The Fabric of the Cosmos: Space, Time, and the Texture of Reality - Brian Greene (2004)
Part III. SPACETIME AND COSMOLOGY
Chapter 10. Deconstructing the Bang
A common misconception is that the big bang provides a theory of cosmic origins. It doesn’t. The big bang is a theory, partly described in the last two chapters, that delineates cosmic evolution from a split second after whatever happened to bring the universe into existence, but it says nothing at all about time zero itself. And since, according to the big bang theory, the bang is what is supposed to have happened at the beginning, the big bang leaves out the bang. It tells us nothing about what banged, why it banged, how it banged, or, frankly, whether it ever really banged at all.1 In fact, if you think about it for a moment, you’ll realize that the big bang presents us with quite a puzzle. At the huge densities of matter and energy characteristic of the universe’s earliest moments, gravity was by far the dominant force. But gravity is an attractive force. It impels things to come together. So what could possibly be responsible for the outward force that drove space to expand? It would seem that some kind of powerful repulsive force must have played a critical role at the time of the bang, but which of nature’s forces could that possibly be?
For many decades this most basic of all cosmological questions went unanswered. Then, in the 1980s, an old observation of Einstein’s was resurrected in a sparkling new form, giving rise to what has become known as inflationary cosmology. And with this discovery, credit for the bang could finally be bestowed on the deserving force: gravity. It’s surprising, but physicists realized that in just the right environment gravity can be repulsive, and, according to the theory, the necessary conditions prevailed during the earliest moments of cosmic history. For a time interval that would make a nanosecond seem an eternity, the early universe provided an arena in which gravity exerted its repulsive side with a vengeance, driving every region of space away from every other with unrelenting ferocity. So powerful was the repulsive push of gravity that not only was the bang identified, it was revealed to be bigger—much bigger—than anyone had previously imagined. In the inflationary framework, the early universe expanded by an astonishingly huge factor compared with what is predicted by the standard big bang theory, enlarging our cosmological vista to a degree that dwarfed last century’s realization that ours is but one galaxy among hundreds of billions.2
In this and the next chapter, we discuss inflationary cosmology. We will see that it provides a “front end” for the standard big bang model, offering critical modifications to the standard theory’s claims about events during the universe’s earliest moments. In doing so, inflationary cosmology resolves key issues that are beyond the reach of the standard big bang, makes a number of predictions that have been and in the near future will continue to be experimentally tested, and, perhaps most strikingly, shows how quantum processes can, through cosmological expansion, iron tiny wrinkles into the fabric of space that leave a visible imprint on the night sky. And beyond these achievements, inflationary cosmology gives significant insight into how the early universe may have acquired its exceedingly low entropy, taking us closer than ever to an explanation of the arrow of time.
Einstein and Repulsive Gravity
After putting the finishing touches on general relativity in 1915, Einstein applied his new equations for gravity to a variety of problems. One was the long-standing puzzle that Newton’s equations couldn’t account for the so-called precession of the perihelion of Mercury’s orbit—the observed fact that Mercury does not trace the same path each time it orbits the sun: instead, each successive orbit shifts slightly relative to the previous. When Einstein redid the standard orbital calculations with his new equations, he derived the observed perihelion precession precisely, a result he found so thrilling that it gave him heart palpitations.3 Einstein also applied general relativity to the question of how sharply the path of light emitted by a distant star would be bent by spacetime’s curvature as it passed by the sun on its way to earth. In 1919, two teams of astronomers—one camped out on the island of Principe off the west coast of Africa, the other in Brazil— tested this prediction during a solar eclipse by comparing observations of starlight that just grazed the sun’s surface (these are the light rays most affected by the sun’s presence, and only during an eclipse are they visible) with photographs taken when the earth’s orbit had placed it between these same stars and the sun, virtually eliminating the sun’s gravitational impact on the starlight’s trajectory. The comparison revealed a bending angle that, once again, confirmed Einstein’s calculations. When the press caught wind of the result, Einstein became a world-renowned celebrity overnight. With general relativity, it’s fair to say, Einstein was on a roll.
Yet, despite the mounting successes of general relativity, for years after he first applied his theory to the most immense of all challenges—understanding the entire universe—Einstein absolutely refused to accept the answer that emerged from the mathematics. Before the work of Friedmann and Lemaître discussed in Chapter 8, Einstein, too, had realized that the equations of general relativity showed that the universe could not be static; the fabric of space could stretch or it could shrink, but it could not maintain a fixed size. This suggested that the universe might have had a definite beginning, when the fabric was maximally compressed, and might even have a definite end. Einstein stubbornly balked at this consequence of general relativity, because he and everyone else “knew” that the universe was eternal and, on the largest of scales, fixed and unchanging. Thus, notwithstanding the beauty and the successes of general relativity, Einstein reopened his notebook and sought a modification of the equations that would allow for a universe that conformed to the prevailing prejudice. It didn’t take him long. In 1917 he achieved the goal by introducing a new term into the equations of general relativity: the cosmological constant.4
Einstein’s strategy in introducing this modification is not hard to grasp. The gravitational force between any two objects, whether they’re baseballs, planets, stars, comets, or what have you, is attractive, and as a result, gravity constantly acts to draw objects toward one another. The gravitational attraction between the earth and a dancer leaping upward causes the dancer to slow down, reach a maximum height, and then head back down. If a choreographer wants a static configuration in which the dancer floats in midair, there would have to be a repulsive force between the dancer and the earth that would precisely balance their gravitational attraction: a static configuration can arise only when there is a perfect cancellation between attraction and repulsion. Einstein realized that exactly the same reasoning holds for the entire universe. In just the same way that the attractive pull of gravity acts to slow the dancer’s ascent, it also acts to slow the expansion of space. And just as the dancer can’t achieve stasis—it can’t hover at a fixed height—without a repulsive force to balance the usual pull of gravity, space can’t be static—space can’t hover at a fixed overall size—without there also being some kind of balancing repulsive force. Einstein introduced the cosmological constant because he found that with this new term included in the equations, gravity could provide just such a repulsive force.
But what physics does this mathematical term represent? What is the cosmological constant, from what is it made, and how does it manage to go against the grain of usual attractive gravity and exert a repulsive outward push? Well, the modern reading of Einstein’s work—one that goes back to Lemaître—interprets the cosmological constant as an exotic form of energy that uniformly and homogeneously fills all of space. I say “exotic” because Einstein’s analysis didn’t specify where this energy might come from and, as we’ll shortly see, the mathematical description he invoked ensured that it could not be composed of anything familiar like protons, neutrons, electrons, or photons. Physicists today invoke phrases like “the energy of space itself” or “dark energy” when discussing the meaning of Einstein’s cosmological constant, because if there were a cosmological constant, space would be filled with a transparent, amorphous presence that you wouldn’t be able to see directly; space filled with a cosmological constant would still look dark. (This resembles the old notion of an aether and the newer notion of a Higgs field that has acquired a nonzero value throughout space. The latter similarity is more than mere coincidence since there is an important connection between a cosmological constant and Higgs fields, which we will come to shortly.) But even without specifying the origin or identity of the cosmological constant, Einstein was able to work out its gravitational implications, and the answer he found was remarkable.
To understand it, you need to be aware of one feature of general relativity that we have yet to discuss. In Newton’s approach to gravity, the strength of attraction between two objects depends solely on two things: their masses and the distance between them. The more massive the objects and the closer they are, the greater the gravitational pull they exert on each other. The situation in general relativity is much the same, except that Einstein’s equations show that Newton’s focus on mass was too limited. According to general relativity, it is not just the mass (and the separation) of objects that contributes to the strength of the gravitational field. Energy and pressure also contribute. This is important, so let’s spend a moment to see what it means.
Imagine that it’s the twenty-fifth century and you’re being held in the Hall of Wits, the newest Department of Corrections experiment employing a meritocratic approach to disciplining white-collar felons. The convicts are each given a puzzle, and they can regain their freedom only by solving it. The guy in the cell next to you has to figure out why Gilligan’s Island reruns made a surprise comeback in the twenty-second century and have been the most popular show ever since, so he’s likely to be calling the Hall home for quite some time. Your puzzle is simpler. You are given two identical solid gold cubes—they are the same size and each is made from precisely the same quantity of gold. Your challenge is to find a way to make the cubes register different weights when gently resting on a fixed, exquisitely accurate scale, subject to one stipulation: you’re not allowed to change the amount of matter in either cube, so there’s to be no chipping, scraping, soldering, shaving, etc. If you posed this puzzle to Newton, he’d immediately declare it to have no solution. According to Newton’s laws, identical quantities of gold translate into identical masses. And since each cube will rest on the same, fixed scale, earth’s gravitational pull on them will be identical. Newton would conclude that the two cubes must register an identical weight, no ifs, ands, or buts.
With your twenty-fifth-century high school knowledge of general relativity, though, you see a way out. General relativity shows that the strength of the gravitational attraction between two objects does not just depend on their masses5 (and their separation), but also on any and all additional contributions to each object’s total energy. And so far we have said nothing about the temperature of the golden cubes. Temperature is a measure of how quickly, on average, the atoms of gold that make up each cube are moving to and fro—it’s a measure of how energetic the atoms are (it reflects their kinetic energy). Thus, you realize that if you heat up one cube, its atoms will be more energetic, so it will weigh a bit more than the cooler cube. This is a fact Newton was unaware of (an increase of 10 degrees Celsius would increase the weight of a one-pound cube of gold by about a millionth of a billionth of a pound, so the effect is minuscule), and with this solution you win release from the Hall.
Well, almost. Because your crime was particularly devious, at the last minute the parole board decides that you must solve a second puzzle. You are given two identical old-time Jack-in-the-box toys, and your new challenge is to find a way to make each have a different weight. But in this go-around, not only are you forbidden to change the amount of mass in either object, you are also required to keep both at exactly the same temperature. Again, were Newton given this puzzle, he would immediately resign himself to life in the Hall. Since the toys have identical masses, he would conclude that their weights are identical, and so the puzzle is insoluble. But once again, your knowledge of general relativity comes to the rescue: On one of the toys you compress the spring, tightly squeezing Jack under the closed lid, while on the other you leave Jack in his popped-up posture. Why? Well, a compressed spring has more energy than an uncompressed one; you had to exert energy to squeeze the spring down and you can see evidence of your labor because the compressed spring exerts pressure, causing the toy’s lid to strain slightly outward. And, again, according to Einstein, any additional energy affects gravity, resulting in additional weight. Thus, the closed Jack-in-the-box, with its compressed spring exerting an outward pressure, weighs a touch more than the open Jack-in-the-box, with its uncompressed spring. This is a realization that would have escaped Newton, and with it you finally do earn back your freedom.
The solution to that second puzzle hints at the subtle but critical feature of general relativity that we’re after. In his paper presenting general relativity, Einstein showed mathematically that the gravitational force depends not only on mass, and not only on energy (such as heat), but also on any pressures that may be exerted. And this is the essential physics we need if we are to understand the cosmological constant. Here’s why. Outward-directed pressure, like that exerted by a compressed spring, is called positive pressure. Naturally enough, positive pressure makes a positive contribution to gravity. But, and this is the critical point, there are situations in which the pressure in a region, unlike mass and total energy, can be negative, meaning that the pressure sucks inward instead of pushing outward. And although that may not sound particularly exotic, negative pressure can result in something extraordinary from the point of view of general relativity: whereas positive pressure contributes to ordinary attractive gravity, negative pressure contributes to “negative” gravity, that is, to repulsive gravity!6
With this stunning realization, Einstein’s general relativity exposed a loophole in the more than two-hundred-year-old belief that gravity is always an attractive force. Planets, stars, and galaxies, as Newton correctly showed, certainly do exert an attractive gravitational pull. But when pressure becomes important (for ordinary matter under everyday conditions, the gravitational contribution of pressure is negligible) and, in particular, when pressure is negative (for ordinary matter like protons and electrons, pressure is positive, which is why the cosmological constant can’t be composed of anything familiar) there is a contribution to gravity that would have shocked Newton. It’s repulsive.
This result is central to much of what follows and is easily misunderstood, so let me emphasize one essential point. Gravity and pressure are two related but separate characters in this story. Pressures, or more precisely, pressure differences, can exert their own, nongravitational forces. When you dive underwater, your eardrums can sense the pressure difference between the water pushing on them from the outside and the air pushing on them from the inside. That’s all true. But the point we’re now making about pressure and gravity is completely different. According to general relativity, pressure can indirectly exert another force—it can exert a gravitational force—because pressure contributes to the gravitational field. Pressure, like mass and energy, is a source of gravity. And remarkably, if the pressure in a region is negative, it contributes a gravitational push to the gravitational field permeating the region, not a gravitational pull.
This means that when pressure is negative, there is competition between ordinary attractive gravity, arising from ordinary mass and energy, and exotic repulsive gravity, arising from the negative pressure. If the negative pressure in a region is negative enough, repulsive gravity will dominate; gravity will push things apart rather than draw them together. Here is where the cosmological constant comes into the story. The cosmological term Einstein added to the equations of general relativity would mean that space is uniformly suffused with energy but, crucially, the equations show that this energy has a uniform, negative pressure. What’s more, the gravitational repulsion of the cosmological constant’s negative pressure overwhelms the gravitational attraction coming from its positive energy, and so repulsive gravity wins the competition: a cosmological constant exerts an overall repulsive gravitational force.7
For Einstein, this was just what the doctor ordered. Ordinary matter and radiation, spread throughout the universe, exert an attractive gravitational force, causing every region of space to pull on every other. The new cosmological term, which he envisioned as also being spread uniformly throughout the universe, exerts a repulsive gravitational force, causing every region of space to push on every other. By carefully choosing the size of the new term, Einstein found that he could precisely balance the usual attractive gravitational force with the newly discovered repulsive gravitational force, and produce a static universe.
Moreover, because the new repulsive gravitational force arises from the energy and pressure in space itself, Einstein found that its strength is cumulative; the force becomes stronger over larger spatial separations, since more intervening space means more outward pushing. On the distance scales of the earth or the entire solar system, Einstein showed that the new repulsive gravitational force is immeasurably tiny. It becomes important only over vastly larger cosmological expanses, thereby preserving all the successes of both Newton’s theory and his own general relativity when they are applied closer to home. In short, Einstein found he could have his cake and eat it too: he could maintain all the appealing, experimentally confirmed features of general relativity while basking in the eternal serenity of an unchanging cosmos, one that was neither expanding nor contracting.
With this result, Einstein no doubt breathed a sigh of relief. How heart-wrenching it would have been if the decade of grueling research he had devoted to formulating general relativity resulted in a theory that was incompatible with the static universe apparent to anyone who gazed up at the night sky. But, as we have seen, a dozen years later the story took a sharp turn. In 1929, Hubble showed that cursory skyward gazes can be misleading. His systematic observations revealed that the universe is not static. It is expanding. Had Einstein trusted the original equations of general relativity, he would have predicted the expansion of the universe more than a decade before it was discovered observationally. That would certainly have ranked among the greatest discoveries—it might have been the greatest discovery—of all time. After learning of Hubble’s results, Einstein rued the day he had thought of the cosmological constant, and he carefully erased it from the equations of general relativity. He wanted everyone to forget the whole sorry episode, and for many decades everyone did.
In the 1980s, however, the cosmological constant resurfaced in a surprising new form and ushered in one of the most dramatic upheavals in cosmological thinking since our species first engaged in cosmological thought.
Of Jumping Frogs and Supercooling
If you caught sight of a baseball flying upward, you could use Newton’s law of gravity (or Einstein’s more refined equations) to figure out its subsequent trajectory. And if you carried out the required calculations, you’d have a solid understanding of the ball’s motion. But there would still be an unanswered question: Who or what threw the ball upward in the first place? How did the ball acquire the initial upward motion whose subsequent unfolding you’ve evaluated mathematically? In this example, a little further investigation is all it generally takes to find the answer (unless, of course, the aspiring big-leaguers realize that the ball just hit is on a collision course with the windshield of a parked Mercedes). But a more difficult version of a similar question dogs general relativity’s explanation of the expansion of the universe.
The equations of general relativity, as originally shown by Einstein, the Dutch physicist Willem de Sitter, and, subsequently, Friedmann and Lemaître, allow for an expanding universe. But, just as Newton’s equations tell us nothing about how a ball’s upward journey got started, Einstein’s equations tell us nothing about how the expansion of the universe got started. For many years, cosmologists took the initial outward expansion of space as an unexplained given, and simply worked the equations forward from there. This is what I meant earlier when I said that the big bang is silent on the bang.
Such was the case until one fateful night in December 1979, when Alan Guth, a physics postdoctoral fellow working at the Stanford Linear Accelerator Center (he is now a professor at MIT), showed that we can do better. Much better. Although there are details that today, more than two decades later, have yet to be resolved fully, Guth made a discovery that finally filled the cosmological silence by providing the big bang with a bang, and one that was bigger than anyone expected.
Guth was not trained as a cosmologist. His specialty was particle physics, and in the late 1970s, together with Henry Tye from Cornell University, he was studying various aspects of Higgs fields in grand unified theories. Remember from the last chapter’s discussion of spontaneous symmetry breaking that a Higgs field contributes the least possible energy it can to a region of space when its value settles down to a particular nonzero number (a number that depends on the detailed shape of its potential energy bowl). In the early universe, when the temperature was extraordinarily high, we discussed how the value of a Higgs field would wildly fluctuate from one number to another, like the frog in the hot metal bowl whose legs were being singed, but as the universe cooled, the Higgs would roll down the bowl to a value that would minimize its energy.
Guth and Tye studied reasons why the Higgs field might be delayed in reaching the least energetic configuration (the bowl’s valley in Figure 9.1c). If we apply the frog analogy to the question Guth and Tye asked, it was this: what if the frog, in one of its earlier jumps when the bowl was starting to cool, just happened to land on the central plateau? And what if, as the bowl continued to cool, the frog hung out on the central plateau (leisurely eating worms), rather than sliding down to the bowl’s valley? Or, in physics terms, what if a fluctuating Higgs field’s value should land on the energy bowl’s central plateau and remain there as the universe continues to cool? If this happens, physicists say that the Higgs field has supercooled, indicating that even though the temperature of the universe has dropped to the point where you’d expect the Higgs value to approach the low-energy valley, it remains trapped in a higher-energy configuration. (This is analogous to highly purified water, which can be supercooled below 0 degrees Celsius, the temperature at which you’d expect it to turn into ice, and yet remain liquid because the formation of ice requires small impurities around which the crystals can grow.)
Guth and Tye were interested in this possibility because their calculations suggested it might be relevant to a problem (the magnetic monopole problem8) researchers had encountered with various attempts at grand unification. But Guth and Tye realized that there might be another implication and, in retrospect, that’s why their work proved pivotal. They suspected that the energy associated with a supercooled Higgs field— remember, the height of the field represents its energy, so the field has zero energy only if its value lies in the bowl’s valley—might have an effect on the expansion of the universe. In early December 1979, Guth followed up on this hunch, and here’s what he found.
A Higgs field that has gotten caught on a plateau not only suffuses space with energy, but, of crucial importance, Guth realized that it also contributes a uniform negative pressure. In fact, he found that as far as energy and pressure are concerned, a Higgs field that’s caught on a plateau has the same properties as a cosmological constant: it suffuses space with energy and negative pressure, and in exactly the same proportions as a cosmological constant. So Guth discovered that a supercooled Higgs field does have an important effect on the expansion of space: like a cosmological constant, it exerts a repulsive gravitational force that drives space to expand.9
At this point, since you are already familiar with negative pressure and repulsive gravity, you may be thinking, All right, it’s nice that Guth found a specific physical mechanism for realizing Einstein’s idea of a cosmological constant, but so what? What’s the big deal? The concept of a cosmological constant had long been abandoned. Its introduction into physics was nothing but an embarrassment for Einstein. Why get excited over rediscovering something that had been discredited more than six decades earlier?
Well, here’s why. Although a supercooled Higgs field shares certain features with a cosmological constant, Guth realized that they are not completely identical. Instead, there are two key differences—differences that make all the difference.
First, whereas a cosmological constant is constant—it does not vary with time, so it provides a constant, unchanging outward push—a supercooled Higgs field need not be constant. Think of a frog perched on the bump in Figure 10.1a. It may hang out there for a while, but sooner or later a random jump this way or that—a jump taken not because the bowl is hot (it no longer is), but merely because the frog gets restless— will propel the frog beyond the bump, after which it will slide down to the bowl’s lowest point, as in Figure 10.1b. A Higgs field can behave similarly. Its value throughout all of space may get stuck on its energy bowl’s central bump while the temperature drops too low to drive significant thermal agitation. But quantum processes will inject random jumps into the Higgs field’s value, and a large enough jump will propel it off the plateau, allowing its energy and pressure to relax to zero.10Guth’s calculations showed that, depending on the precise shape of the bowl’s bump, this jump could have happened rapidly, perhaps in as short a time as .00000000000000000000000000000001 (10−35) seconds. Subsequently, Andrei Linde, then working at the Lebedev Physical Institute in Moscow, and Paul Steinhardt, then working with his student Andreas Albrecht at the University of Pennsylvania, discovered a way for the Higgs field’s relaxation to zero energy and pressure throughout all of space to happen even more efficiently and significantly more uniformly (thereby curing certain technical problems inherent to Guth’s original proposal11). They showed that if the potential energy bowl had been smoother and more gradually sloping, as in Figure 10.2, no quantum jumps would have been necessary: the Higgs field’s value would quickly roll down to the valley, much like a ball rolling down a hill. The upshot is that if a Higgs field acted like a cosmological constant, it did so only for a brief moment.
Figure 10.1 (a) A supercooled Higgs field is one whose value gets trapped on the energy bowl’s high-energy plateau, like the frog on a bump. (b) Typically, a supercooled Higgs field will quickly find its way off the plateau and drop to a value with lower energy, like the frog’s jumping off the bump.
The second difference is that whereas Einstein carefully and arbitrarily chose the value of the cosmological constant—the amount of energy and negative pressure it contributed to each volume of space—so that its outward repulsive force would precisely balance the inward attractive force arising from the ordinary matter and radiation in the cosmos, Guth was able to estimate the energy and negative pressure contributed by the Higgs fields he and Tye had been studying. And the answer he found was more than 1000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000 (10100) times larger than the value Einstein had chosen. This number is huge, obviously, and so the outward push supplied by the Higgs field’s repulsive gravity is monumental compared with what Einstein envisioned originally with the cosmological constant.
Figure 10.2 A smoother and more gradually sloping bump allows the Higgs field value to roll down to the zero-energy valley more easily and more uniformly throughout space.
Now, if we combine these two observations—that the Higgs field will stay on the plateau, in the high-energy, negative-pressure state, only for the briefest of instants, and that while it is on the plateau, the repulsive outward push it generates is enormous—what do we have? Well, as Guth realized, we have a phenomenal, short-lived, outward burst. In other words, we have exactly what the big bang theory was missing: a bang, and a big one at that. That’s why Guth’s discovery is something to get excited about.12
The cosmological picture emerging from Guth’s breakthrough is thus the following. A long time ago, when the universe was enormously dense, its energy was carried by a Higgs field perched at a value far from the lowest point on its potential energy bowl. To distinguish this particular Higgs field from others (such as the electroweak Higgs field responsible for giving mass to the familiar particle species, or the Higgs field that arises in grand unified theories13) it is usually called the inflaton field.25 Because of its negative pressure, the inflaton field generated a gigantic gravitational repulsion that drove every region of space to rush away from every other; in Guth’s language, the inflaton drove the universe to inflate. The repulsion lasted only about 10−35 seconds, but it was so powerful that even in that brief moment the universe swelled by a huge factor. Depending on details such as the precise shape of the inflaton field’s potential energy, the universe could easily have expanded by a factor of 1030, 1050, or 10100 or more.
These numbers are staggering. An expansion factor of 1030—a conservative estimate—would be like scaling up a molecule of DNA to roughly the size of the Milky Way galaxy, and in a time interval that’s much shorter than a billionth of a billionth of a billionth of the blink of an eye. By comparison, even this conservative expansion factor is billions and billions of times the expansion that would have occurred according to the standard big bang theory during the same time interval, and it exceeds the total expansion factor that has cumulatively occurred over the subsequent 14 billion years! In the many models of inflation in which the calculated expansion factor is much larger than 1030, the resulting spatial expanse is so enormous that the region we are able to see, even with the most powerful telescope possible, is but a tiny fraction of the whole universe. According to these models, none of the light emitted from the vast majority of the universe could have reached us yet, and much of it won’t arrive until long after the sun and earth have died out. If the entire cosmos were scaled down to the size of earth, the part accessible to us would be much smaller than a grain of sand.
Roughly 10−35 seconds after the burst began, the inflaton field found its way off the high-energy plateau and its value throughout space slid down to the bottom of the bowl, turning off the repulsive push. And as the inflaton value rolled down, it relinquished its pent-up energy to the production of ordinary particles of matter and radiation—like a foggy mist settling on the grass as morning dew—that uniformly filled the expanding space.14 From this point on, the story is essentially that of the standard big bang theory: space continued to expand and cool in the aftermath of the burst, allowing particles of matter to clump into structures like galaxies, stars, and planets, which slowly arranged themselves into the universe we currently see, as illustrated in Figure 10.3.
Guth’s discovery—dubbed inflationary cosmology—together with the important improvements contributed by Linde, and by Albrecht and Steinhardt, provided an explanation for what set space expanding in the first place. A Higgs field perched above its zero energy value can provide an outward blast driving space to swell. Guth provided the big bang with a bang.
The Inflationary Framework
Guth’s discovery was quickly hailed as a major advance and has become a dominant fixture of cosmological research. But notice two things. First, in the standard big bang model, the bang supposedly happened at time zero, at the very beginning of the universe, so it is viewed as the creation event. But just as a stick of dynamite explodes only when it’s properly lit, in inflationary cosmology the bang happened only when conditions were right— when there was an inflaton field whose value provided the energy and negative pressure that fueled the outward burst of repulsive gravity—and that need not have coincided with the “creation” of the universe. For this reason, the inflationary bang is best thought of as an event that the preexisting universe experienced, but not necessarily as the event that created the universe. We denote this in Figure 10.3 by maintaining some of the fuzzy patch of Figure 9.2, indicating our continuing ignorance of fundamental origin: specifically, if inflationary cosmology is right, our ignorance of why there is an inflaton field, why its potential energy bowl has the right shape for inflation to have occurred, why there are space and time within which the whole discussion takes place, and, in Leibniz’s more grandiose phrasing, why there is something rather than nothing.
Figure 10.3 (a) Inflationary cosmology inserts a quick, enormous burst of spatial expansion early on in the history of the universe. ( b) After the burst, the evolution of the universe merges into the standard evolution theorized in the big bang model.
A second and related observation is that inflationary cosmology is not a single, unique theory. Rather, it is a cosmological framework built around the realization that gravity can be repulsive and can thus drive a swelling of space. The precise details of the outward burst—when it happened, how long it lasted, the strength of the outward push, the factor by which the universe expanded during the burst, the amount of energy the inflaton deposited in ordinary matter as the burst drew to a close, and so on—depend on details, most notably the size and shape of the inflaton field’s potential energy, that are presently beyond our ability to determine from theoretical considerations alone. So for many years physicists have studied all sorts of possibilities—various shapes for the potential energy, various numbers of inflaton fields that work in tandem, and so on—and determined which choices give rise to theories consistent with astronomical observations. The important thing is that there are aspects of inflationary cosmological theories that transcend the details and hence are common to essentially any realization. The outward burst itself, by definition, is one such feature, and hence any inflationary model comes with a bang. But there are a number of other features inherent to all inflationary models that are vital because they solve important problems that have stumped standard big bang cosmology.
Inflation and the Horizon Problem
One such problem is called the horizon problem and concerns the uniformity of the microwave background radiation that we came across previously. Recall that the temperature of the microwave radiation reaching us from one direction in space agrees with that coming from any other direction to fantastic accuracy (to better than a thousandth of a degree). This observational fact is pivotal, because it attests to homogeneity throughout space, allowing for enormous simplifications in theoretical models of the cosmos. In earlier chapters, we used this homogeneity to narrow down drastically the possible shapes for space and to argue for a uniform cosmic time. The problem arises when we try to explain how the universe became so uniform. How is it that vastly distant regions of the universe have arranged themselves to have nearly identical temperatures?
If you think back to Chapter 4, one possibility is that just as nonlocal quantum entanglement can correlate the spins of two widely separated particles, maybe it can also correlate the temperatures of two widely separated regions of space. While this is an interesting suggestion, the tremendous dilution of entanglement in all but the most controlled settings, as discussed at the end of that chapter, essentially rules it out. Okay, perhaps there is a simpler explanation. Maybe a long time ago when every region of space was nearer to every other, their temperatures equalized through their close contact much as a hot kitchen and a cool living room come to the same temperature when a door between them is opened for a while. In the standard big bang theory, though, this explanation also fails. Here’s one way to think about it.
Imagine watching a film that depicts the full course of cosmic evolution from the beginning until today. Pause the film at some arbitrary moment and ask yourself: Could two particular regions of space, like the kitchen and the living room, have influenced each other’s temperature? Could they have exchanged light and heat? The answer depends on two things: The distance between the regions and the amount of time that has elapsed since the bang. If their separation is less than the distance light could have traveled in the time since the bang, then the regions could have influenced each other; otherwise, they couldn’t have. Now, you might think that all regions of the observable universe could have interacted with each other way back near the beginning because the farther back we wind the film, the closer the regions become and hence the easier it is for them to interact. But this reasoning is too quick; it doesn’t take account of the fact that not only were regions of space closer, but there was also less time for them to have communicated.
To do a proper analysis, imagine running the cosmic film in reverse while focusing on two regions of space currently on opposite sides of the observable universe—regions that are so distant that they are currently beyond each other’s spheres of influence. If in order to halve their separation we have to roll the cosmic film more than halfway back toward the beginning, then even though the regions of space were closer together, communication between them was still impossible: they were half as far apart, but the time since the bang was less than half of what it is today, and so light could travel only less than half as far. Similarly, if from that point in the film we have to run more than halfway back to the beginning in order to halve the separation between the regions once again, communication becomes more difficult still. With this kind of cosmic evolution, even though regions were closer together in the past, it becomes more puzzling—not less—that they somehow managed to equalize their temperatures. Relative to how far light can travel, the regions become increasingly cut off as we examine them ever farther back in time.
This is exactly what happens in the standard big bang theory. In the standard big bang, gravity acts only as an attractive force, and so, ever since the beginning, it has been acting to slow the expansion of space. Now, if something is slowing down, it will take more time to cover a given distance. For instance, imagine that Secretariat left the gate at a blistering pace and covered the first half of a racecourse in two minutes, but because it’s not his best day, he slows down considerably during the second half and takes three more minutes to finish. When viewing a film of the race in reverse, we’d have to roll the film more than halfway back in order to see Secretariat at the course’s halfway mark (we’d have to run the five-minute film of the race all the way back to the two-minute mark). Similarly, since in the standard big bang theory gravity slows the expansion of space, from any point in the cosmic film we have to wind more than halfway back in time in order to halve the separation between two regions. And, as above, this means that even though the regions of space were closer together at earlier times, it was more difficult—not less—for them to influence each other and hence more puzzling—not less—that they somehow reached the same temperature.
Physicists define a region’s cosmic horizon (or horizon for short) as the most distant surrounding regions of space that are close enough to the given region for the two to have exchanged light signals in the time since the bang. The analogy is to the most distant things we can see on earth’s surface from any particular vantage point.15 The horizon problem, then, is the puzzle, inherent in the observations, that regions whose horizons have always been separate—regions that could never have interacted, communicated, or exerted any kind of influence on each other—somehow have nearly identical temperatures.
The horizon problem does not imply that the standard big bang model is wrong, but it does cry out for explanation. Inflationary cosmology provides one.
In inflationary cosmology, there was a brief instant during which gravity was repulsive and this drove space to expand faster and faster. During this part of the cosmic film, you would have to wind the film less than halfway back in order to halve the distance between two regions. Think of a race in which Secretariat covers the first half of the course in two minutes and, because he’s having the run of his life, speeds up and blazes through the second half in one minute. You’d only have to wind the three-minute film of the race back to the two-minute mark—less than halfway back—to see him at the course’s halfway point. Similarly, the increasingly rapid separation of any two regions of space during inflationary expansion implies that halving their separation requires winding the cosmic film less—much less—than halfway back toward the beginning. As we go farther back in time, therefore, it becomes easier for any two regions of space to influence each other, because, proportionally speaking, there is more time for them to communicate. Calculations show that if the inflationaryexpansion phase drove space to expand by at least a factor of 1030, an amount that is readily achieved in specific realizations of inflationary expansion, all the regions in space that we currently see—all the regions in space whose temperatures we have measured—were able to communicate as easily as the adjacent kitchen and living room and hence efficiently come to a common temperature in the earliest moments of the universe.16 In a nutshell, space expands slowly enough in the very beginning for a uniform temperature to be broadly established and then, through an intense burst of ever more rapid expansion, the universe makes up for the sluggish start and widely disperses nearby regions.
That’s how inflationary cosmology explains the otherwise mysterious uniformity of the microwave background radiation suffusing space.
Inflation and the Flatness Problem
A second problem addressed by inflationary cosmology has to do with the shape of space. In Chapter 8, we imposed the criterion of uniform spatial symmetry and found three ways in which the fabric of space can curve. Resorting to our two-dimensional visualizations, the possibilities are positive curvature (shaped like the surface of a ball), negative curvature (saddle-shaped), and zero curvature (shaped like an infinite flat tabletop or like a finite-sized video game screen). Since the early days of general relativity, physicists have realized that the total matter and energy in each volume of space—the matter/energy density—determine the curvature of space. If the matter/energy density is high, space will pull back on itself in the shape of a sphere; that is, there will be positive curvature. If the matter/energy density is low, space will flare outward like a saddle; that is, there will be negative curvature. Or, as mentioned in the last chapter, for a very special amount of matter/energy density—the critical density, equal to the mass of about five hydrogen atoms (about 10−23 grams) in each cubic meter—space will lie just between these two extremes, and will be perfectly flat: that is, there will be no curvature.
Now for the puzzle.
The equations of general relativity, which underlie the standard big bang model, show that if the matter/energy density early on was exactly equal to the critical density, then it would stay equal to the critical density as space expanded.17 But if the matter/energy density was even slightly more or slightly less than the critical density, subsequent expansion would drive it enormously far from the critical density. Just to get a feel for the numbers, if at one second ATB, the universe was just shy of criticality, having 99.99 percent of the critical density, calculations show that by today its density would have been driven all the way down to .00000000001 of the critical density. It’s kind of like the situation faced by a mountain climber who is walking across a razor-thin ledge with a steep drop off on either side. If her step is right on the mark, she’ll make it across. But even a tiny misstep that’s just a little too far left or right will be amplified into a significantly different outcome. (And, at the risk of having one too many analogies, this feature of the standard big bang model also reminds me of the shower years ago in my college dorm: if you managed to set the knob perfectly, you could get a comfortable water temperature. But if you were off by the slightest bit, one way or the other, the water would be either scalding or freezing. Some students just stopped showering altogether.)
For decades, physicists have been attempting to measure the matter/ energy density in the universe. By the 1980s, although the measurements were far from complete, one thing was certain: the matter/energy density of the universe is not thousands and thousands of times smaller or larger than the critical density; equivalently, space is not substantially curved, either positively or negatively. This realization cast an awkward light on the standard big bang model. It implied that for the standard big bang to be consistent with observations, some mechanism—one that nobody could explain or identify—must have tuned the matter/energy density of the early universe extraordinarilyclose to the critical density. For example, calculations showed that at one second ATB, the matter/energy density of the universe needed to have been within a millionth of a millionth of a percent of the critical density; if the matter/energy density deviated from the critical value by any more than this minuscule amount, the standard big bang model predicts a matter/energy density today that is vastly different from what we observe. According to the standard big bang model, then, the early universe, much like the mountain climber, teetered along an extremely narrow ledge. A tiny deviation in conditions billions of years ago would have led to a present-day universe very different from the one revealed by astronomers’ measurements. This is known as the flatness problem.
Although we’ve covered the essential idea, it’s important to understand the sense in which the flatness problem is a problem. By no means does the flatness problem show that the standard big bang model is wrong. A staunch believer reacts to the flatness problem with a shrug of the shoulders and the curt reply “That’s just how it was back then,” taking the finely tuned matter/energy density of the early universe—which the standard big bang requires to yield predictions that are in the same ball-park as observations—as an unexplained given. But this answer makes most physicists recoil. Physicists feel that a theory is grossly unnatural if its success hinges on extremely precise tunings of features for which we lack a fundamental explanation. Without supplying a reason for why the matter/energy density of the early universe would have been so finely tuned to an acceptable value, many physicists have found the standard big bang model highly contrived. Thus, the flatness problem highlights the extreme sensitivity of the standard big bang model to conditions in the remote past of which we know very little; it shows how the theory must assume the universe was just so, in order to work.
By contrast, physicists long for theories whose predictions are insensitive to unknown quantities such as how things were a long time ago. Such theories feel robust and natural because their predictions don’t depend delicately on details that are hard, or perhaps even impossible, to determine directly. This is the kind of theory provided by inflationary cosmology, and its solution to the flatness problem illustrates why.
The essential observation is that whereas attractive gravity amplifies any deviation from the critical matter/energy density, the repulsive gravity of the inflationary theory does the opposite: it reduces any deviation from the critical density. To get a feel for why this is the case, it’s easiest to use the tight connection between the universe’s matter/energy density and its curvature to reason geometrically. In particular, notice that even if the shape of the universe were significantly curved early on, after inflationary expansion a portion of space large enough to encompass today’s observable universe looks very nearly flat. This is a feature of geometry we are all well aware of: The surface of a basketball is obviously curved, but it took both time and thinkers with chutzpah before everyone was convinced that the earth’s surface was also curved. The reason is that, all else being equal, the larger something is, the more gradually it curves and the flatter a patch of a given size on its surface appears. If you draped the state of Nebraska over a sphere just a few hundred miles in diameter, as in Figure 10.4a, it would look curved, but on the earth’s surface, as just about all Nebraskans concur, it looks flat. If you laid Nebraska out on a sphere a billion times larger than earth, it would look flatter still. In inflationary cosmology, space was stretched by such a colossal factor that the observable universe, the part we can see, is but a small patch in a gigantic cosmos. And so, like Nebraska laid out on a giant sphere as in Figure 10.4d, even if the entire universe were curved, the observable universe would be very nearly flat.18
Figure 10.4 A shape of fixed size, such as that of the state of Nebraska, appears flatter and flatter when laid out on larger and larger spheres. In this analogy, the sphere represents the entire universe, while Nebraska represents the observable universe—the part within our cosmic horizon.
It’s as if there are powerful, oppositely oriented magnets embedded in the mountain climber’s boots and the thin ledge she is crossing. Even if her step is aimed somewhat off the mark, the strong attraction between the magnets ensures that her foot lands squarely on the ledge. Similarly, even if the early universe deviated a fair bit from the critical matter/energy density and hence was far from flat, the inflationary expansion ensured that the part of space we have access to was driven toward a flat shape and that the matter/energy density we have access to was driven to the critical value.
Progress and Prediction
Inflationary cosmology’s insights into the horizon and flatness problems represent tremendous progress. For cosmological evolution to yield a homogeneous universe whose matter/energy density is even remotely close to what we observe today, the standard big bang model requires precise, unexplained, almost eerie fine-tuning of conditions early on. This tuning can be assumed, as the staunch adherent to the standard big bang advocates, but the lack of an explanation makes the theory seem artificial. To the contrary, regardless of the detailed properties of the early universe’s matter/energy density, inflationary cosmological evolution predicts that the part we can see should be very nearly flat; that is, it predicts that the matter/energy density we observe should be very nearly 100 percent of the critical density.
Insensitivity to the detailed properties of the early universe is a wonderful feature of the inflationary theory, because it allows for definitive predictions irrespective of our ignorance of conditions long ago. But we must now ask: How do these predictions stand up to detailed and precise observations? Do the data support inflationary cosmology’s prediction that we should observe a flat universe containing the critical density of matter/energy?
For many years the answer seemed to be “Not quite.” Numerous astronomical surveys carefully measured the amount of matter/energy that could be seen in the cosmos, and the answer they came up with was about 5 percent of the critical density. This is far from the enormous or minuscule densities to which the standard big bang naturally leads— without artificial fine-tuning—and is what I alluded to earlier when I said that observations establish that the universe’s matter/energy density is not thousands and thousands of times larger or smaller than the critical amount. Even so, 5 percent falls short of the 100 percent inflation predicts. But physicists have long realized that care must be exercised in evaluating the data. The astronomical surveys tallying 5 percent took account only of matter and energy that gave off light and hence could be seen with astronomers’ telescopes. And for decades, even before the discovery of inflationary cosmology, there had been mounting evidence that the universe has a hefty dark side.
A Prediction of Darkness
During the early 1930s, Fritz Zwicky, a professor of astronomy at the California Institute of Technology (a famously caustic scientist whose appreciation for symmetry led him to call his colleagues spherical bastards because, he explained, they were bastards any way you looked at them19), realized that the outlying galaxies in the Coma cluster, a collection of thousands of galaxies some 370 million light-years from earth, were moving too quickly for their visible matter to muster an adequate gravitational force to keep them tethered to the group. Instead, his analysis showed that many of the fastest-moving galaxies should be flung clear of the cluster, like water droplets thrown off a spinning bicycle tire. And yet none were. Zwicky conjectured that there might be additional matter permeating the cluster that did not give off light but supplied the additional gravitational pull necessary to hold the cluster together. His calculations showed that if this explanation was right, the vast majority of the cluster’s mass would comprise this nonluminous material. By 1936, corroborating evidence was found by Sinclair Smith of the Mount Wilson observatory, who was studying the Virgo cluster and came to a similar conclusion. But since both men’s observations, as well as a number of subsequent others, had various uncertainties, many remained unconvinced that there was voluminous unseen matter whose gravitational pull was keeping the groups of galaxies together.
Over the next thirty years observational evidence for nonluminous matter continued to mount,20 but it was the work of the astronomer Vera Rubin from the Carnegie Institution of Washington, together with Kent Ford and others, that really clinched the case. Rubin and her collaborators studied the movements of stars within numerous spinning galaxies and concluded that if what you see is what there is, then many of the galaxy’s stars should be routinely flung outward. Their observations showed conclusively that the visible galactic matter could not exert a gravitational grip anywhere near strong enough to keep the fastest-moving stars from breaking free. However, their detailed analyses also showed that the stars would remain gravitationally tethered if the galaxies they inhabited were immersed in a giant ball of nonluminous matter (as in Figure 10.5), whose total mass far exceeded that of the galaxy’s luminous material. And so, like an audience that infers the presence of a dark-robed mime even though it sees only his white-gloved hands flitting to and fro on the unlit stage, astronomers concluded that the universe must be suffused with dark matter—matter that does not clump together in stars and hence does not give off light, and that thus exerts a gravitational pull without revealing itself visibly. The universe’s luminous constituents—stars— were revealed as but floating beacons in a giant ocean of dark matter.
But if dark matter must exist in order to produce the observed motions of stars and galaxies, what’s it made of? So far, no one knows. The identity of the dark matter remains a major, looming mystery, although astronomers and physicists have suggested numerous possible constituents ranging from various kinds of exotic particles to a cosmic bath of miniature black holes. But even without determining its composition, by closely analyzing its gravitational effects astronomers have been able to determine with significant precision how much dark matter is spread throughout the universe. And the answer they’ve found amounts to about 25 percent of the critical density.21 Thus, together with the 5 percent found in visible matter, the dark matter brings our tally up to 30 percent of the amount predicted by inflationary cosmology.
Figure 10.5 A galaxy immersed in a ball of dark matter (with the dark matter artificially highlighted to make it visible in the figure).
Well, this is certainly progress, but for a long time scientists scratched their heads, wondering how to account for the remaining 70 percent of the universe, which, if inflationary cosmology was correct, had apparently gone AWOL. But then, in 1998, two groups of astronomers came to the same shocking conclusion, which brings our story full circle and once again reveals the prescience of Albert Einstein.
The Runaway Universe
Just as you may seek a second opinion to corroborate a medical diagnosis, physicists, too, seek second opinions when they come upon data or theories that point toward puzzling results. Of these second opinions, the most convincing are those that reach the same conclusion from a point of view that differs sharply from the original analysis. When the arrows of explanation converge on one spot from different angles, there’s a good chance that they’re pointing at the scientific bull’s-eye. Naturally then, with inflationary cosmology strongly suggesting something totally bizarre—that 70 percent of the universe’s mass/energy has yet to be measured or identified—physicists have yearned for independent confirmation. It has long been realized that measurement of the deceleration parameter would do the trick.
Since just after the initial inflationary burst, ordinary attractive gravity has been slowing the expansion of space. The rate at which this slowing occurs is called the deceleration parameter. A precise measurement of the parameter would provide independent insight into the total amount of matter in the universe: more matter, whether or not it gives off light, implies a greater gravitational pull and hence a more pronounced slowing of spatial expansion.
For many decades, astronomers have been trying to measure the deceleration of the universe, but although doing so is straightforward in principle, it’s a challenge in practice. When we observe distant heavenly bodies such as galaxies or quasars, we are seeing them as they were a long time ago: the farther away they are, the farther back in time we are looking. So, if we could measure how fast they were receding from us, we’d have a measure of how fast the universe was expanding in the distant past. Moreover, if we could carry out such measurements for astronomical objects situated at a variety of distances, we would have measured the universe’s expansion rate at a variety of moments in the past. By comparing these expansion rates, we could determine how the expansion of space is slowing over time and thereby determine the deceleration parameter.
Carrying out this strategy for measuring the deceleration parameter thus requires two things: a means of determining the distance of a given astronomical object (so that we know how far back in time we are looking) and a means of determining the speed with which the object is receding from us (so that we know the rate of spatial expansion at that moment in the past). The latter ingredient is easier to come by. Just as the pitch of a police car’s siren drops to lower tones as it rushes away from us, the frequency of vibration of the light emitted by an astronomical source also drops as the object rushes away. And since the light emitted by atoms like hydrogen, helium, and oxygen—atoms that are among the constituents of stars, quasars, and galaxies—has been carefully studied under laboratory conditions, a precise determination of the object’s speed can be made by examining how the light we receive differs from that seen in the lab.
But the former ingredient, a method for determining precisely how far away an object is, has proven to be the astronomer’s headache. The farther away something is, the dimmer you expect it to appear, but turning this simple observation into a quantitative measure is difficult. To judge the distance to an object by its apparent brightness, you need to know its intrinsic brightness—how bright it would be were it right next to you. And it is difficult to determine the intrinsic brightness of an object billions of light-years away. The general strategy is to seek a species of heavenly bodies that, for fundamental reasons of astrophysics, always burn with a standard, dependable brightness. If space were dotted with glowing 100-watt lightbulbs, that would do the trick, since we could easily determine a given bulb’s distance on the basis of how dim it appears (although it would be a challenge to see 100-watt bulbs from significantly far away). But, as space isn’t so endowed, what can play the role of standard-brightness lightbulbs, or, in astronomy-speak, what can play the role of standard candles? Through the years astronomers have studied a variety of possibilities, but the most successful candidate to date is a particular class of supernova explosions.
When stars exhaust their nuclear fuel, the outward pressure from nuclear fusion in the star’s core diminishes and the star begins to implode under its own weight. As the star’s core crashes in on itself, its temperature rapidly rises, sometimes resulting in an enormous explosion that blows off the star’s outer layers in a brilliant display of heavenly fireworks. Such an explosion is known as a supernova; for a period of weeks, a single exploding star can burn as bright as a billion suns. It’s truly mind-boggling: a single star burning as bright as almost an entire galaxy! Different types of stars— of different sizes, with different atomic abundances, and so on—give rise to different kinds of supernova explosions, but for many years astronomers have realized that certain supernova explosions always seem to burn with the same intrinsic brightness. These are type Ia supernova explosions.
In a type Ia supernova, a white dwarf star—a star that has exhausted its supply of nuclear fuel but has insufficient mass to ignite a supernova explosion on its own—sucks the surface material from a nearby companion star. When the dwarf star’s mass reaches a particular critical value, about 1.4 times that of the sun, it undergoes a runaway nuclear reaction that causes the star to go supernova. Since such supernova explosions occur when the dwarf star reaches the same critical mass, the characteristics of the explosion, including its overall intrinsic brightness, are largely the same from episode to episode. Moreover, since supernovae, unlike 100-watt lightbulbs, are so fantastically powerful, not only do they have a standard, dependable brightness but you can also see them clear across the universe. They are thus prime candidates for standard candles.22
In the 1990s, two groups of astronomers, one led by Saul Perlmutter at the Lawrence Berkeley National Laboratory, and the other led by Brian Schmidt at the Australian National University, set out to determine the deceleration—and hence the total mass/energy—of the universe by measuring the recession speeds of type Ia supernovae. Identifying a supernova as being of type Ia is fairly straightforward because the light their explosions generate follows a distinctive pattern of steeply rising then gradually falling intensity. But actually catching a type Ia supernova in the act is no small feat, since they happen only about once every few hundred years in a typical galaxy. Nevertheless, through the innovative technique of simultaneously observing thousands of galaxies with wide-field-of-view telescopes, the teams were able to find nearly four dozen type Ia supernovae at various distances from earth. After painstakingly determining the distance and recessional velocities of each, both groups came to a totally unexpected conclusion: ever since the universe was about 7 billion years old, its expansion rate has not been decelerating. Instead, the expansion rate has been speeding up.
The groups concluded that the expansion of the universe slowed down for the first 7 billion years after the initial outward burst, much like a car slowing down as it approaches a highway tollbooth. This was as expected. But the data revealed that, like a driver who hits the gas pedal after gliding through the EZ-Pass lane, the expansion of the universe has been accelerating ever since. The expansion rate of space 7 billion years ATB was less than the expansion rate 8 billion years ATB, which was less than the expansion rate 9 billion years ATB, and so on, all of which are less than the expansion rate today. The expected deceleration of spatial expansion has turned out to be an unexpected acceleration.
But how could this be? Well, the answer provides the corroborating second opinion regarding the missing 70 percent of mass/energy that physicists had been seeking.
The Missing 70 Percent
If you cast your mind back to 1917 and Einstein’s introduction of a cosmological constant, you have enough information to suggest how it might be that the universe is accelerating. Ordinary matter and energy give rise to ordinary attractive gravity, which slows spatial expansion. But as the universe expands and things get increasingly spread out, this cosmic gravitational pull, while still acting to slow the expansion, gets weaker. And this sets us up for the new and unexpected twist. If the universe should have a cosmological constant—and if its magnitude should have just the right, small value—up until about 7 billion years ATB its gravitational repulsion would have been overwhelmed by the usual gravitational attraction of ordinary matter, yielding a net slowing of expansion, in keeping with the data. But then, as ordinary matter spread out and its gravitational pull diminished, the repulsive push of the cosmological constant (whose strength does not change as matter spreads out) would have gradually gained the upper hand, and the era of decelerated spatial expansion would have given way to a new era of accelerated expansion.
In the late 1990s, such reasoning and an in-depth analysis of the data led both the Perlmutter group and the Schmidt group to suggest that Einstein had not been wrong some eight decades earlier when he introduced a cosmological constant into the gravitational equations. The universe, they suggested, does have a cosmological constant.23 Its magnitude is not what Einstein proposed, since he was chasing a static universe in which gravitational attraction and repulsion matched precisely, and these researchers found that for billions of years repulsion has dominated. But that detail notwithstanding, should the discovery of these groups continue to hold up under the close scrutiny and follow-up studies now under way, Einstein will have once again seen through to a fundamental feature of the universe, one that this time took more than eighty years to be confirmed experimentally.
The recession speed of a supernova depends on the difference between the gravitational pull of ordinary matter and the gravitational push of the “dark energy” supplied by the cosmological constant. Taking the amount of matter, both visible and dark, to be about 30 percent of the critical density, the supernova researchers concluded that the accelerated expansion they had observed required an outward push of a cosmological constant whose dark energy contributes about 70 percent of the critical density.
This is a remarkable number. If it’s correct, then not only does ordinary matter—protons, neutrons, electrons—constitute a paltry 5 percent of the mass/energy of the universe, and not only does some currently unidentified form of dark matter constitute at least five times that amount, but also the majority of the mass/energy in the universe is contributed by a totally different and rather mysterious form of dark energy that is spread throughout space. If these ideas are right, they dramatically extend the Copernican revolution: not only are we not the center of the universe, but the stuff of which we’re made is like flotsam on the cosmic ocean. If protons, neutrons, and electrons had been left out of the grand design, the total mass/energy of the universe would hardly have been diminished.
But there is a second, equally important reason why 70 percent is a remarkable number. A cosmological constant that contributes 70 percent of the critical density would, together with the 30 percent coming from ordinary matter and dark matter, bring the total mass/energy of the universe right up to the full 100 percent predicted by inflationary cosmology! Thus, the outward push demonstrated by the supernova data can be explained by just the right amount of dark energy to account for the unseen 70 percent of the universe that inflationary cosmologists had been scratching their heads over. The supernova measurements and inflationary cosmology are wonderfully complementary. They confirm each other. Each provides a corroborating second opinion for the other.24
Combining the observational results of supernovae with the theoretical insights of inflation, we thus arrive at the following sketch of cosmic evolution, summarized in Figure 10.6. Early on, the energy of the universe was carried by the inflaton field, which was perched away from its minimum energy state. Because of its negative pressure, the inflaton field drove an enormous burst of inflationary expansion. Then, some 10−35 seconds later, as the inflaton field slid down its potential energy bowl, the burst of expansion drew to a close and the inflaton released its pent-up energy to the production of ordinary matter and radiation. For many billions of years, these familiar constituents of the universe exerted an ordinary attractive gravitational pull that slowed the spatial expansion. But as the universe grew and thinned out, the gravitational pull diminished. About 7 billion years ago, ordinary gravitational attraction became weak enough for the gravitational repulsion of the universe’s cosmological constant to become dominant, and since then the rate of spatial expansion has been continually increasing.
About 100 billion years from now, all but the closest of galaxies will be dragged away by the swelling space at faster-than-light speed and so would be impossible for us to see, regardless of the power of telescopes used. If these ideas are right, then in the far future the universe will be a vast, empty, and lonely place.
Figure 10.6 A time line of cosmic evolution. (a) Inflationary burst. (b) Standard Big Bang evolution. (c) Era of accelerated expansion.
Puzzles and Progress
With these discoveries, it thus seemed manifest that the pieces of the cosmological puzzle were falling into place. Questions left unanswered by the standard big bang theory—What ignited the outward swelling of space? Why is the temperature of the microwave background radiation so uniform? Why does space seem to have a flat shape?—were addressed by the inflationary theory. Even so, thorny issues regarding fundamental origins have continued to mount: Was there an era before the inflationary burst, and if so, what was it like? What introduced an inflaton field displaced from its lowest-energy configuration to initiate the inflationary expansion? And, the newest question of all, why is the universe apparently composed of such a mishmash of ingredients—5 percent familiar matter, 25 percent dark matter, 70 percent dark energy? Despite the immensely pleasing fact that this cosmic recipe agrees with inflation’s prediction that the universe should have 100 percent of the critical density, and although it simultaneously explains the accelerated expansion found by supernova studies, many physicists view the hodgepodge composition as distinctly unattractive. Why, many have asked, has the universe’s composition turned out to be so complicated? Why are there a handful of disparate ingredients in such seemingly random abundances? Is there some sensible underlying plan that theoretical studies have yet to reveal?
No one has advanced any convincing answers to these questions; they are among the pressing research problems driving current cosmological research and they serve to remind us of the many tangled knots we must still unravel before we can claim to have fully understood the birth of the universe. But despite the significant challenges that remain, inflation is far and away the front-running cosmological theory. To be sure, physicists’ belief in inflation is grounded in the achievements we’ve so far discussed. But the confidence in inflationary cosmology has roots that run deeper still. As we’ll see in the next chapter, a number of other considerations— coming from both observational and theoretical discoveries—have convinced many physicists who work in the field that the inflationary framework is our generation’s most important and most lasting contribution to cosmological science.