around a star like our Sun (a so-called G-type star), there are some features of the Universe, some constraints on the possible values of physical constants, which can be inferred quite straightforwardly. This line of reasoning even helps us to understand the sheer size of the Universe.
A Universe Big Enough for Life
At first sight, it might seem that one planet like the Earth, circling one star like our Sun, would be sufficient to provide a home for life and the opportunity for intelligence to evolve. There is no way to set a precise figure on the extent of our Universe and the number of stars and planets it contains, but at the very least it contains a billion billion (10 18 ) stars, and at least 1 percent of that number—some 10 million billion stars—are likely to be reasonably similar to our Sun. If we guessed that just 1 percent of those Sun-like stars actually possessed a retinue of planets that included a planet like the Earth, that would still provide a hundred thousand billion homes for life as we know it. This is a number so extravagantly large that it makes our place in the Universe seem utterly insignificant. And yet it may be necessary that all those billions of potential homes for life exist, simply because one home for life, our Earth, exists.
Consider the implications in terms of the linear size of the Universe, rather than the number of stars it contains. Cosmologists estimate, for good, sound reasons,* that the observable Universe is about 15 billion light-years across. A light-year is simply the distance that light can travel in one year, so it is no coincidence that this size is linked to the estimated age of the Universe—15 billion years. We can, in principle, "see" as far as light has had time to travel since the Universe began.
The fireball of the Big Bang was a simple place, in the sense that matter was broken down into its component parts there. As the Universe expanded and cooled, those basic building blocks of matter formed into the simplest elements, hydrogen and helium. But studies of the light from very old stars show that scarcely any heavier elements than these emerged from the Big Bang. The essential molecules of life, which include carbon, oxygen, nitrogen, and phosphorus, were manufactured by thermonuclear processes inside stars after the Big Bang. Our own Sun is not one of the first stars that formed when the Universe was young. Those stars went through their life cycles, converting hydrogen and helium into more complex nuclei, and some of those stars then exploded as supernovae, scattering the fruits of stellar nucleosynthesis through the dust and gas clouds of the young Galaxy. Only later generations of stars, born out of collapsing fragments of those interstellar clouds, contained enough of the heavier elements to form planets like the Earth, and allowed life forms like ourselves to emerge.
All that took time. In round terms, it takes a few billion years for a galaxy to form, for the first stars in it to process hydrogen and helium into heavier elements,
*The details can be found in In Search of the Big Bang, by John Gribbin (see bibliography).
How Special Is the Universe?
13
EARLY UNIVERSE
I
HYDROGEN & HELIUM ONLY
FIRST STARS
i
CARBON, ETC.,
SYNTHESISED BY
NUCLEAR REACTIONS
i
SUPERNOVA EXPLOSIONS
INTERSTELLAR CLOUDS
I
SECOND-GENERATION STARS (INCLUDING OUR SOLAR SYSTEM )
Figure 1.1 The history of the atoms on Earth.
live out their lives, and die in a blaze of glory, scattering those elements in the process. It then takes more time for new stars to form out of the debris, and for life to evolve on the planets circling those stars. In order for us to be here wondering about it all, the Universe must be about 15 billion years old, and therefore about 15 billion light-years across!
This insight demonstrates the power of anthropic reasoning. Simply from the fact that we are a carborr-based life form we can deduce that the Universe must be a certain size and a certain age. Sometimes, those who argue that the Universe cannot possibly have been designed, or created, expressly in order to produce a carbon-based, intelligent life form inhabiting a single
planet orbiting an ordinary star, point out that the Universe seems ludicrously overdesigned for such a task bigger and older, and containing far more stars, than seems necessary. Provided that the laws of physics had to be as they are, the argument falls down. Given the laws of physics that operate in our Universe, all those billions of stars and billions of light-years are necessary for our existence. The argument returns in full force, however, if you assume that whoever designed the Universe could have chosen different values of the constants of nature.
It is, perhaps, also worth pointing out that the argument is not affected, one way or the other, if there are forms of intelligent life in the Universe that do not depend on carbon chemistry for their being. Science fiction authors, and some who write nonfiction, have speculated on the possibilities of, for example, life on the surface of a neutron star, or intelligence generated by magnetic fields that eddy through a black cloud in space. But we are a carbon-based life form, and therefore it is no surprise to find that we see a Universe 15 billion years old and 15 billion light-years across. We do not observe the Universe at a randomly chosen instant of cosmic time, but at just about the earliest time that life forms like us could begin to be asking questions about the Universe at large.
But still, there is something very curious about the fact that the Universe has expanded away from the Big Bang at just the right speed to allow galaxies, stars, and planets to form, and for carbon-based life forms to exist on at least one of those planets. It is a puzzle that is almost too obvious to seem worthy of attention— why is there anything interesting here at all?—but that points to the most astonishing cosmic coincidence of all. It has to do with how much matter the Universe contains, and how fast it expands: In more technical language, how "flat" the spacetime of the Universe must be.
The Primary Puzzle
One way to get a grip on the most extreme cosmic coincidence of all is by looking again at the variety of chemical elements in our Universe, and especially on our planet. The reason hydrogen and helium can be converted into heavier elements inside stars is that heavier elements, once formed, represent a more efficient way of storing matter. Protons and neutrons stored in the form of carbon nuclei are held together more effectively .than similar particles in nuclei of helium. This is why converting helium nuclei into carbon nuclei releases energy, which helps to keep a star hot. Because all atomic nuclei carry a positive charge, proportional to the number of protons they contain, they must be pushed together hard enough to overcome the electrical repulsion force, and close enough to allow the nuclear force, which is stronger but has a shorter range than the electrical force, to dominate. Nuclear fusion won't happen, therefore, unless the nuclei have big random motions, leading to hard collisions—unless, in other words, the temperature is very high. If 10° 7 particles are gathered together in a star, gravity can confine and squeeze them to sufficiently high temperatures. Gravity overcomes the electrical force and allows the nuclear force to get to work.
Conditions in the Big Bang were also extreme enough to do the trick. It was hot, and the pressure was very high. At first, however, protons and neutrons, which had just been manufactured out of pure energy, could not stick together in complex nuclei because they would be torn apart by the battering of repeated collisions with other particles. But as the Universe expanded it started to cool—in exactly the same way as gas expanding out of a confined space cools, the principle on which a domestic refrigerator operates. There must have come a time when conditions were right for protons and
neutrons to be welded together into nuclei of heavy elements. The process began with the production of helium nuclei, each containing two protons and two neutrons, and it would have proceeded quite quickly to heavier elements, if those conditions had persisted. The most energetically stable nucleus of all is that of iron, and if the Universe had cooled slowly enough, then most of the protons and neutrons would have been locked up in iron nuclei. Had that been the case, the Universe would have been a dull place in which no further interesting reactions could have occurred; stars would not exist, and there would have been no opportunity to build up the familiar biological complexity of life on Earth.
The crucial factor that prevented all the primordial matter from turning into iron, but allowed stars like our Sun to form, and to build up a variety of elements starting from hydrogen and helium, was the rate at which the early Universe expanded. The faster the expansion, the quicker the cooling; and the higher the density of nuclei, the more likely that reactions will go completely through to equilibrium within the time available. Analysis of the light from old stars shows that just 25 percent of the matter emerging from the Big Bang was in the form of helium, and virtually all the rest was still in the form of hydrogen. Hardly any nuclei more massive than helium formed in the Big Bang. This simple number, the ratio of hydrogen to helium in old stars, actually tells cosmologists a great deal about the content of the Universe when it was only one second old, and how quickly it was expanding and cooling during the Big Bang.
The early Universe must have been a mixture of nuclei and radiation, with the radiation component being overwhelmingly dominant. Calculations of nuclear reactions suggest that there was only 1 nucleus for
every 2 x 10 9 quanta of radiation—or photons. This ratio has held throughout the subsequent life of the Universe. Today there are around 400 photons in even-cubic centimetre of space, so the calculations imply a mean density of 1 atom in every 5 cubic metres of space. This is, indeed, roughly consistent with what astronomers see, if all the matter in all the stars were spread out evenly; we will put these numbers in their proper perspective later.
Are there other constraints on the rate at which the Universe could be "allowed" to expand, given that we exist? After the hydrogen and helium that emerged from the Big Bang had cooled, they began to form into clouds of gas that were held together by gravity. Some of those clouds collapsed, under the pull of their own gravity, even though the Universe as a whole was expanding. Embryonic galaxies could have been simply regions of the Universe where the density was slightly greater than the average, regions whose expansion therefore lagged behind the overall expansion of the Universe, forming collapsed clouds of gas that became stars and galaxies. This happened when the Universe was about 10 percent of its present age—between 1 and 2 billion years after the Big Bang. We don't know exactly how galaxies formed, but it is clear that if the Universe had been expanding too rapidly, the clouds would have been spread thin and pulled apart before gravity could dominate, even on a local scale, and make them collapse into galaxies and stars. Without that collapse, no heavy elements would have been cooked in stellar interiors and, once again, we would not be here to wonder about the nature of the Universe. On the other hand, if the Universe had started off expanding too slowly, it would have come to a halt and started to recollapse by now, with galaxies falling towards each other. We can
even imagine a universe in which the expansion reversed within the first million years; incipient galaxies and stars would have been snuffed out before they could even have had a chance to form.
So our existence tells us that the Universe must have expanded, and be expanding, neither too fast nor too slow, but at just the "right" rate to allow elements to be cooked in stars.
This may not seem a particularly impressive insight. After all, perhaps there is a large range of expansion rates that qualify as "right" for stars like the Sun to exist. But when we convert the discussion into the proper description of the Universe, Einstein's mathematical description of space and time, and work backwards to see how critical the expansion rate must have been at the time of the Big Bang, we find that the Universe is balanced far more crucially than the metaphorical knife edge. If we push back to the earliest time at which our theories of physics can be thought to have any validity, the implication is that the relevant number, the so-called "density parameter," was set, in the beginning, with an accuracy of 1 part in 10 60 . Changing that parameter, either way, by a fraction given by a decimal point followed by 60 zeroes and a 1, would have made the Universe unsuitable for life as we know it. The implications of this finest of finely tuned cosmic coincidences form the heart of this book, and in part 2 we shall discuss the strange forms of dark matter that may exist in the Universe today, and against which all the matter in all the bright stars of all the visible galaxies represents less than the tip of the proverbial iceberg. That dark matter may be as crucial to the existence of those stars as the plenitude of stars is to the existence of life on Earth.
The Flat Universe
Gravity is the controlling force of planets, stars, and all large astronomical systems, including the Universe itself. On Earth, and throughout the Solar System, Newton's theory of gravity, which says that the force of attraction acting between two bodies is inversely proportional to the square of their distance apart, is an excellent approximation (although some recent investigations suggest that Newton's law may need to be modified very slightly, even on Earth, by an effect known as the "fifth force"). But when gravity is stronger, which happens when objects are compressed into very small volumes or masses even larger than stars are involved, Newtonian ideas are inadequate to describe gravitational effects. The theory that goes beyond Newton to provide a working description of gravity under such extreme conditions is Einstein's theory—general relativity.
In academic libraries, the old back numbers of scientific journals are usually seldom consulted and are relegated to remote stockrooms. But two particular volumes—the issues of Annalen der Physik for 1905 and 1916—are treasured collectors' items: They contain the papers by Albert Einstein that established him as the greatest physicist since Newton.
In 1905, the 26-year-old Einstein not only elucidated his theory of "special relativity"; he also proposed that light is quantised into packets of energy (photons), and formulated the statistical theory of how tiny particles move through the air or a liquid (Brownian motion). These contributions alone rank him among the half-dozen great pioneers of twentieth-century physics.
But it is his gravitational theory, "general" relativity, developed ten years later, that puts Einstein in a class by himself. Even if he had contributed none of his 1905 papers, it would not have been long before the same concepts were put forward by some of his distin-
guished contemporaries. The ideas were "in the air"; well-known inconsistencies in earlier theories, and puzzling experimental results, were focussing attention on these problems. But general relativity, the interpretation of gravity in terms of curved spacetime so that "space tells matter how to move; matter tells space how to curve," was not a response to any particular observational enigma. True, it did account for an old puzzle about the orbit of Mercury, and it was famously confirmed by measurements made during an eclipse of the Sun in 1919. But Einstein was motivated by the quest for simplicity and unity. When he announced his new work, he commented that "scarcely anyone who has fully understood the theory can escape from its magic.',' Herman Weyl, a contemporary and mathematical colleague of Einstein, described it as "the greatest example of the power of speculative thought"; and Max Born, one of the fathers of quantum physics, said it was "the greatest feat of human thinking about Nature." Had it not been for Einstein, an equally comprehensive theory of gravity might not have come until decades later, and been approached by a quite different route. Einstein is unique among scientists of this century in the degree to which his work retains its individual identity.
Indeed, general relativity was put forward so far in advance of any real application that it remained, for forty years after its discovery, an austere intellectual monument, a somewhat sterile topic isolated from the mainstream of physics and astronomy. This is in glaring contrast to its present status as one of the liveliest frontiers of fundamental research. Dramatic observational advances that suggest that black holes may exist, and that made terms such as quasar, pulsar, and Big Bang part of the general vocabulary, have brought Einstein's master work in from the cold to the mainstream of modern research.
Einstein's theory is crucially important to cosmology, which is the description of our Universe as a single dynamic entity.* Scientific cosmology is, when you think about it, a rather unusual branch of science. Cosmolo-gists study a unique object—the Universe—and a unique event—the Big Bang. No physicist would be happy to base a theory (let alone a career) on a single, unrepeatable experiment; no biologist would formulate general ideas on animal behaviour after observing just one rat running through a single maze once. But we cannot check our cosmological ideas by applying them to other universes. Nor can we repeat the past evolution of the Universe—although the fact that light travels at a finite speed does allow us to sample the past, by looking at very remote objects, which we see by light that left them long ago. Despite these handicaps, scientific cosmology has proved possible. The reason for its success is that the observed Universe, in its large-scale structure, is simpler than we had any right to expect.
In the 1920s, when cosmologists first devised mathematical descriptions of the Universe ("cosmological models") using Einstein's equations of relativity, they assumed simplicity in order to make the equations tractable. The surprising thing is that those models, deliberately chosen to be as simple as possible, remain relevant today; as observational techniques have improved, they have shown that the Universe itself is as simple as the models—that it is the same in all directions (isotropic) and, as far as we can tell, almost the same everywhere (homogeneous), on the broad picture. (Galaxies are grouped in clusters and superclusters, but even the largest superclusters are still fine-scale detail compared to the entire observable Universe.) It is those equations, combined with observations of the way gal-
*We use the term cosmogony for the Much of how individual parts of the Universe, such as galaxies, came to be as they arc.
axies recede from one another, and measurements of the background radiation that fills all of space, that lend weight to the idea that the Universe began in a Big Bang.
The cosmological evidence has strengthened over the past two decades, but it is still conceivable that our satisfaction with the Big Bang model will ultimately prove as illusory and transitory as that of a Ptolemaic astronomer who, believing the Earth to be at the center of the universe, successfully fits a new epicycle to the motion of a planet. Nobody can go back in time to study the Big Bang itself, but we can learn about it by studying "fossils" from the earliest eras, just as a geologist or paleontologist can infer the early history of the Earth by studying the record in the rocks today. The theory can never, of course, be "proved," but it is certainly more plausible than any equally detailed alternative model, and we certainly believe it has a better than even chance of survival.
Since general relativity, and the Big Bang model built with its aid, provide the best description available of how the Universe got to be the way it is, they also provide the best basis for investigating how the Universe will develop in the future. Will it expand forever, and the galaxies fade and disperse as time goes by? Or will it one day recollapse, with the sky falling in to re-create a fireball like the Big Bang?
The answer depends on how much gravitating stuff there is in the Universe. Imagine a big sphere or asteroid that is shattered by an explosion, the debris flying off in all directions. Each fragment feels the gravitational pull of all the others, causing deceleration. If the explosion was sufficiently violent, the debris would fly apart forever, but, because of this gravitational effect, at an ever-decreasing rate. However, if the fragments were not moving quite so fast, gravity would bind them together, so that eventually the expansion would halt
and the fragments would then fall back together. According to general relativity, much the same argument applies for the Universe.
If the expansion of the Universe is to continue forever, then the curvature of spacetime, described by Einstein's equations, is of a form called, for obvious reasons, "open." If the Universe is destined ultimately to recollapse, then spacetime is said to be "closed." The balance point between these two possibilities, when the expansion goes on forever but eventually just comes to a halt (with each part of space ending up as empty and static), corresponds to flat spacetime, or to a "flat universe" model. It is easy to calculate how much matter is needed for its total gravitational influence to bring the universal expansion we observe today to a halt; it works out at about three atoms per cubic metre of the Universe today. Long ago, when the Universe was young and expanding more rapidly, a greater density of matter would have been needed for gravity to exactly balance the faster expansion. But, of course, long ago the Universe was more dense. As you might expect, the equations show that provided the Universe starts out with more than the critical density it would recollapse, and at any epoch we could calculate what fraction of the cycle had elapsed if we knew the fractional amount by which the density exceeded the critical value; similarly, if the initial density were too low to stop the expansion, then during the evolution of the Universe it would stay below the critical value. Indeed, as the Universe expands, the actual density always moves further away from the critical density as time passes.*
*Such mathematical models of what the Universe might be like are usually referred to as "universes," with a small u. The capital is, strictly speaking, reserved for discussion of the way our Universe is observed to be. We can talk of open or closed universes, meaning mathematical models, even though we do not know for certain whether our Universe is open or closed.
Dark Matter Does the Trick
This is what bring us up against the astonishing cosmic coincidence mentioned earlier. The density of visible matter—bright stars and galaxies—in the Universe today can be inferred by counting the number of galaxies in our region of space, and also by measuring the way in which galaxies move. Changes in the light from distant galaxies (redshifts and blueshifts) tell us how fast the galaxies are moving, both as part of the Universal expansion and through space as they orbit around one another in groups called clusters. Just as the speed of the Earth in its orbit around the Sun is related to the mass of the Sun, so the relative speeds of different galaxies in a cluster tell us how much matter the cluster contains. Putting all this dynamical evidence together, cosmologists find that, in very round terms, there is enough matter in the Universe to provide one-tenth of the "critical" density.
Not all this matter is visible; the dynamics show that the total "luminous" mass of galaxies (bright stars and gas) is barely 1 percent of the critical density, and falls far short of what is needed even to hold big galaxies and clusters of galaxies together. And this may not be the end of the story; there could be more dark matter, in the seemingly empty spaces between clusters of galaxies, which would not show up by these tests but that would contribute to the overall slowing down of the Universal expansion. Just how much more dark stuff there may be is a matter of fierce debate today among the experts. No cosmologist of our acquaintance believes that the Universe contains as much matter as ten times the critical density; most would regard twice the critical density as a wild overestimate.
Studies of the overall expansion of the Universe confirm these estimates, as far as they go. The light reach-
How Special Is the Universe? 25
ing us from the most distant observed galaxies has spent several billion years on its journey, and can therefore reveal how fast the Universe was expanding in the remote past. By comparing the recession velocities of more-distant galaxies with those of nearby galaxies, cosmologists could, in principle, infer how quickly the expansion is decelerating and so deduce whether it will eventually halt and reverse. In practice, these measurements show only that the Universe sits so closely on the dividing line—it is so nearly flat—that we cannot tell on which side of the line it lies. Today, 15 billion years after the Big Bang, the density of the Universe is within a factor of ten (between one-tenth and ten times) of the critical value corresponding to a flat universe. And yet, for 15 billion years this density parameter has been steadily moving further away from the critical value! How close must it have been in the beginning, if it is still only a factor of ten away?
The calculation is one of the easiest to carry out using the cosmological equations. It tells us that one second after the moment of creation, the Universe must have been flat to within a factor of 10 l3 —that is, the amount by which the density differed from the critical value, one way or the other, was by a decimal point followed by 15 zeroes and a 1. How much further back in time the laws of physics as we know them can be applied is, to some extent, uncertain. But in quantum physics there is a fundamental limit to the accuracy with which time can be described—in a sense, the "quantum" of time. This unit, the Planck time, is 10 -43 of a second. Cosmologists today, drawing on theories developed by particle physicists, are attempting to describe the actual origin of the Universe in terms of quantum events that happen on this sort of time scale. Such theories, which we discuss in more detail later, are as yet far less well established than the standard model of the Big Bang; nevertheless, if we take them at face
value we deduce that the Universe has been expanding since 10" 43 seconds after "time zero"—but we have no way of knowing what went on between time zero and 10" 43 seconds. Pushing back to that moment, the nearest definition we have to a beginning, the flatness of the Universe must have been precise to within 1 part in 10 60 . This makes the flatness parameter the most accurately determined number in all of physics, and suggests a fine-tuning of the Universe, to set up conditions suitable for the emergence of stars, galaxies, and life, of exquisite precision.
If this were indeed a coincidence, then it would be a fluke so extraordinary as to make all other cosmic coincidences pale into insignificance. It seems much more reasonable to suppose that there is something in the laws of physics that requires the Universe to be precisely flat. After all, the critical density for flatness is the only special density; no other value has any cosmic significance at all. It makes more sense to accept that the Universe had to be born with exactly the critical expansion rate than to believe that by blind luck it happened to start out within 1 part in 10 60 of the critical value. Physicists apply a similar argument when they say that the mass of a photon, a quantum of radiation, is precisely zero. No experiment can measure a precisely zero mass; the best that can be done is to set a limit, from experiments, and say that the mass must be less than 10~ 58 of a gram. In both cases, we infer that there is no deviation from the interesting value of the number.
There is, indeed, a theory (rather, a group of theories) that makes flatness a required feature of the Universe. Such models go by the name inflation, because they suggest that very early in its lifetime (during the first split-second) the Universe expanded by an enormous factor, with a volume of spacetime smaller than a proton expanding to the size of a basketball in a tiny fraction (about 10~ 35 ) of a second. This phase of rapid
accelerating expansion, or inflation, would have smoothed out any wrinkles in spacetime and flattened the fabric of the Universe. The process is the opposite of what happens to a smooth plum when it dries up to become a wrinkly prune; any wrinkles in spacetime got smoothed away during inflation, according to these models.
Inflation is interesting in its own right, and the exotic physical processes that occurred at ultra-early stages have implications that we will discuss later. From our immediate point of view, however, it is important because it offers the best physical reason why our Universe should be exactly flat. The implications of this are profound indeed, and at one level seem to remove humankind further than ever from the centre of the cosmic stage.
As we have mentioned, studies of the way galaxies move within clusters show that clusters contain about one-tenth of the matter required to make the Universe flat. These estimates correspond to about 0.3 atom per cubic metre, and are in fact quite nicely in line with calculations of conditions during the Big Bang (starting at about one-hundredth of a second after the moment of creation and going up to the end of the first four minutes) required to produce the right mix of hydrogen, helium, and deuterium. Those calculations show that the amount of energy that could have been processed into protons and neutrons in the Big Bang was only about one-tenth of the amount needed to make the Universe flat, perhaps a little less. For twenty years or so, most cosmologists took this at face value, to mean that the Universe must be open. They simply never considered seriously the possibility that there might be other forms of matter besides protons and neutrons (and their associated, but lightweight, electrons) in the Universe.
In the 1980s, however, some theorists began to worry
much more about the cosmic coincidence implied by the near-flatness of the Universe today, while particle physicists began to suspect that there might be other forms of matter allowed (even required) by the laws of physics, which could have been created in large quantities during the Big Bang. Just because our own bodies, planet Earth, the Sun, and all the stars in the sky are composed of protons and neutrons (collectively dubbed baryons), cosmologists realised, that was no proof that all of the stuff of the Universe had to be in the form of baryons. The argument that we are made of baryons and therefore the Universe must be made of baryons is in fact as anthropocentric and unfounded as the argument that because we see stars surrounding the Earth on the bowl of the sky, the Earth must be the centre of the Universe. Indeed, if the Universe were made only of baryons, in the numbers that theory tells us were produced in the Big Bang, and contained no nonbaryonic dark stuff at all, then matter would be spread so thin that galaxies (and clusters of galaxies) almost certainly could not have formed in the way we see them around us. Without the dark stuff, galaxies, and ourselves, might not exist at all.
So, the answer to the question posed by the title of this chapter must be that the Universe is a special place, balanced on a knife edge between being open and closed. We cannot be sure what made it special— why the laws of physics require it to be flat—but this line of argument tells us that there is more to the Universe than the kind of atoms that make up our own bodies and the protons and neutrons that form the stuff of stars. At least 90 percent of the stuff of the Universe is in the form of dark matter, which cannot all be made of baryons. And yet, without the dark matter— the invisible stuff of the Universe—the Universe itself would be a very different place, and we would not
exist. Does the dark stuff exist, in a sense, for our benefit? Is it there because we are here? What is it? Where is it? And how has it been responsible for the emergence of the kinds of structures we see in the Universe?
CHAPTER TWO
The Geography of the Universe
J
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AS WE HAVE SEEN, astronomers and cosmologists deal with billions of light-years of space, and billions of years of time. Our own Sun is 4.5 billion years old, and is destined to evolve for at least as long again before its nuclear fuel runs out. The geography of the Universe is the geography of both space and time, because when we look out into space we see things as they were when the light now reaching our telescopes actually left the objects we are studying. Even the Sun, our nearest star, is so remote that its light takes more than eight minutes to reach the Earth.
Clearly, astronomers cannot learn about the life cycles of stars by watching an individual star, like our Sun, live out its life. But just as a botanist could find out about the life cycle of a tree by wandering about a forest and examining trees in different stages of growth, so an astronomer can infer the life cycle of a star by studying many stars of different ages. Stars like the Sun start their lives by condensing, under the inward tug of gravity, from interstellar clouds. After a few hiccups, signs of youthful exuberance, they settle down into a state where they are kept hot by the steady
fusion of hydrogen into helium in their interiors. During this phase of quiet life, which our Sun is now about halfway through, a star is said to be on the "main sequence."
When hydrogen in the core of a star like our Sun is exhausted, however, it first swells up to become a red giant, then shrinks in upon itself, cooling into a ball roughly the size of the Earth, called a white dwarf.
All this is well understood. But not everything in the cosmos happens on quite such a leisurely time scale, and with so little excitement. Some stars, which are much heavier than our Sun, end their lives by exploding violently, as supernovae. Such events are relatively rare—in 1987, astronomers were excited by the opportunity to study the first "nearby" supernova seen since the invention of the astronomical telescope in the seventeenth century; but even this "nearby" event was 170,000 light-years away, in a neighbouring galaxy to the Milky Way, known as the Large Magellanic Cloud. The light that astronomers saw in the supernova in 1987 had set out on its journey before the beginning of the most recent ice age on Earth. Nevertheless, super-novae are important. They mark the violent end point of stellar evolution, when a star too massive to become a white dwarf exhausts its available nuclear energy. The core of the star collapses catastrophically (it "implodes"), while the outer layers are blown away into space; what is left is a dense stellar cinder, a neutron star only 10 kilometres across, but containing about as much matter as our Sun.
In such a star, material is squeezed to nuclear densities, 10 14 times greater than the density of ordinary solids. The gravitational force on the surface of a neutron star is 10 12 (a thousand billion) times greater than on the surface of the Earth, and in order to escape from the gravitational pull of such a star a rocket leaving its surface would have to be fired upward at about half the
COSMIC COINCIDENCES
Remaining core:the neutron star
Figure 2.1 The "onion skin" structure of a massive star before it explodes as a supernova. The hotter inner shells have been processed further up the periodic table; this releases progressively more energy until the material is converted into iron, the most tightly bound nucleus. Endothermic nuclear reactions occurring behind the shock wave that blows off the star's outer layers can synthesise small quantities of still heavier nuclei.
speed of light. The conditions inside a neutron star are more extreme than those in the stars we see shining in the sky. In a neutron star, gravity has squeezed out of the system all memory of its original nuclear composition. The internal structure is still poorly understood, because the conditions are so exotic and unfamiliar. But neutron stars provide a good example of the way in which physicists can test their theories—perhaps to the
s
INFALL .INTO /GALAXY
Figure 2.2 Processes whereby the content of a galaxy gets gradually converted into heavy elements and long-lived stars.
breaking point—by applying them to the behaviour of matter under extreme conditions. The Big Bang was a time when conditions were even more extreme; and while the relevant physics is still uncertain, it may prove to be simpler than that of neutron stars—there were fewer options available for matter then.
Supernovae, even the nearest ones, may seem a long way away and a long time ago. But it is only by studying such events that astronomers can tackle such an everyday question as where the atoms we are made of came from. Complex chemical elements are built up from hydrogen, as we shall explain in chapter 10, by the nuclear reactions that provide the power source in the cores of ordinary stars. When solar-type stars die, the elements that have been built up stay there, as part of the cooling white dwarf. But when massive stars explode as supernovae, they scatter traces of heavy elements into their surroundings. Some of those atoms have become us. Biologists can trace our ancestry back to primitive protozoa, but the astronomer goes back further still. Each carbon atom in your body can be
traced back to stars that died violently before the Solar System formed. We are, quite literally, made from the ashes of long-dead stars.
Without supernovae, we would not be here. So the rules of physics that allow supernovae to exist also allow us to exist; they are part of the pattern of an-thropic cosmological coincidences. All of this, however, is a parochial view of cosmic events. Interesting though the production of heavy elements in supernovae in the Milky Way may be for our own existence (and it is doubly interesting, as we shall see, in view of the exquisite precision of those cosmic coincidences that allow just the right nuclear reactions to take place in stars), our whole Milky Way Galaxy is tiny in the perspective of the whole known Universe. A galaxy like our own may contain a hundred billion (10 11 ) stars, and millions of those stars may, for all we know, have retinues of life-bearing planets. But to a cosmologist a galaxy is simply a speck in space, regarded as a "test particle" that is useful primarily as a marker by which the cosmologist can measure the rate at which space is expanding. The redshift is, indeed, the key to measurements across the Universe; it is the cosmologist s equivalent of the geographer's theodolite.
Redshifts, Galaxies, and Quasars
Observational cosmology became possible in the 1920s, when Edwin Hubble discovered a key to the Universe. He found that for all but the closest neighbours of the Milky Way (such as the Large Magellanic Cloud, which is held in orbit around our Galaxy by gravity), the redshift of a galaxy is proportional to its distance from us. This discovery was part of a revolution in understanding the cosmos in which, for the first time, scientists realised fully that our Milky Way is just one
ordinary, fairly typical galaxy similar to millions of others, and that galaxies are the basic units making up the large-scale Universe. They are systems of stars held in equilibrium by a balance between the effect of gravity, which tends to make the stars fall together, and the countering influence of stellar motions, which, if gravity did not act, would make the system fly apart. In some galaxies, like our own, the stars move in nearly circular orbits in giant discs; in others, the less photogenic elliptical galaxies, the stars swarm about in more random fashion, each feeling the gravitational pull of all the others.
Galaxies are to astronomers what ecosystems are to biologists. They are not only dynamical units, held together by gravitation, but act as chemical units as well. The atoms we are made of come from all over our Milky Way Galaxy. They were forged in many different stars, and they may have spent a billion years or more wandering in interstellar space before finding themselves in the gas cloud that became our Solar System. But few of the atoms in our bodies come from other galaxies. Each galaxy experiences its own ongoing evolution as new stars—the "organisms" of the galactic ecosystem—continue to form from the debris of their predecessors.
The light from most galaxies is due essentially to the stars and gas they contain. Stars in other galaxies are too faint to be detected individually (except in our nearest galactic neighbours), but the light from billions of stars combines to make a fuzzy patch in the field of view of a telescope, converted into a bright image only by long exposure on an astronomical photograph. That fuzzy patch of light can be studied spectroscopically, and the positions of familiar features in its spectrum—the distinctive pattern of colours from sodium, for instance— can be determined. Even without knowing why the redshift should be proportional to a galaxy's distance
from us (a fact now known as Hubble's law), cosmolo-gists could make use of the discovery. The "law" was first established by measurements of light from relatively nearby galaxies, whose distances can be estimated by other means. For most of the fuzzy blobs they photograph, astronomers have no direct means of estimating distance. But Hubble's law is corroborated by the evidence that galaxies of the same standard type, which are presumed to have the same intrinsic brightness, appear fainter when their redshifts are larger—as they should if redshift is a measure of distance. Insofar as the law is correct, then distance is proportional to redshift. Turning Hubble's law around, astronomers are now able to estimate the distance to any galaxy whose spectrum they can take, simply by measuring its redshift. There are still uncertainties in all this. The distances to nearby galaxies are only estimated by a complex chain of arguments. Further uncertainty comes in because galaxies don't move exactly with the Hubble "flow" but also have their own "peculiar velocities" of a few hundred kilometres per second. These velocities are a substantial part of the overall velocity for the relatively nearby galaxies whose distances are independently measurable, which are the very ones used to relate redshift and distance. This relationship is consequently still uncertain by a factor of two; so some cosmologists would estimate all distances across the Universe to be twice as big as the estimates favoured by other cosmologists. Hubble's law also implies a time-scale —the time it would have taken for galaxies to move apart to their present positions, each at the constant speed indicated by their redshifts, if they started out touching one another. This time is between 10 and 20 billion years. To alleviate the uncertainty, most experts include in their equations a factor dubbed h, which is 1 if the "Hubble time" is 10 billion years and 0.5 if it is 20 billion years; that way, the numbers the
cosmologists give you can be instantly adjusted, by adjusting h, to match one's favoured value for the cosmic distance scale.
Another problem is understanding why the redshift-distance relation should hold. The standard explanation is the one we have already mentioned in passing. Light from an object that is moving fast enough away from you will be redshifted, by a process known as the Doppler effect; indeed, the same thing happens to sound waves in the air when the source of the sound waves speeds away, deepening the note of a train whistle or the siren of a police car. Similarly, an object moving towards you will produce blueshifted light, with shorter wavelengths, or a higher pitch from the same siren that sounds deeper when the car is moving away. The waves are more spaced out, or more crowded together, simply because of the motion of the object that emits them. This Doppler shift (both red and blue) is very useful throughout astronomy; it can tell us something about how stars and gas clouds are moving within our Galaxy, how other galaxies rotate, and how galaxies in a cluster move relative to one another.
There is another, equivalent way to envisage Hub-ble's law. The Universe (that is, the space between the galaxies) is expanding, and can be envisaged as carrying galaxies along with it. As light travels through expanding space, it is stretched to longer wavelengths, and longer wavelengths are those at the red end of the spectrum. In a uniformly expanding universe, the effect will be bigger for more distant galaxies, and redshift will indeed be proportional to distance.
A different way of producing a redshift is with the aid of a strong gravitational field. Light struggling out from the surface of a neutron star, for example, has to work so hard against gravity that it is redshifted. Light cannot be slowed down, but it can lose energy. As well
as having a longer wavelength than blue light, red light has less energy.
These processes are well understood. But a few people worry that there may be still other ways to produce redshifts, which we do not yet understand, and that some of our ideas about the geography of the Universe may be at fault because we have placed too much faith in Hubble's law. These concerns usually centre on the objects that include, if the Hubble's law interpretation of their redshifts is correct, the most distant and most energetic entities ever observed—the quasars.
Galaxies show up as fuzzy patches on astronomical photographs, quite different from stars, which look like pinpoints of light. But in the 1960s astronomers discovered that some of the bright pinpoints of light that they see in their telescopes and photograph with astronomical cameras have very large redshifts, comparable to those of distant galaxies. Because they look like stars but have redshifts appropriate for galaxies, these sources were called quasistellar objects, which was soon contracted to quasar. Quasars look like stars because they are very small. But if they are at the distances implied by the Hubble law interpretation of their redshifts, they must also be very bright—as bright as a galaxy that contains a thousand billion stars, in some cases far brighter. All of the energy that makes a quasar shine so brightly must be coming from a very small region, a volume of space no bigger than the distance across our Solar System. Although a quasar produces more energy than our whole Milky Way Galaxy, it would fit within the orbit of Pluto around the Sun.
Some astronomers, in the 1960s, found this too much to swallow. They suggested, instead, that the redshifts seen in quasars are not due to the stretching of space-time as the Universe expands, but are familiar Doppler shifts. On that picture, it was argued, quasars might simply be starlike objects (not quasistellar at all) that
had been shot out from the middle of a nearby galaxy at very high speeds. The argument fell down for several reasons. For example, more and more quasars were discovered, but none showed a blueshift, although surely some fragments of a nearby cosmic catastrophe would have been moving towards us. And as observing instruments have improved, astronomers have now obtained evidence that many quasars, perhaps all, are actually embedded within galaxies; they have come to realise that there is a whole range of violent activity that occurs in the centres of galaxies, with quasars just the most extreme example. In a handful of cases, beautifully precise measurements have been able to take the redshift of a quasar in the nucleus of a galaxy and, quite separately, to measure the redshift of the material of the galaxy outside the nucleus. Both redshifts are the same, and the spectrum of the light from the faint outer regions resembles that of light from the stars and gas of an ordinary galaxy. There is other evidence that supports the Hubble law for quasars, as well. On balance, the general interpretation of quasar redshifts as an effect of the expanding Universe—as cosmological redshifts—seems sound. But we should, in fairness, mention the dissenting minority who believe that the conventional "cosmological" view of quasars is as distorted and incomplete as Ptolemy's picture of the Solar System.
Most investigations into the nature of the Universe, including the main themes of this book, deal with the broad brush strokes of the cosmic picture, the general view of what is going on in the cosmos. A few cosmolo-gists, however, prefer to focus their attention on peculiarities and oddities that do not easily fit in to the broader picture. This is always the way in science. Sometimes, studies of the oddities turn out to reveal new insights that lead to a redrawing of the broad picture; more often, the oddities become incorporated
into the overall scheme as a fuller understanding develops. The particular redshift oddities that worry a few researchers deeply concern the appearance on the sky (and therefore in astronomical photographs) of objects that have different redshifts but seem to be physically connected to one another. The best examples of these peculiar connections have been photographed by Halton Arp, an American astronomer who is now based in Germany. He has obtained pictures of systems where these "discrepant" redshifts occur, in chains of galaxies and in situations where a quasar seems to lie at the end of a jet of material shot out from a galaxy.
At one extreme, a few astronomers argue that these pictures cast doubt on the whole idea of cosmological redshifts. Obviously, if two objects are physically connected then they are at the same distance from us, and should, if Hubble's law is a guide, have the same redshift. If even one redshift is "wrong," runs the argument, perhaps they all are. At the other extreme, some astronomers dismiss all of Arp's photographs as coincidences. The "bridge" seemingly joining a galaxy to a quasar with a different redshift is, they argue, always an optical illusion, and there is no problem at all. That dismissal was easy when Arp had found only one or two peculiar associations, but becomes less tenable with every new "coincidence" he turns up.
We stand somewhere in between the two extremes. Along with most astronomers who have followed Arp's work, we judge that the case for anomalous redshifts has not gained strength over the years, and has even weakened as extragalactic astronomy has advanced. Arp himself attributes this scepticism to a blinkered antipathy on the part of his colleagues towards radical new ideas. A few astronomers, especially some who have staked years of effort on research programmes based on "conventional" cosmological assumptions, might indeed be psychologically indisposed to accept
that the standard picture might be wrong. But most would surely be delighted at the prospect of uncovering fundamentally new phenomena and even "new physics." Astronomers are generally only too eager to embrace novel ideas in whose further exploration they can share. The reluctance of astronomers to devote their observing time to following Arp's lead is perhaps analogous to the reluctance of most scientists to study ESP; if such phenomena were real, there would be a colossal payoff, but the probability seems so minuscule that the most open-minded enquirer is wary of investing effort. Arp has, however, now gathered so much evidence of peculiar associations that it is hard to deny that, in some cases at least, there is more than coincidence and optical illusion at work. Something odd is going on, in some cases, but it by no means follows that conventional ideas will not be able to explain these phenomena when they are better understood. In astronomy, as in other sciences, phenomena often elude our understanding for decades, even when they eventually turn out to be fully explainable in terms of known laws. So it seems premature to throw in the sponge and invoke new physics until astronomers have thought longer and harder about these associations.
However the details may change, the broad picture seems secure—there are now thousands of quasars known, and relatively few show the peculiarities Arp is fascinated by. Dimmer quasars, by and large, have larger redshifts, which is what you would expect if large redshift implies large distance, and there is a nice gradation of activity seen in galaxies, from quiet ones like our own through various kinds of energetic outbursts right up to quasars. It is disappointing, in a way, that we are not in the midst of a revolution in our understanding of redshifts, a revolution that would be as exciting for astronomers as the revolutionary discovery by Hubble that the Universe is expanding. But we
shouldn't be greedy—after all, we are living through another revolution in our understanding of the Universe, which is the main theme of this book.
All of the debate about anomalous redshifts is, to some extent, a side issue in our present discussion. The geography of the Universe as we know it is primarily the geography of the distribution of galaxies. Even Arp does not suggest that there is any real doubt about the redshift-distance relationship as applied to most of the galaxies studied by astronomers; so whatever is happening in a few peculiar objects, we can still map out the visible region of the Universe with some confidence by measuring redshifts, and therefore distances, to large numbers of galaxies. When we do so, we find surprises as exciting and far-reaching as any of the implications of Arp's interpretations of peculiar redshifts. We find confirmation that 90 percent of the Universe is not in the form of bright stars and galaxies, and clues as to what form it is in. This unseen dark matter dominates the geography of the Universe and has set the scene for the emergence of intelligent life on at least one planet. We shall discuss its nature shortly. But first, for completeness, we should make the best use we can of measurements of quasar redshifts, since the largest of these are far larger than any measured redshift for a normal galaxy, and provide the cosmic geographer with a distant view of the edge of our Universe.
To the Edge of the Universe
Redshift is, by everyday standards, a rather peculiar measure of distance. By convention, astronomers denote the redshift of an object by the letter z (which denotes the fractional increase in the measured wavelength of light). When they map out the distances to
The Geography of the Universe
43
Figure 2.3 Escher's infinite lattice.
galaxies in various directions around the Milky Way Galaxy, the values of z they measure are usually smallish fractions—a redshift of 1 is big for a galaxy, although astronomers using new techniques in the 1990s should readily be able to identify galaxies even farther away and measure their redshifts. Hubble's law, that redshift is proportional to distance, is based on measurements of nearby galaxies. If all the rods in Escher's infinite lattice (figure 2.3) were to lengthen at the same rate, the lattice would keep its shape but would expand— space would stretch. But there is no centre. An observer at any vertex would see all other vertices receding, the recession rate being faster for the more distant ones, in accordance with Hubble's law. This is a good analogy to the expanding Universe—except, of course, that the galaxies are actually scattered in a complicated pattern of groups and clusters, rather than being equally spaced.
General relativity confirms that this is the redshift law that "ought" to be seen for nearby galaxies in a universe expanding in line with Einstein's equations. But general relativity also tells us that this is only an approximation to a more complicated rule that applies in general across the Universe. For fairly nearby galaxies, redshift is indeed closely proportional to distance. The farther out we look into space, however, the more the redshift law deviates from this simplicity. Using general relativity, we can still calculate distances to remote galaxies, and quasars, by measuring redshifts. But a redshift of 2 does not mean that a galaxy is exactly twice as far away from us as a galaxy that has a redshift of 1. Astronomers are wary of quoting distances to galaxies in terms of light-years because of the uncertainty in their estimates of the constant that appears in Hubble's law, and in the relativistic version of the law. It is better to envisage the redshift as a measure of how much the Universe has expanded—how much the wavelengths have stretched—since the epoch when the light set out on its journey towards us.
If a galaxy or quasar has redshift z, the scale of the Universe (the separation of two typical galaxies) is now (1 + z) times as large as when the light set out. So if z — 3, for example, the expansion factor is 4. How does the redshift relate to the look-back time—the time since the light set out? If the galaxies had always moved at the same speed, the answer would be straightforward: When the Universe was a quarter of its present scale (z = 3), it would have been one-quarter of its present age, and we would be looking back three-quarters of the way to the Big Bang. More generally, a redshift z would correspond to 1/(1 + z) of the present age. Moreover, the age of the Universe would simply be the Hubble time, 10//z billion years. However, there is no reason to expect that the galaxies have always moved at their present speeds; indeed, we expect a deceleration, due to
the gravitational pull of each galaxy on every other. The average speed of galaxies over their past history must have been higher than the speeds we measure today using their redshifts. This somewhat reduces our estimate of the time since the Big Bang.
The deceleration also changes the relationship between redshift and look-back time. For our favoured flat Universe, the relation is fairly simple: The age of that universe at a redshift z is not 1/(1 -I- z), but about the three-halves power of this fraction (the square root of the cube of the number). So when we look at a quasar with a redshift of 3, we see it as it was when the Universe was one-eighth of its present age (4 3/2 = 8) — when it was less than 2 billion years old (figure 2.4).
This simple calculation highlights a fundamental cosmic puzzle: How could the Universe have been so smooth and uniform long ago? When the Universe was one-quarter of its present size, it was only one-eighth of its present age. So there had been proportionately less time available for any influence, which can never travel faster than light, to spread across the Universe. Regions that cannot "communicate" with each other cannot come into synchrony, so why are different parts of the Universe so similar to one another? The closer we probe back towards the Big Bang, the worse this problem becomes— as a fraction of the time light takes to cross the Universe, there is less and less time available for the different parts of the Universe to interact with one another. This causality problem, highlighted in figure 2.4, arises because gravity decelerates the cosmic expansion. The inflation hypothesis, which we shall discuss later, postulates an early stage of rapidly accelerating expansion, and offers an explanation of why the Universe was very uniform even in the earliest stages of the Big Bang.
As we look farther out across the Universe we are also, of course, looking back in time, seeing the Universe as it was when the light we see left those galaxies.
COSMIC COINCIDENCES
TIME
SEPARATION PROPORTIONAL TO (TIME) 273
Figure 2.4 Communication between different parts of the Universe was more difficult at earlier times. Consider, for instance, a galaxy whose distance from us is X A of the Hubble radius. We can now exchange light signals 4 times during the expansion timescale of the Universe. However, when the Universe was X A its present size (redshift z=3) it was Vfe its present age; therefore, even though this galaxy was then 4 times closer, there would have been time for only 2 signals to be exchanged. Extension of this line of argument implies that no two galaxies (or protogalaxies) would have been in causal contact at very early times. It is therefore a mystery why the Universe started its expansion in such a uniform and apparently well-synchronised fashion. In this example, the time since the Big Bang is actually only % of the Hubble time, because expansion was faster in the past.
But the redshift imposes a kind of barrier between us and the Big Bang itself. Each doubling of the measured redshift does not double the measured distance, either in terms of space or of time. Instead, the farther away you look—the farther back in time—the bigger the step in redshift you need to cover a chosen distance. An imperfect, but helpful, analogy is with a climber who tackles a high mountain. At first it is easy to make progress, and for a small effort the climber gains a lot of height. As the mountaineer gets higher and the route gets steeper, however, that same amount of effort brings
The Geography of the Universe
47
Figure 2.5 Because of the finite speed of light, we observe remote regions as they were at early epochs when everything was closely packed together. The Universe as we actually see it resembles this Escher picture: Objects seem more and more crowded together towards our observational "horizon."
ever-diminishing returns. In the case of the Universe, the Big Bang itself, the moment of creation, is at infinite redshift, and can never be seen directly. It is as if you can always get a little bit farther up the mountain, if you try hard enough; but to get to the very top requires infinite effort.
Quasars have now been found with redshifts of about 4.5, and in round terms this means that we are looking
back across more than 90 percent of the history of the Universe, to a time only about a billion years after the Big Bang. Increasing the redshift record to z = 10 would push us back to when the Universe was 3 percent of its present age. We don't know whether galaxies had formed by then; because of the time required for galaxies to form after the Big Bang, we may already be close to "seeing" the practicable "edge of the Universe," an "edge" that has the rather peculiar property that it corresponds to a time when the Universe was smaller, and more densely packed, than it is in our neighbourhood today.
This "edge" doesn't imply in any sense that we are in the middle of the Universe. A better analogy is with a sailor who seems, from the deck of a ship, to be surrounded by a circle of ocean with a distinct edge, the horizon; if the sailor climbs the mast of the ship, the extra height will give a view of a bigger circle of ocean. The new horizon still looks like an "edge," even if the ocean is boundless.
Cosmologists, in fact, turn the redshift relation around and use it, for high values of z, as a convenient means of labelling the sequence of events in their mathematical models (based on general relativity) of how a universe like ours may have evolved out of the Big Bang. They talk of events that happen at a redshift of 1,000 or 100, or whatever the figure might be, instead of speaking of the time in years after the moment of creation. This is a convenient shorthand, but it does not mean that any astronomer has ever measured a redshift that big, or that there is any hope that such a cosmological redshift could ever be observed—except for the special case of the background radiation that fills the whole of the Universe. This is interpreted as the light of the white-hot Universe, a few hundred thousand years after the Big Bang itself, redshifted so much that it now shows up as a feeble hiss of energy in the microwave part of
Figure 2.6 This diagram illustrates various "redshift shells" around us. The microwave background comes from the "cosmic photosphere" at z = 1,000, corresponding to an epoch when the Universe was about a million years old. The most distant quasars emitted the light now reaching us when the Universe was about a billion (10 9 ) years old. We know very little about the era of cosmic history between 10 6 and 10 9 years.
the electromagnetic spectrum. This corresponds to a redshift of about 1,000. Nothing has been detected from the part of cosmic history corresponding to the gulf between z = 1,000 and z = 5, covering about 6 percent of the history of the Universe. Somewhere in that region, the processes that led to the formation of galaxies took place. Lacking any direct observations of those processes at work, we have to work out how galaxies formed by looking at the way they are distributed in the Universe today. Which brings us back from the edge of the Universe to the geography of our own cosmic neighbourhood.
The Bright Stuff
We live in a galaxy. Galaxies contain stars, and stars are made of baryons—the same sort of stuff, to a physicist, as our own bodies are made of. Galaxies, the visible, bright stuff of the Universe, are also the basic units we use to study the geography of the Universe, but not all galaxies are the same. Differences between various kinds of galaxies may provide important clues to the way in which galaxies formed, long ago when the Universe was young, and may help us to estimate how reliable the distribution of galaxies is as a guide to the distribution of all the matter in the Universe, including the dark matter. If galaxies had not formed, we would not be here. Understanding galaxies is one of the keys to understanding our existence.
Our Milky Way is a disc galaxy. Disc galaxies are also known as spirals, because the pattern of bright stars in such a galaxy often forms a prominent spiral*; however, not all disc galaxies show pronounced "spiral arms," so we prefer the term disc. In addition to the disc itself, such a galaxy has two other distinct components—a central bulge of stars around the nucleus, giving the galaxy something of the appearance of a fried egg, and a halo of old stars surrounding both the disc and the bulge in a huge, roughly spherical distribution. Some of the stars in the halo are grouped together in spherical, or globular, clusters, aggregations of stars that move together through space as a unit. A globular cluster may contain up to a million stars held together by gravity within a radius of 100 light-years;
*The pattern is produced by waves moving through the galaxy; each star follows a nearly circular orbit around the centre of the galaxy, and does not move along a spiral "arm." This is rather like the way a pattern of waves moves across the surface of the sea, even though each molecule of water is bobbing up and down as the wave passes, not moving forward with it.
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Figure 2.7 Schematic "edge on" view of a disc galaxy like our own Milky Way, showing its three main components: central bulge, disc, and halo.
but there are only about 200 globular clusters in the Milky Way Galaxy. Halo stars are a small fraction of the hundred billion stars that make up a disc galaxy.
Measurements of the way disc galaxies rotate, using the ubiquitous redshift (the straightforward Doppler version, this time) also reveal that there must be a great deal of dark matter in the halo of such a galaxy, holding the bright matter of the disc in place and stabilising the rotation (see chapter 5).
The disc of such a galaxy really is thin, compared with its diameter. In the case of our own Galaxy, for example, it forms the band of light across the sky that gives the Milky Way its name, and it is less than 1,000 light-years thick in the region of our Solar System, which is about 28,000 light-years out from the centre of
the Galaxy, two-thirds of the way to the edge of the bright disc. These are fairly typical measurements. Old stars, called Population II, occur mainly in the halo and the nuclear bulge, which extends out about halfway to the position of the Solar System. Younger stars, which have formed out of clouds laced with the debris of former supernovae, lie mainly in the disc. Most of the bright stars in a galaxy like our own are young stars, called Population I.
By measuring the speeds with which other galaxies close to our own, in what is called the Local Group of galaxies, are moving, astronomers can calculate how much mass our Galaxy must have in order for its gravitational influence to explain those movements. (Some of these galaxies are moving away from us; others, such as the Andromeda Galaxy, are moving towards us.) The minimum amount of mass in our Galaxy, estimated in this way, is about a thousand billion times the mass of the Sun. Since, in round terms, the Galaxy contains a hundred billion stars and the average mass of a star is close to the mass of our Sun, that means that there is at least ten times more dark matter in the Galaxy than there is in the form of bright stars. This figure Is typical of estimates for other disc galaxies—by and large, such galaxies contain ten times more dark matter than bright.
The other main type of galaxy is the elliptical. These come in a variety of shapes and sizes. Some are spherical, like an enormous globular cluster; some are elongated, like a football or a cigar; many are oblate, like a slightly squashed sphere. They are all made up almost entirely of old stars, and in many ways they look like the nucleus and halo of a disc galaxy, without the disc. Some "dwarf" elliptical galaxies are very small compared to our Galaxy. At the other extreme, the so-called "CDs" are the largest galaxies known, with their stars stretching out across more than 300,000 light-years from the centre. Such a galaxy may contain up to a hundred
times as many stars as our own Galaxy. Dwarf ellipticals, however, may be the most common galaxies in the Universe; or that honour may go to another kind of small galaxy, called dwarf irregulars since they come in all kinds of irregular shapes.
Getting ahead of our story slightly, it seems that galaxies must have formed from clouds of gas, chiefly hydrogen and helium produced in the Big Bang, which were held together both by their own gravity and by the gravity of clouds of dark matter in which they were embedded. The dark matter produced a kind of gravitational pothole, or potential well, into which the gas settled and became dense enough to collapse under its own gravity, and condense into stars. Without the gravitational influence of the dark matter, a galaxy like the Milky Way, with its stars and star systems, might never have formed. The key question, which we shall address shortly, is how the initial irregularities, the gravitational potholes, formed in a universe expanding smoothly away from the Big Bang.
The distribution of galaxies in the Universe today is by no means perfectly smooth. More than half of all known galaxies occur in groups. Small groups, which might contain ten or twenty galaxies held together by gravity, are called just that—"groups." Larger groups, which contain hundreds or thousands of galaxies that lie in the same part of the Universe, are called clusters. A group of galaxies within a cluster is rather like a single island in an archipelago. Some clusters are regular in shape, spread over spherical volumes of space with more galaxies in the centre of the cluster and relatively few farther out; others have a more lumpy appearance, and usually these irregular clusters contain a higher proportion of disc galaxies.
Clusters themselves congregate together in superclus-ters. For example, the Local Group of galaxies, of which our Milky Way is a member, is part of the Local Super-
COSMIC COINCIDENCES
Figure 2.8 This diagram (courtesy of Ofer Lahav) shows the more luminous galaxies in the northern sky out to a distance of 50-100 megaparsecs. Three well-known clusters are marked; the complex and "filamentary" character of the galaxy distribution is evident from this picture.
cluster, a straggling collection of thousands of galaxies that seems to be centred on the Virgo cluster. The Virgo cluster is named after the constellation in which it is seen in the sky—a common astronomical practice. But this group of galaxies is, the redshift test shows us, actually far beyond the constellation Virgo (which is simply a pattern formed by stars within our Milky Way Galaxy), at a distance of about 50/h million light-years from our Galaxy. Its appearance "in" Virgo is a chance alignment of two objects on the sky, rather as we might see a high-flying aircraft passing behind the branches
of a tree under which we are sitting, so that it looks like a toy airplane "in" the tree.
Mapping out superclusters of galaxies is a time-consuming process that involves measuring thousands of redshifts. This is a task that has only recently proved practicable; it has shown that there are other super-clusters and that, like the Local Supercluster, they tend to form sheets across the Universe, with most of the galaxies in a supercluster lying in more or less the same plane. Some superclusters show up as long filaments, chains of galaxies stretching across millions of light-years of space. The counterparts to these great superclusters are great voids, regions of space perhaps 200/h million light-years across, which seem to contain very few bright disc or elliptical galaxies at all, although they may contain dwarf galaxies. The archetypical "void" lies in the constellation Bootes (that is, it lies in the same direction but far beyond Bootes). On one side of the void there is a huge supercluster, the Hercules supercluster; on the other side lies the Corona Borealis supercluster; in between, apparently nothing.
Even superclusters may not be the end of the story. Brent Tully, of the University of Hawaii, was one of the astronomers who first mapped out the extent of the Local Supercluster. This is roughly 100 million light-years across, if h = 0.5. In 1987, Tully presented evidence that the whole supercluster may be physically associated with other superclusters, forming a structure he calls the "Pisces-Cetus complex," stretching for more than a billion light-years across the Universe. The whole "complex" lies in a flat plane, and this is the same flat plane that the galaxies of the Local Super-cluster lie in. As yet, both observers and theorists are sceptical about Tully's claims. The Pisces-Cetus complex may be no more than a random pattern of galaxies and clusters in space—after all, the clusters have to be somewhere. The occurrence of super clusters and voids is,
however, now beyond question. They represent the largest structures definitely identified in the Universe, geography on the grand scale. But on still larger scales—the largest observable scales—things do smooth out. Counts of the numbers of very high redshift galaxies seen in different parts of the sky show that the Universe is uniform on the grandest scale of all. Theorists seeking to explain how galaxies come to be here at all not only have to explain how individual galaxies form in those gravitational potholes, but why galaxies congregate in sheets and filaments in this way, with dark voids in between. One of the key puzzles is whether the dark matter in the Universe is distributed in the same way as the superclusters, so that the voids really are empty, or whether galaxies containing bright stars form only in special places, so that the voids may contain plenty of dark matter even if they contain few bright galaxies. The weight of evidence today is that bright galaxies are not good "tracers" of the way mass is distributed across the Universe, and that the Universe is a much smoother place than the pattern of galaxies on the sky would suggest.
A Background of Smoothness
Radio telescopes operating in the microwave band, sensitive to electromagnetic radiation with wavelengths of a few centimetres or less, detect a faint hiss of radio noise coming from all directions in space. This is the famous cosmic background radiation; even intergalac-tic space is not completely cold, but is filled with the dilute remnant, or "echo," of the hot radiation from the early phases of cosmic expansion. For the first few minutes, the temperature of this radiation exceeded a billion Kelvin (10 9 K)—hot enough for rapid nuclear
reactions to occur. Such conditions can be described by equations tried and tested in the present-day Universe— they are used to calculate the workings of stars and of nuclear bombs. For the first microsecond, temperatures and energies were so high that we have less confidence in our understanding of the applicable physics. Throughout its first 10,000 years, the Universe must have been an opaque fireball. Then, the conditions everywhere resembled those in the centre of the Sun today. The radiation that radio astronomers detect as the cosmic background has propagated freely from the slightly later epoch when the whole Universe had cooled roughly to the temperature of the surface of the Sun today, a few thousand degrees Celsius. Until that time, the entire expanding Universe was still so hot that any electron that attached itself to a positively charged nucleus, such as a proton, would promptly have been knocked off again.
But at a critical moment in the evolution of the Universe, about half a million years after the moment of creation (or, looking back from our present perspective, at a redshift of about 1,000), the Universe cooled to the point where atoms could form and stay formed. From that moment on, essentially all of the electrically charged particles in the Universe, the electrons and protons, were locked up in stable, electrically neutral atoms. Because electromagnetic radiation cannot interact directly with neutral particles, but only with particles that carry electrical charge, from that moment on matter and radiation went their separate ways, and had very little more to do with each other. They "decoupled," and ever since that radiation has been cooling as the expansion of the Universe has redshifted its waves. Now, it is at a temperature of-270 degrees C, or 3 K—but it still pervades all of space; it fills the Universe and has nowhere else to go.
The exact temperature of the cosmic background radiation (actually a fraction less than 3 K) tells cosmolo-
gists about conditions in the early Universe and bears out the validity of calculations of the Big Bang based on general relativity. From our present point of view, however, what matters is not the precise temperature of this radiation but the fact that this temperature is exactly the same in all directions. Because the radiation has not interacted with matter since the time corresponding to z = 1,000, this tells us that the Universe was extremely smooth and uniform half a million years after the Big Bang. At that time, just before electrons and protons fused into atoms, they were still strongly coupled to the radiation that filled the Universe. So these measurements of the background radiation also tell us that the distribution of baryons at the time of decoupling was extremely smooth and uniform.
The most accurate measurements of the uniformity of the microwave background involve comparing the temperature of the radiation coming from different parts of the sky to an accuracy better than a thousandth of a degree. They show that patches of the sky that are each a few minutes of arc across (the angular size, viewed from Earth, of a protocluster of galaxies at redshift z = 1,000) all have the same temperature to within 1 part in 20,000. When the Universe was compressed by a factor 1,000 in linear dimensions, its average density was a billion times greater than it is now—far higher than the present-day average density even within a galaxy. Galaxies could not, therefore, have then existed as separate entities and it should not surprise us that the Universe was less "structured" at early times. But it is still surprising that we detect no hints of any irregularities over the sky due to "embryo" galaxies and clusters, which must already have been present at that stage. The question then arises of how quickly the structure can emerge from amorphous beginnings—are the conspicuous galaxies and clusters we now see around us compatible with such a smooth fireball?
Galaxies and clusters could condense from much less extreme initial fluctuations. A region that started off slightly denser than average, or expanding slightly slower than average, would lag further and further behind the rest of the Universe (so the contrast between the density inside the region and the density outside would steadily increase) until its expansion eventually halted and it formed a system held together by its own gravity. The density contrast grows in proportion to the scale of the Universe, and no faster. So any object, such as a cluster of galaxies, that has now stopped expanding must have been "overdense" by at least 1 part in 1,000 at z = 1,000. Since individual galaxies probably formed at a redshift of 5, the overdensity of an embryonic galaxy at z = 1,000 must already have been 1 part in 200. If the Universe was as uniform as the isotropy of the background radiation implies at a redshift of 1,000, but contained only the matter we can see today in the form of bright galaxies, irregularities as large as the superclusters we see today could never have grown as big as they are now.
This dilemma can be eased if there is dark matter in the Universe, in either of two ways. First, there might be a lot more matter filling in the gaps between the visible clusters and superclusters, distributed more smoothly than the distribution of galaxies, so that the density contrast today between a cluster of galaxies and a dark void is smaller than it seems. Some of this dark matter could be ordinary atoms—baryonic matter— like the stuff stars are made of. The second alternative is that the dark matter could have been distributed less smoothly than the baryons at z = 1,000. That is possible only if it is not baryonic matter and carries no electrical charge. Before that time, the Universe was dominated by radiation, and this sea of radiant energy would have prevented baryons from clumping together. Electrically neutral dark matter that did not interact
COSMIC COINCIDENCES
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Figure 2.9 This graph shows how the density contrast of perturbations grows during the expansion of a "flat" Universe. If pressure forces can be neglected, the growth factor is proportional to the expansion and amounts to 1,000 since the epoch when baryons decoupled from the radiation. Radiation pressure prevents baryonic fluctuations from growing before that time; fluctuations in "cold dark matter" (CDM), however, are not inhibited in this way. The CDM therefore has a head start, and can create potential wells into which the baryons condense after decoupling. If the Universe is dominated by CDM, we can more readily reconcile the present "lumpiness" of the Universe with the apparently smooth baryon distribution at decoupling indicated by the microwave background isotropy.
with radiation, however, could have begun the segregation process and already produced regions of overdensity by the time of decoupling at z = 1,000. Such regions would not show up in the background radiation but would give the baryons a head start on the road to galaxy formation once they had formed neutral atoms and were no longer influenced by the radiation.
Either way, the background radiation is telling us that galaxies, and ourselves, could not have evolved without the help of dark matter. The dark matter would pervade the voids between the superclusters, even though
the bright galaxies, the tip of the iceberg, only highlight unusual regions of space. The reasons for that highlighting—why bright galaxies should not be accurate tracers of the overall mass distribution—are at present a subject of debate among astronomers.
Blowing Bubbles?
Exactly how galaxies formed is still a mystery. Theorists can compute how structures might have emerged from an amorphous cosmic fireball. But so far we just have simple "scenarios," based on different assumptions about the dark matter and the initial irregularities.
Some scenarios are as ephemeral as soap bubbles, soon burst by the sharp prick of new observations. Sometimes, progress is made by combining the best features of several scenarios into a new model. But the most powerful insights come when different scenarios based on different assumptions, all point to the same requirement. One key feature of galaxy-formation see narios based on up-to-date observations of the Universt is that they all use the simple laws of physics that hav< been developed from experiment and observation hen on Earth. There is no evidence that any "new" laws are needed in order to explain how things came to be as they are. But it does seem clear that there is more to the Universe than the bright stars and galaxies.
Copernicus dethroned the Earth from a central position in the Universe; the cosmologists of the 1920s and 1930s demoted us from any privileged location in space, and taught us that the Milky Way Galaxy is simply an ordinary collection of stars located in an ordinary, typical region of the Universe. But now even "particle chauvinism" may have to be abandoned. The protons, neutrons, and electrons of which we and the entire astronomical world are made could be a kind of afterthought in a
universe where totally different kinds of particles control the overall dynamics. Any hopes of quick progress towards understanding the stuff of the Universe may be quenched when we note that according to different scenarios (discussed later) 90 percent of the Universe is in the form of entities whose individual masses may range from 10~ 32 grams to 10 39 grams—an "uncertainty" of more than 70 powers of 10. (Astrophysics may not always be an exact science, but seldom is the uncertainty as gross as this!) The uncertainty, however, lies in the choice between different scenarios, not within the scenarios themselves. By narrowing down our choice of options, we can still paint our pictures of how the Universe might have got to be the way it is, and search for the underlying deep truths and cosmic coincidences that link so many of the scenarios together.
CHAPTER THREE
Two Kinds of Dark Matter
THE SIZES OF STARS, planets, and people are, as we saw in chapter 1, inevitable consequences of the relative strengths of the basic forces and constants of nature. Can galaxies and clusters of galaxies, the tracers by which we study the geography of the Universe, fit into the same basic scheme? One piece of evidence that suggests that some kind of cosmic rule must govern the size of galaxies, as well as the size of ourselves, is provided when we plot a graph showing how the mass of each kind of known object is related to its size. Figure 3.1 makes the point.
If there were no simple rule governing the sizes of things, then the points on this graph would be scattered all over the place. The fact that they are not reveals order in the Universe, and the nature of the regular distribution of the points, more or less along a straight line, gives a clue to what that order is.
First, there are two "forbidden zones" on the left of the diagram. To the upper left, there is a region corresponding to black holes, objects that have either a very large mass or a very large density, or both. The gravitational field of a black hole is so strong that nothing, not
COSMIC COINCIDENCES
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20
Figure 3.1 The characteristic masses and radii of various objects—from atoms to the entire Universe—plotted on a single diagram (on a logarithmic scale).
even light, can escape from it—so it is no surprise that we cannot see any objects in the Universe with sizes and masses corresponding to this part of the diagram. What is very interesting, and surely significant, is that the Universe itself sits just on the dividing line between this forbidden zone and the region occupied by stars, planets, galaxies, and ourselves (this is another manifestation of the flatness of the Universe). The whole Universe could, indeed, resemble a gigantic black hole, with spacetime bent around on itself. The other forbidden zone is a little harder to under-
stand in terms of everyday concepts. It corresponds to things that are very light, or very small, or both—at the bottom left of the diagram. Quantum physics tells us that such objects do not have a "real" existence in the everyday sense. While it (just) makes some sort of sense to think of an object such as a proton or an atom as a kind of tiny billiard ball with a definite identity as a particle, objects that are even smaller or lighter, such as electrons, are described not simply as particles but as waves as well. There is no absolute certainty about the location of an object that small and light, and the concept of size becomes diffuse. So the range of sizes of all known things lies in a relatively narrow band from the proton, on the edge of the quantum zone, to the Universe, on the edge of the black hole zone.
The boundaries of the two forbidden zones meet at the point corresponding to masses of about 10 -5 grams and distances of 10~ 33 centimetres. This is where gravity and quantum effects both become important, but those conditions are very different from any conditions around today. This is why physicists can get by without having a synthesis of gravity and quantum theory in one complete mathematical package, and yet still come up with a good description of the way things behave in the Universe. Either gravity or quantum effects may be important for different objects in the Universe today, but never the two together. There has been no overlap between the gravity and quantum zones, except in the Big Bang.
Sizing Up Galaxies
We have already looked at the way a balance between electrical and gravitational forces keeps planets, stars, and ourselves on this line. But what are the balances— the cosmic coincidences—that restrict galaxies and
clusters to well-defined parts of the diagram? The restrictions are not so clear-cut as they are for stars or ourselves, but there is a clear hint that even on the greatest scale the sizes of things are determined by the same basic laws of physics.
For the moment, we will ignore the dark matter that makes up 90 percent of the mass of the Universe, and puzzle only over the bright galaxies. Galaxies formed from huge clouds of gas, held together by gravity, which fragmented into stars. The type of galaxy that emerged (disc or elliptical) depends on details of the process— and, in particular, on how rapidly and efficiently stars formed while the protogalaxy was contracting. Even though there are many varieties of galaxy, there is no problem in identifying rough typical dimensions: around 10 11 (a hundred billion) stars in a radius of 10 kilopar-secs (30,000 light-years). Is there a straightforward reason why the large-scale cosmic scene should be dominated by entities with this characteristic size and mass, just as there are physical reasons for the natural scale of stars? One suggestive physical argument has been taken seriously in the past few years and could offer a partial answer.
Imagine a collection of gas spheres, each held together by its own gravity. Such a sphere could be in equilibrium if it were hot enough for pressure to balance self-gravitation. The required temperature depends on just the mass and radius of each sphere (in fact, on mass divided by radius; this is a version of the two-thirds-power law mentioned in chapter 1) and is easy to work out. Any hot gas loses energy by radiating it away into its surroundings; the radiation rate, which depends on how hot and dense the gas is, is also easy to calculate. If a cloud radiates slowly, it will gradually deflate but stay in equilibrium as a single homogenous mass. On the other hand, if the cooling proceeds too fast, the cloud cannot retain its pressure support. It
would then collapse in a free fall and fragment into smaller pieces. Any protogalaxy in which stars can form must be in this second, "fast cooling," regime.
It isn't difficult to calculate the demarcation between the two regimes and discover which masses and sizes of clouds could fragment. This depends on basic physical constants—the strength of gravity and the atomic constants that control how much radiation a hot gas emits. It turns out that fragmentation occurs for any clouds less massive than 10 12 times the mass of our Sun and with radii below 75 kiloparsecs—but not for heavier and larger clouds. These critical dimensions (which few physicists would have guessed beforehand, even to within a factor of a million) are similar to those of the biggest galaxies. The "cooling versus collapse" argument plays a role in most detailed cosmogenic schemes; it offers a convincing explanation of why galaxies cannot be even bigger than they are.
One amusing result of this—not really a coincidence, since it depends on simple rules of physics—relates to the geometric means of the sizes of important features of our Universe. The geometric mean is obtained by multiplying the lengths of two things (or their diameters) together and taking the square root of the product; it is a more useful way of averaging things with very different sizes than the arithmetic mean we use in everyday life. The size of a human being is the geometric mean of the size of a planet and the size of an atom; the size of a planet is the geometric mean of the size of an atom and the size of the Universe. Both, like the sizes of galaxies, are a result of the balance between gravitational and electrical forces.
It is, however, unreasonable to expect that galaxies can be explained as straightforwardly as stars. After all, we can see stars forming now, close at hand in the Milky Way. Galaxies formed during a remote cosmic epoch. Any understanding of galaxies must entail plac-
ing them in a cosmological context; physical processes can perhaps select the appropriate range of masses and radii, but only if the cosmologists can give us a variety of protogalactic clouds in the first place.
The Universal "thermal soup" of the Big Bang started off almost featureless, but not quite. There must have been (we don't know why) small initial fluctuations from place to place in the expansion rate or the density. Structures would then have emerged, as overdense regions lagged more and more behind the Universal expansion, and eventually halted and formed systems bound together by gravity.
Theorists trace the history of the Big Bang right back to the so-called Planck time (10 -43 seconds), smaller by about 60 powers of 10 (60 "decades") than the Universe's present age. Many key features of the Universe, including the initial fluctuations, were imprinted during the very early stages. Because the physics of the ultracompressed, high-density stages is speculative, we have no firm understanding of exactly where the fluctuations came from. This is related to the problem of why, on the largest scales, the Universe is so uniform and flat. We shall return to this issue later, but for the moment it must be regarded as a coincidence that the initial fluctuations were adequate to initiate galaxy formation, without being so large that the Universe ended up in a chaotic mess.
Physicists have identified various phases in the expanding Universe where crucial processes, or transitions, would have occurred. Without engaging in technicalities, we can divide cosmic history into three parts. For the first 10" 4 seconds (the first 40 "decades" of logarithmic time) everything was squeezed to supernuclear densities, and particles had such high energies that the relevant physics is not merely unfamiliar but in some regards completely unknown (or, at best, controversial). After this time, the microphysics becomes less
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exotic—less remote from conditions created in laboratories on Earth. During this era after 10" 4 seconds, nuclear reactions would have occurred. The rates at which these reactions took place, and the abundances of the elements produced in those reactions, depend on how densely packed the baryons were when the temperature was 10 9 -10 10 K. Since we know the present temperature of the Universe (2.7 K), we can relate the element abundances to the present-day density of baryons in the Universe. Confidence in the Big Bang theory was boosted by the gratifying agreement between the observed abundances of helium and deuterium in stars and these theoretical predictions. Indeed, cosmologists use these calculations to infer the density of baryons from the measured element abundances; the evidence about the first few minutes of the Universe, provided by these relic chemical elements, is no less firm than some of the inferences geologists and paleontologists make about the early history of Earth.
The second, and "theoretically easy," era of cosmic history continues until the overdense regions, which have become even more distinct from their surroundings because gravity gives them an above-average deceleration, start to condense out and collapse. After this stage, discrete objects would exist, and astronomers could in principle observe them. But theorists are then faced with a new set of difficulties. The essential physics is just Newtonian gravity and gas dynamics; but the complications are those of "nonlinearity," and the phenomena become hard to understand for the same reasons as, for example, weather prediction is difficult— each little bit of the system obeys simple physical laws, but vast numbers of little bits interact with one another in complex ways.
A key cosmogenic question is: How much of galaxy formation can, even in principle, be explained by processes occurring at the relatively recent epochs accessi-
TOP DOWN:
CLUSTER-MASS
CLOUDS fragmentation
GALAXIES
BOTTOM UP:
SUB-GALACTIC CLUSTERS
► GALAXIES ►
MASSES hierarchical hierarchical OF GALAXIES
clustering clustering
Figure 3.3 The contrast between a "bottom up" cosmogenic scheme, where small systems condense first and then cluster hierarchically, and a "top down" scheme, where the first systems to condense have the mass of an entire cluster of galaxies and subsequently fragment. A Universe dominated by cold dark matter (CDM) exemplifies the first option. If, however, hot dark matter (e.g., fast-moving neutrinos) were dynamically dominant, then fluctuations on all scales smaller than a cluster of galaxies would be homogenised, and galaxies would form after clusters.
ble to observation, and how much has to be attributed to features imprinted at earlier times? There is no obvious feature of the early Universe that would "know" the scale of galaxies in advance, so we would expect the initial fluctuations to have a smooth "spectrum," with all kinds of variations on many different scales. If all the fluctuations, on all scales, grew by gravitational amplification as the Universe expanded, the relative amplitudes of fluctuations on different scales would stay the same, just as set up by the initial conditions. But there are other processes at work, connected with pressure forces and the random diffusion of particles, which can selectively damp down some fluctuations and amplify others; these are also fairly straightforward to analyse during the "theoretically easy" era, when the amplitudes are still small. Although the Universe as a whole expands, overdense irregularities expand more slowly, and eventually reach a maximum size before beginning to fall back upon themselves as their own
gravity overcomes the expansion of the Universe. In a so-called bottom-up scenario, objects like dwarf galaxies and globular clusters formed first and the pieces were then grouped together by gravity to make galaxies and clusters. In the alternative top-down scenario, clusters or superclusters formed first and then fragmented. Neither picture gives a perfect description of the real Universe, but each provides insights into how things got to be the way they are. When we try to paint a slightly more realistic picture of the Universe, however, we find that the existence of galaxies is intimately connected with the presence of dark matter.
A Biased View
The distribution of galaxies across the sky is just about the only piece of evidence we have about the geography of the Universe at large. The total amount of mass associated with galaxies can best be estimated by studying the distribution and motion of bright galaxies in clusters. Studies of the spectra of these galaxies show, by the Doppler effect, how they are moving. Knowing how fast the galaxies in a cluster are moving relative to one another, we can estimate the total mass needed to stop the cluster from flying apart and make it gravita-tionally bound. Such studies corroborate the evidence from studies of individual galaxies: there is about ten times as much matter in some dark form as in the stars and gas we see. But the average smoothed-out density of all this dynamically inferred matter is still no more than 10 to 20 percent of the "critical" density needed to make the Universe flat. Curiously, detailed calculations of element production during the Big Bang also say that the density of baryons (protons plus neutrons) in the fireball is no more than 20 percent of what would be required for the Universe to be flat. This may
Two Kinds of Dark Matter
73
. • • • • r mi m^> • •
Figure 3.4 The random motions of the galaxies in a cluster can be inferred from the Doppler effect. To stop the cluster from flying apart, it must contain ten times as much dark matter as trie aggregate mass observed in all its constituent galaxies.
be a genuine coincidence, not one of the cosmic coincidences we are interested in, and one that misled cos-mologists for twenty years into accepting that baryons (some in bright galaxies but 90 percent in some dark form) constitute all the matter there is in the Universe. Most cosmologists now rate the theoretical case for a flat Universe as quite compelling, however, and the only other piece of evidence we have, the uniformity of the background radiation, supports that view. Motivated as much by theoretical prejudice as by observational evidence, they have become sceptical as to whether bright galaxies really do tell the whole story about the way matter is distributed in the Universe. Big "voids" in the distribution of bright galaxies are
now known to be quite common. Within voids, bright galaxies are at least ten times more sparsely distributed than across the Universe at large. One way of trying to understand how such features can emerge in the real Universe is with the aid of computer simulations. Starting out with a distribution of galaxies, long ago, that matches the requirements of the measurements of the background radiation, the computer models are allowed to "evolve" with the points representing galaxies clumping together under the influence of their mutual gravitational attraction, while the clumps themselves drift apart as the model universe expands. Such simulations show that it is impossible to evacuate the voids as completely as the voids in the real Universe. If the Universe contains exactly enough matter to make it flat, and this is all distributed initially in the same way as bright galaxies are, no void can have less than 25 percent of the average density today. If the Universe contains less mass, it is even harder to evacuate the voids. Mass must "hide" in the voids to escape detection, while bright galaxies provide a biased view of the Universe.
There is no rule of nature that says all of the dark matter must be the same stuff, and it would be surprising if it were. But the simplest way to begin to understand what the dark matter might be is to sketch out scenarios that are each based on the assumption that only one kind dominates. The key point is that the dark matter that dominates the dynamics of a flat universe cannot be the kind of matter (baryonic matter) found in stars, planets, and ourselves, since the maximum amount that could have emerged from the Big Bang, if our ideas on element production are correct, falls short of what is needed by at least a factor of 5. If there is indeed only one important kind of dark matter, the flatness of the Universe tells us that it is less clumped than galaxies, that voids are not as empty as they look.
There are two principal ways in which this could have come about.
First, the baryons themselves could be segregated from the dominant dark matter, all the baryons being in the bright galaxies that form the sheets and filaments we can see, while most of the dark matter is in the voids. Alternatively, the baryons and the dark matter may be similarly distributed in the Universe at large so that the two forms of matter intermingle even in the voids. We would then see bright galaxies distributed in bubbles and filaments around those voids because some special conditions are needed to trigger the creation of clusters of bright galaxies, and those special conditions simply do not occur everywhere. Baryons may be present in the voids, but they have failed to light up and display their presence to us.
One specific possibility, the front-runner among such theories today, is that bright galaxies formed only in regions of space where the density of the matter in the Universe was exceptionally high. You can think of this in terms of waves on the ocean, or the high peaks of a mountain range. Only the highest wave crests, or tallest mountain peaks, represent galaxies; the troughs of the waves, and the valleys of the mountain range, represent the dark voids, which still contain an enormous amount of matter (water or rock, depending on which image you prefer). If the density of the Universe varies from place to place in a random manner, with minor fluctuations occurring within larger fluctuations (like waves on top of a long ocean swell), this would provide a very natural way to produce clusters and superclus-ters of galaxies, with voids in between. In a region where a large fluctuation (a swell) has increased the density already, places where there is a small extra fluctuation (a wave) that increases density a little more will form galaxies. In a region where there is a correspondingly large reduction in average density (the trough
PROTOGALAXIES THRESHOLD
AVERAGE DENSITY
PROTOCLUSTER PROTOVOID
Figure 3.5 If galaxies form only from exceptionally high peaks in the initial density distribution, they will be strongly concentrated in the crests rather than the troughs of long-wave perturbations. They will therefore form more readily in incipient clusters and be deficient in incipient voids. The galaxies will consequently be more "clumpy" than the overall distribution of mass.
of the swell), small-scale fluctuations (waves) that increase density a little can never become dense enough to form galaxies.
Furthermore, once bright galaxies do form in a developing cluster or supercluster, their very presence may trigger the formation of more galaxies in the high-density region in which they are embedded. If galaxy formation spread like an epidemic, galaxies would naturally end up in clusters, and large regions (the voids) might escape "infection" completely.
Rather than this "biasing" being some kind of desperate last resort by theorists trying to reconcile the geography of the Universe indicated by studies of bright galaxies with the requirement that the Universe is flat, it would be astonishing if no such effects were at work; indeed, several different biasing processes might each have played a role when the Universe was young, producing a cumulative effect. The notion that galaxies trace mass is an unjustified assumption, and finding the actual bias mechanism is a problem that is intimately related to finding the actual nature of the dark
matter. A full roll call of candidates will be the subject of part 2 of this book; the broad categories, however, can be outlined now.
Two Sorts of Stuff
The Big Bang created about a billion photons (packets of energy, also known as quanta of radiation) for every baryon. But these photons (which now make up the microwave background) have zero rest mass, and the mass-equivalent of the energy each one carries (calculated from Einstein's E = mc 2 ) is so small that, in spite of their overwhelming numbers, they only contribute one ten-thousandth of the actual cosmological density. It is a firm prediction of the Big Bang theory that there should also be a "neutrino background"; about as many neutrinos are produced in the Big Bang as there are photons. Neutrinos must therefore, like photons, outnumber baryons by a factor of about 10 9 ; so their overall gravitational influence on the dynamics of the Universe will be important even if their individual masses are tiny compared with those of the more familiar elementary particles such as electrons and protons. The electron, which is about the lightest thing that has any direct influence on our daily lives, has a mass of about 500,000 electron Volts, or eV. This is roughly 10~ 30 kilograms, but it isn't really helpful to try to relate eVs to everyday units; nobody can get a real "feel" for the mass of an electron. What matters is that if neutrinos provide enough dark stuff to flatten the Universe then each would weigh a few tens of electron Volts—less than one ten-thousandth of the mass of an electron.
Because they are very light, such particles are born, in the fireball of the Big Bang or in nuclear reactions inside stars today, travelling at very nearly the speed of light. It is very difficult for particles travelling so rap-
idly to be bound together into clumps by gravitational bonds, and in the early stages of the expanding Universe they would have streamed in all directions very smoothly and uniformly, homogenising their distribution throughout space; their presence would also have tended to smooth out all small-scale irregularities in the distribution of baryonic matter, just as the tide rushing in over a beach smooths out the footprints left in the sand, even though each grain of sand is much more massive than a molecule of water. As the Universe expanded and cooled, neutrinos would have been spread more thinly, and they would have slowed down from their initial superhigh speeds. Eventually, they would be moving slowly enough to allow irregularities to begin to grow by gravitational attraction, and at that point the first structures would form. But those structures would not be on the scale of globular clusters, galaxies, or even clusters of galaxies, because the neutrinos would have been homogenised on these relatively small scales. The first structures to appear in a neutrino-dominated universe are on the scale of superclusters, shaped like huge sheets and filaments, and wrapped around enormous voids in which no gravitational condensations occur.
For a while, this made the neutrino-dominated scenario attractive to cosmologists. But it soon ran into serious difficulties. In such a top-down scenario, super-clusters break up into clusters, which break up into galaxies, which break up into stars. All this takes time, and computer simulations show that superclusters would not form before z = 3. Galaxies (which, in this scheme, cannot form until later) would then emerge only very recently, at a redshift much less than 3. This is hard to reconcile with the discovery of quasars at redshifts greater than 4, since quasars are thought to be the active cores of young galaxies. There are other problems. Why, if galaxies form so late, do the oldest stars
in our Galaxy, notably the stars of the globular clusters, seem to be nearly as old as the Universe itself? And where do structures as small as globular clusters and dwarf galaxies come from? Neutrinos with the right mass range cannot form gravitational condensations that small at all, if our understanding of the Big Bang and the laws of physics is correct.
Most of these difficulties would be resolved if the dominant dark matter consisted of particles that were "cold," in the sense that they had low random speeds and therefore did not disperse and homogenise on galactic scales, as would neutrinos (which are, by contrast, described as "hot" dark matter). The distinction is like the difference between molecules of liquid water, which are cold and do not move very fast, and molecules of water vapour, which move faster because they are hotter. But the analogy is not exact, because in cosmology "hot" particles are not simply "cold" particles that carry more energy, they are a different family of particles altogether. That is why, ten years ago, the proposal that the Universe might be dominated gravi-tationally by cold, dark matter was a rather daring proposal. The cold matter could not simply be neutrinos that had run out of steam; it had to be something new entirely. Cosmologists can define the properties dark stuff "ought" to have in order to explain observed features of the Universe, but no particles with those properties were known at the time. Indeed, none are known to exist even today. But at around the same time, and throughout the 1980s, particle physicists studying interactions at high energies in accelerators here on Earth (such as the machines at CERN, the European Centre for Nuclear Research, in Switzerland, and Fermilab in the United States) were proposing the existence of "new" particles to plug gaps in their theories. Several of the particles required by those theories have exactly the right kind of properties to make them
80 COSMIC COINCIDENCES
suitable candidates for cold dark matter particles in a flat universe. The disadvantage is that their existence is not proven; the encouraging sign is that the same kinds of particles are required to explain observations at opposite ends of the spectrum of science, in the Universe at large and on scales smaller than an atom.
This is another remarkable coincidence, though of a slightly different kind from the ones we have been discussing so far. It is worth emphasising the point. Particle theorists, trying to develop a complete description of the world of the very small, are forced to postulate exactly the kind of particles that cosmologists, contemplating the world of the very large, need to explain the structure of the Universe.
So what is cold dark matter (CDM) and what happens in a universe that contains enough of it to be flat? The important thing about CDM is that the particles move slowly, much slower than the speed of light. Slow motions would automatically be expected if the individual particles were heavy, compared with, say, an electron. Some candidates are particles with several times the mass of a proton, which is itself almost 1 billion electron Volts (1 GeV), 1,840 times the mass of an electron. (One CDM candidate, however, has a very light mass, like the neutrino, but is born with low velocity. This is the axion, described in chapter 4.) The low velocity of all CDM particles means that they can be bound together by gravity more easily than, for instance, "hot" neutrinos. Where the dark matter forms a clump, baryons have to follow, tugged inward by the gravity of the dark stuff, like water flooding into a pothole in the road.