James M Cline. American Scientist. Volume 92, Issue 2. Mar/Apr 2004.
Where did matter come from? The fact that we exist, surrounded by something rather than nothing, may not puzzle many of us. But to a cosmologist the existence of stuff is a troubling business, a question that has resisted an answer since it was placed before theoretical physicists nearly half a century ago. The best theories of the origin of the universe still fail to explain how it managed not to turn up empty.
The existence of matter is an unfinished piece of the big-bang theory of the origin of the universe, which successfully explains almost everything that we can observe about our physical world. In the earliest moments of the big bang, it’s thought that matter and antimatter exactly balanced each other. Since matter and antimatter cannot coexist-they annihilate each other-this situation, had it continued, would have created a boring, empty universe. So how did matter take over and come to dominate the universe?
The Russian dissident physicist Andrei Sakharov was ahead of his time when he proposed ideas for matter creation in 1967. At that time, when I was still learning my multiplication tables, the origin of matter was more or less taken for granted. Sakharov framed the question as an important one, showing that matter creation could not be taken for granted, and described the conditions that would have to be satisfied to formulate a plausible explanation.
The matter we are made of, Sakharov knew, consists mainly of protons and neutrons, the components of the atomic nucleus. Physicists call these particles baryons, from the Greek word barys, meaning heavy, and they are in fact some 2,000 times heavier than electrons. Experiments have shown that they are combinations of smaller particles, called quarks. And there are a fair number of them. If you asked a cosmologist, she’d tell you that the average density of baryons is about 0.2 per cubic meter. But curiously, if you’d asked how many photons, or particles of light, there are in the same average volume of space, she’d have answered ten billion. These are the cosmic microwave photons left over from the big bang.
Among the things cosmologists know about baryons and photons is that the ratio between these two densities stays the same over time, even as the universe expands and becomes more dilute. The baryon asymmetry of the universe, the number of baryons divided by the number of photons, is 6 × 10s-10. This is a strange number that never fails to trouble theoretical physicists. If the ratio were closer to 1, we might imagine that nothing very special happened in the early universe, all particles behaving roughly alike at extremely high temperatures, producing baryons and photons in approximately equal numbers. Another natural possibility would be to have exactly zero baryons-the case in which matter and antimatter cancel each other out. In calculating the baryon asymmetry, you subtract the antibaryons, and so you’d end up with zero.
Of course, then there would be no physicists losing sleep over these questions-there would be nothing but microwave photons dancing about the universe! But a zero-baryon universe must be considered a natural possibility because elsewhere in physics we can find symmetry principles operating. Such a principle exists for electric charge: We know that for every positively charged particle in the universe, there must be a negatively charged one.
The baryonic universe, by contrast, appears to require an asymmetry to exist, and the magnitude of that asymmetry gives us a target for the equations that a theory of baryogenesis, the origin of matter, must supply. Disappointingly, aside from this constraint, the multitude of theories appear to be largely untestable even with any experiments we can foresee within our lifetimes. This is because the very earliest, hottest moments of the universe correspond to conditions we cannot hope to reproduce in any laboratory. Is this area of theory merely a game, in which we construct clever possibilities and can use only self-consistency and elegance as criteria for judging them? Perhaps, but in fact experimentalists have been able to gather enough data to dash several proposals, including one on which I worked for five years. Since new theories are perennially born of failure, we remain hopeful that ideas now being developed-including the possibility that the baryon asymmetry arose from an asymmetry in the lighter particles that are related to electrons-might give experimentalists some ideas for novel tests. New findings or new ways of thinking might pull old ideas off the shelf. In any event, we will surely learn much as we test our theories against the new wealth of data and other ideas about the early universe that will come from astronomical measurements and accelerator experiments over the coming decade.
The Genesis of Baryogenesis
Andrei Sakharov spent two decades designing nuclear weapons for the Soviet Union. But gradually he became one of the harshest critics of the Soviet regime, and in 1968 he was sent into exile. As his political views were making headlines abroad and trouble in Moscow, he had been breaking new ground in cosmology. Among his extraordinary achievements was the unexpected realization of the ingredients necessary for the creation of a baryon asymmetry. I say “unexpected” because nobody else at the time was thinking along these lines. Proponents of big-bang theory assumed that the baryon content of the universe was an initial condition that must be imposed-a starting point rather than an event that would have to be included in a full theory of cosmological evolution. Most of Sakharov’s colleagues at the Lebedev Physical Institute in Moscow did not immediately appreciate the importance of his discovery. Today, however, cosmologists realize he was dead on.
Sakharov had been thinking about a phenomenon called CP violation, an asymmetry between certain particles and their antiparticles. This asymmetry, which will be important in the story I tell below, was one of a number of discoveries coming out of the growing field of experimental particle physics, as physicists smashed beams of particles together in ever-larger and more powerful accelerators to discover phenomena unseen in the mild conditions prevailing on the surface of Earth. Theorists also had some useful information about the properties of the universe itself.
One of the crucial pieces of information has to do with the relative abundances of light elements in the universe. Light elements such as helium and lithium, as well as the hydrogen isotope deuterium, were formed just a few minutes after the big bang, in a stage that has come to be known as bigbang nucleosynthesis, or BBN. As the universe cools down after the big bang, individual protons and neutrons begin to stick together to form atomic nuclei. Collisions with high-energy photons tend to blast apart these nuclei, but gradually the photons lose energy through the cooling that comes from the expansion of the universe. It is not too surprising that the efficiency with which nuclei are produced depends on the ratio of baryons to photons. One of the great triumphs of big-bang theory is the fact that you can choose one value for the baryon asymmetry of the universe and correctly predict the abundances of all of the light elements formed during BBN.
Over the last year, new precision measurements of the tiny fluctuations of temperature in the cosmic microwave radiation have independently confirmed the known value of the baryon asymmetry. These fluctuations reveal intricate details of the sound (or pressure) waves that existed at the time when electrons were combining with atomic nuclei to form atoms. At the same time the universe would have become transparent to photons, no longer confined by the hot plasma that dominated the first 100,000 years after nucleosynthesis. This is another dramatic success for big-bang cosmology; the baryon asymmetry is confirmed by two completely independent measurements.
But physicists can find loopholes in any seemingly airtight argument. We can imagine, for example, that antibaryons are just as numerous as baryons over very large distance scales; we just happen to live in a region dominated by baryons. Thus the true baryon number is zero. The antimatter regions would have to lie beyond the edge of the visible universe; if antimatter galaxies existed in the part of the universe we can see, we would expect to detect boundary regions where the annihilations between matter and antimatter produce highly energetic photons, or gamma rays. We don’t, but neither is there a plausible way that the early universe could have segregated matter from antimatter in very large neighborhoods. In fact, it is much easier to invent theories of baryogenesis than of matter-antimatter segregation.
Still, how necessary is an explanation of the baryon asymmetry? Possibly 6 × 10-10 is as good a number as any. Are we certain that it wasn’t just a random initial value arising from the chaos of the big bang, as earlier big-bang theorists believed? In fact, there is considerable evidence that a special mechanism for baryogenesis is necessary.
One important consideration is the strong case for inflation-a period of exponentially fast expansion preceding the big bang, during which the temperature of the universe was essentially zero. Inflation is a modification of big-bang theory developed in the 1980s by Alan Guth, Andrei Linde, Paul Steinhardt and Andreas Albrecht, currently at MIT, Stanford, Princeton and the University of California, Davis, respectively. In this view, inflation ends with a process called reheating, when potential energy stored in the vacuum is converted into hot particles with some finite initial temperature. (In the standard big-bang model, temperatures become arbitrarily high as one goes back toward the beginning of time.) Powerful support for this scenario has come from the new measurements of the cosmic microwave background radiation. Inflation provides an explanation of why the fluctuations in temperature of the microwave background are tiny (on the order of 0.001 percent) and yet not exactly zero; quantum fluctuations of this size can naturally take place during inflation.
During inflation, baryons are diluted by the volume of the inflated universe. If you assume that a baryon-antibaryon asymmetry was not created during or after reheating, you must also assume that the initial value of the baryon asymmetry was huge; in fact, the calculations suggest a number, 1069, that is even more unnaturally large than the current baryon asymmetry is unnaturally tiny. Inflation thus makes it exceedingly likely that the baryon asymmetry requires a dynamical explanation.
Sakharov’s Laws
As Sakharov was working on the baryogenesis question, another Russian scientist, Vadim Kuzmin, independently realized the necessary conditions. He was three years behind Sakharov in proposing a theory in 1970, yet still seven years ahead of the rest of the world; only in 1977 did the theoretical community start to consider these ideas in earnest. In their papers, Sakharov and Kuzmin listed three conditions that must be met for baryogenesis to take place.
First, the baryon number must not be conserved. That is, there must be some interactions that change the number of baryons in the universe.
Second, two symmetries that relate particles to antiparticles must be violated.
Third, there must be a loss of thermal equilibrium.
The second and third requirements are rather technical. I always understand abstract concepts better when they’re applied to an example, so I will show how these laws are needed by one of the very first frameworks for baryogenesis, the Grand Unified Theories (or GUTs).
The basic idea behind GUT baryogenesis is rather simple: Very heavy particles called X bosons decay at high temperatures so as to leave behind an excess of quarks over antiquarks. For example, suppose particle X follows a certain decay path 51 percent of the time, whereas its antiparticle, X, follows the parallel decay path 49 percent of the time. This asymmetry could quickly cause an excess of baryons.
One plausible scenario is shown in Figure 5. The quarks that make up ordinary baryons, the proton and neutron, come in two “flavors,” up and down, and because there are three in each baryon, the baryon number of a quark is 1/3. The positron is the antiparticle of the electron. Suppose the X boson decays 51 percent of the time into two up quarks, and 49 percent of the time into a down antiquark and a positron. On average, each X decay produces ( 2/3 × 0.51) – ( 1/3 × 0.49) = 0.177 baryons. As you’ll recall, in calculating baryon number the antiparticles are subtracted.
Its antiparticle X decays 49 percent of the time into two up antiquarks and 51 percent of the time into a down quark and an electron. This produces (- 2/3 × 0.49) + ( 1/3 × 0.51) = -0.157 baryons. One hundred decays of each particle yields a net gain of two baryons. This is actually much more efficient than necessary to generate the small baryon asymmetry we observe.
So how are Sakharov’s laws necessary for this scenario to work?
Baryon number violation. If X could decay only into two quarks, we would say that it has a baryon number of 2/3. If X could decay only into an antiquark, we would assign it a number of – 1/3 (since antiquarks have negative baryon numbers). The fact that both channels are available means there is no consistent baryon number to be given to the particle, as would be the case if all interactions respected baryon number-as they do in everyday physics.
Violation of charge-conjugation symmetries. As I mentioned above, there are certain particle properties that must not be perfectly symmetrical; two of the almost-symmetrical properties are called C and CP. C stands for charge conjugation, the operation that changes a particle to an antiparticle, and P for parity, the operation that changes the sign of the spatial coordinates of a system, creating a mirror image. Some physical theories governing microscopic properties look the same when you exchange particles for antiparticles. But in the example above, I arranged for an asymmetry by having a baryon and its antibaryon prefer different decay paths.
Loss of thermal equilibrium. A good example of thermal equilibrium is water boiling in a sealed pressure cooker. Water molecules are continuously going from the liquid to the gas phase. There is equilibrium because, once a constant temperature is reached, the rate of molecules making this transition is exactly equal to the rate of the inverse process, allowing the total amount of liquid and vapor to remain constant. I disrupt this thermal equilibrium by lifting the lid. The vapor escapes, so that the rate of liquid-to-gas transformation becomes bigger than the inverse rate. If I keep supplying heat, the liquid may all boil away.
There is a situation in the early universe analogous to taking the lid off the pressure cooker. In equilibrium, baryons are decaying, but inverse processes are also taking place, quarks fusing to form baryons-and in fact the rates are equal. The decays cannot produce a baryon asymmetry because the inverse decays keep undoing it. However, as the universe expands the temperature is decreasing-pulling the lid off the pressure cooker. At a certain temperature a pair of quarks will no longer have enough energy to produce a heavy particle. Voila-a baryon asymmetry.
CP Violation
Sakharov said that not one but two types of symmetries must be violated for baryogenesis. One of these requires a bit of explanation. CP violation, as I implied above, is the combination of two transformations. C exchanges particles for antiparticles. Parity’s connection is a little less obvious.
The positions of objects in space can be described in terms of three axes, x, y and z. When you look in a mirror, you are seeing a parity transformation on the axis perpendicular to the mirror surface. If this is the y axis, and the real you is located at position x, y and z, then your mirror self is at position x, -y and z. A corner reflector, consisting of three mirrors forming the corner of a cube, shows the complete parity transformation (-x, -y and -z) of all three directions.
Parity is relevant to baryogenesis because quarks not only come in flavors but also can be left- or right-handed. A simple way of thinking about this is as follows: If the fingers of your right hand curl around an imaginary particle, which is traveling in the direction of your outstretched thumb, then a right-handed particle’s spin is the direction in which your fingers are pointing. A left-handed particle spins in the opposite sense.
If CP symmetry held throughout the history of the universe, the only particle asymmetry we could create would be between left-handed quarks and right-handed antiquarks, plus an equal and opposite asymmetry between right-handed quarks and left-handed antiquarks. Unfortunately the total asymmetry between quarks and antiquarks would still be zero.
The search for violations of CP symmetry has been a passion of particle physicists since the 1950s. Previously it was believed that CP was a good symmetry. This belief was shown to be wrong when a process that violated CP symmetry ever so slightly was found in 1964 in experiments at Brookhaven National Laboratory by James Christenson, James Cronin, Val Fitch and Rene Turlay. Two particles that had been thought to be different turned out to be the same particle, called the kaon. It was shown that the neutral kaon decayed into states with different CP values.
The CP violation in kaon decay, however, is so weak that it cannot create a baryon asymmetry even as small as the observed one. Therefore physicists believe that larger sources of CP violation await discovery. The BaBar experiment at the Stanford Linear Accelerator Center and the corresponding Belle experiment in Japan are now searching for CP violation in the interactions of certain heavy quarks.
What’s the Matter with Bubbles?
With the experimental discovery of CP violation, Sakharov had a physical reality to inspire his thinking about the origins of matter. He did not know that another of his symmetry-violating criteria, the need for baryon-number violation, would be present within the Standard Model of particle physics, through a process called the sphaleron (from the Greek for “falling down”).
The Standard Model unifies electromagnetism and the weak nuclear force into a description of so-called electroweak interactions and the particles involved. It predicts an interaction that involves nine quarks and three of the light particles called leptons, which can be counted in much the same way as baryons. Discovered as a mathematical entity in 1984 by Frans Klinkhamer and Nicholas Manton (now at the universities of Karlsruhe and Cambridge, respectively), the sphaleron has never been experimentally confirmed, yet no theorist doubts its validity.
To make baryon violation happen, you bring together three quarks from each of the three “generations” of the Standard Model-the light quarks (up and down, which I introduced above) and the two heavier, or higher-energy, classes of quarks discovered in accelerator experiments-with one lepton from each of the corresponding generations of leptons. At low temperatures, this requires something called quantum tunneling, where a microscopic system undergoes a transition that normally would require an infusion of energy.
The probability of tunneling is so vanishingly small that physicists would not expect to see such an event in the laboratory or the observable universe. So why would this be important? The answer was realized by Kuzmin and fellow Russian physicists Valery Rubakov and Mikhail Shaposhnikov in 1985: At the high temperatures present in the early universe, the energy barrier preventing baryon violation could be surmounted using thermal energy; this is the sphaleron. Even more important, the energy hill actually becomes smaller and even vanishes at sufficiently high temperatures.
Theorists’ widespread acceptance of the validity of the sphaleron means that two of Sakharov’s three criteria-CP-symmetry violation and baryon-number violation-are already realized in nature. Is there a process that satisfies the third condition, loss of thermal equilibrium? If so, we should be able to understand the size of the baryon asymmetry from known principles, without having to form new hypotheses. This understanding would be important for placing stringent constraints on any new physics ideas that would predict a different value for the baryon asymmetry.
Above I used the boiling of water as an example of a loss of thermal equilibrium. As it happens, there is an analogous process in electroweak theory at high temperatures. This process is the opposite of what happens when water boils. In the early universe, bubbles form as the universe cools. The phase existing outside the bubbles is an unfamiliar one where all particles that are normally massive have become massless. Only inside the bubbles have particles regained their masses to produce physics as we know it. The bubbles expand and eventually squeeze all of the exotic massless phase out of the universe. Physicists call this kind of process a first-order phase transition.
What does this have to do with baryogenesis? In this theory, sphalerons, the source of baryon-number violation, are much weaker inside the bubbles (in the realm of conventional physics) than outside. On the outside, the energy “hill” that sphalerons normally must tunnel through is absent, so that they occur with no barrier to overcome. Therefore baryon violation is strong outside the bubbles and much weaker inside. Eventually, as you’ll recall, sphalerons become so weak as to be negligible at low temperatures.
In electroweak theory every particle in the universe must eventually pass through a bubble wall as the bubbles expand and fill all space. Andrew Cohen of Boston University, along with David B. Kaplan and Ann Nelson, now at the University of Washington, realized in 1990 that this provides a mechanism for baryogenesis. When quarks encounter the wall, they have some probability of passing from outside a bubble to the interior, or of bouncing back into the exterior. CP violation allows this probability to be different for quarks and antiquarks, or for left-handed and right-handed quarks. Suppose that an asymmetry of left-handed antiquarks builds up in the massless phase outside the bubbles. The sphalerons try to erase this asymmetry, but in so doing they change the total baryon number, creating a baryon asymmetry. Eventually these baryons fall inside the bubbles, which fill up the universe.
Sphalerons are much slower inside the bubble than outside. Since the rates are not equal, the sphalerons are out of equilibrium inside the bubble. This is crucial; otherwise, the sphalerons inside the bubble would destroy the baryon asymmetry created by those on the outside.
In this discussion we have skimmed along the path that I traveled, with my collaborator Kimmon Kainulainen of the University of Jyvaskyla in Finland, in our recent failed search for a successful theory of baryogenesis. We have arrived at a way of testing the theory, a quantitative question: Are the sphalerons inside the bubbles in our universe slow enough to produce the observed baryon asymmetry? This depends on the size of the energy barrier that they must surmount-or in physics-speak, on the strength of the phase transition. If the transition is too weak, the baryon asymmetry is reduced too much.
Shaposhnikov and others found that within the Standard Model of particle physics, the strength of the phase transition depends on certain particles, called the Higgs boson and the top quark, being sufficiently light. Recent results of accelerator experiments have shown that they are quite heavy; as a result, it must be admitted that the phase transition is too weak to explain baryogenesis without invoking some hypothetical new physics. Sakharov’s conditions could not all be satisfied within the Standard Model.
Supersymmetry
What new physics might come to the rescue? One of the best-motivated ideas is called supersymmetry, or SUSY, which originated in 1970 in work at the Lebedev institute by Yuri Golfand and his colleagues. Supersymmetry extends the symmetries that characterize the particle families in the Standard Model and posits that for every known kind of particle that has one quantum of spin, as do quarks and leptons, there exists a superpartner whose spin is zero. Such particles have not yet been discovered; therefore it is believed that they have large masses beyond the range of our detection abilities. But SUSY succeeds in explaining-and indeed was invented to explain-another of the small-number mysteries of the Standard Model, the mass of the Higgs particle.
The new particles predicted by SUSY can boost the strength of the electroweak phase transition by increasing the size of the sphaleron hill and making the baryons in the bubbles safe from the ravages of unsuppressed sphalerons. SUSY can provide new sources of CP violation bigger than the too-weak processes in the Standard Model. But this property has proved to be the model’s Achilles heel. The same processes that violate CP symmetry create rather large electric dipole moments of quarks, electrons, neutrons and atomic nuclei. These must lie outside the constraints that have come from experiments that measure only upper limits for these quantities. For a while, it was possible to imagine that supersymmetric sources of CP violation could conspire to give a large baryon asymmetry while at the same time giving small electric dipole moments. But over time the accumulation of more experimental data made these imaginings increasingly implausible.
Most experts now concede that the minimal version of electroweak baryogenesis, invoking supersymmetry, is dead or at least unlikely. It is possible to resurrect it by complicating the minimal model with extra particles and interactions. Such complications may even be discovered when the world’s next large particle accelerator, the Large Hadron Collider at the European particle-physics laboratory CERN in Geneva, turns on in 2007. Until then, the embellished versions of the theory look rather speculative.
Leptogenesis
Following the near-demise of electroweak baryogenesis, another idea has stepped in to take its place as the favored scenario: baryogenesis via leptogenesis. Even though electroweak theory can’t easily meet Sakharov’s three conditions using baryons themselves, his ingredients can easily be adapted to create an asymmetry of other kinds of particles. Above I mentioned the particles called leptons, which include electrons, muons, tau particles and neutrinos. One could make an asymmetry between neutrinos and antineutrinos. But we’re made of baryons, not ghostly neutrinos, so is this useful for baryogenesis?
Again the sphaleron process provides a tool for thinking about asymmetry. Remember that sphalerons involve leptons as well as quarks. For this reason it is nearly impossible to create a lepton asymmetry at high temperatures without it being converted, at least partially, into a baryon asymmetry. Turning on sphaleron interactions is like opening a valve that equalizes lepton and baryon asymmetries.
Leptogenesis relies on the decay of heavy neutrinos, whose existence is required for explaining why the neutrinos of the Standard Model are nearly massless. Their lack of electric charge and their near masslessness makes them ghostly. Although they are as numerous in the universe as photons, they move about with only the rarest interactions with other particles. The question of whether they have mass, and whether it is tiny or substantial, has been a tough one to study. Neutrino physicists have used all manner of ingenious techniques to observe neutrinos from the Sun, from cosmic-ray interactions with the Earth’s atmosphere and from nuclear reactors. An exciting development in neutrino studies is the growing accumulation of evidence that neutrinos have nonvanishing masses. This information is fueling interest in leptogenesis as the key to baryogenesis.
Unfortunately, it’s not clear whether leptogenesis can be directly tested. The fact that the known masses of neutrinos are consistent with the requirements of leptogenesis is an encouraging sign, but far from a proof. We can hope that the future observation of rare decays-as when the heavy muon decays to produce its cousin, the electron, and a photon-will provide further circumstantial evidence for leptogenesis. It may be that we can hope only for signs pointing toward leptogenesis and will never have a true test.
Of Strings and Dark Horses
In our attempts to understand the nature of the universe, theorists must often admit to reaching a possible dead end-a question that we may never satisfactorily answer. Many cosmologists’ hope for resolving such matters lies in the quest for a fundamental theory that would make universal predictions, from which answers to smaller questions would unambiguously flow.
Recent developments in one area of fundamental theory, string theory, make us suspect that there may actually be many answers to our small-numbers questions, or effectively a plethora of theories, each applying to a different region of the universe, which practically speaking might as well be considered separate universes, since they cannot communicate with one another. We have no way, a priori, to predict which phase of the theory applies to the region we happen to be in.
Only some of the phases available within string theory, though, are compatible with our existence-others predict universes with conditions quite hostile to the development of life. Some physicists would like to restrict attention to the phases of string theory that are compatible with our existence. Using this “anthropic principle” to approach science has been viewed by many as giving up on doing real science. Its re-emergence in string-theory discussions has polarized the theoretical-physics community.
Human existence constrains many of the parameters in the laws that govern the physics that we know: These laws must be defined so that they match the circumscribed conditions of what we observe, a universe supporting life. What about the baryon asymmetry-is it “anthropically sensitive”? That is, what would it mean if we looked only at values compatible with our own existence? It has been argued that values between 10-4 and 10-11 fit this constraint: They allow stars and galaxies to develop (disallowed if there is too little matter) yet do not allow helium production to overwhelm hydrogen production (which would happen if the asymmetry was too large), in which case there would be no water, and stars would burn out before the temperature of the universe became suitable for life. Because these constraints leave a rather large range of possible values, anthropic arguments do not have a strong influence on the theory. Thus we can sidestep the anthropics debate and keep on seeking a dynamical, deterministic explanation for the origin of matter.
If the currently popular theory, leptogenesis, is true, it has an ironic implication. It would mean that the most massive objects in the universe trace their origin to the most ethereal particles we know of, the neutrinos. For my part, I’m still holding out hopes for the dark horse, supersymmetric electroweak baryogenesis. There may yet be loopholes that have been overlooked-ways to satisfy the experimental constraints on the theory and to test it more closely when the Large Hadron Collider starts operating. Whatever the correct explanation may be, a successful, verifiable theory of matter, if we achieve it in this century, will matter. It is among the highest tributes we can offer to Andrei Sakharov and the other great physics minds behind this question. But more importantly, it will satisfy in an ultimate way that innately human craving: to know where we have come from.