The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos - Brian Greene (2011)
Chapter 3. Eternity and Infinity
The Inflationary Multiverse
A pioneering group of physicists in the mid-1900s realized that if you were to shut off the sun, remove the other stars from the Milky Way, and even sweep away the more distant galaxies, space would not be black. To the human eye it would appear black, but if you could see radiation in the microwave part of the spectrum, then every which way you turned you’d see a uniform glow. Its origin? The origin. Remarkably, these physicists discovered a pervasive sea of microwave radiation filling space that is a present-day relic of the universe’s creation. The story of this breakthrough recounts a phenomenal achievement of the big bang theory, but in time it also revealed one of the theory’s fundamental shortcomings and thus set the stage for the next major breakthrough in cosmology after the pioneering works of Friedmann and Lemaître: the inflationary theory.
Inflationary cosmology modifies the big bang theory by inserting an intense burst of enormously fast expansion during the universe’s earliest moments. This modification, as we will see, proves essential to explaining some otherwise perplexing features of the relic radiation. But more than that, inflationary cosmology is a key chapter in our story because scientists have gradually realized over the last few decades that the most convincing versions of the theory yield a vast collection of parallel universes, radically transforming the complexion of reality.
Relics of a Hot Beginning
George Gamow, a hulking six-foot-three Russian physicist known for important contributions to quantum and nuclear physics in the early twentieth century, was as quick-witted and fun-loving as he was hard-living (in 1932, he and his wife tried to defect from the Soviet Union by paddling across the Black Sea in a kayak stocked with a healthy assortment of chocolate and brandy; when bad weather sent the two scurrying back to shore, Gamow was able to fast-talk the authorities with a tale of the unfortunately failed scientific experiments he’d been undertaking at sea). In the 1940s, after having successfully slipped past the iron curtain (on dry land, with less chocolate) and settled in at Washington University in St. Louis, Gamow turned his attention to cosmology. With critical assistance from his phenomenally talented graduate student Ralph Alpher, Gamow’s research resulted in a far more detailed and vivid picture of the universe’s earliest moments than had been revealed by the earlier work of Friedmann (who had been Gamow’s teacher back in Leningrad) and Lemaître. With a little modern updating, Gamow and Alpher’s picture looks like this.
Just after its birth, the stupendously hot and dense universe experienced a frenzy of activity. Space rapidly expanded and cooled, allowing a particle stew to congeal from the primordial plasma. For the first three minutes, the rapidly falling temperature remained sufficiently high for the universe to act like a cosmic nuclear furnace, synthesizing the simplest atomic nuclei: hydrogen, helium, and trace amounts of lithium. But with the passing of just a few more minutes, the temperature dropped to about 108 Kelvin (K), roughly 10,000 times the surface temperature of the sun. Although immensely high by everyday standards, this temperature was too low to support further nuclear processes, and so from this time on the particle commotion largely abated. For eons that followed, not much happened except that space kept expanding and the particle bath kept cooling.
Then, some 370,000 years later, when the universe had cooled to about 3000 K, half the sun’s surface temperature, the cosmic monotony was interrupted by a pivotal turn of events. To that point, space had been filled with a plasma of particles carrying electric charge, mostly protons and electrons. Because electrically charged particles have the unique ability to jostle photons—particles of light—the primordial plasma would have appeared opaque; the photons, incessantly buffeted by electrons and protons, would have provided a diffuse glow similar to a car’s high beams cloaked by a dense fog. But when the temperature dropped below 3000 K, the rapidly moving electrons and nuclei slowed sufficiently to amalgamate into atoms; electrons were captured by the atomic nuclei and drawn into orbit. This was a key transformation. Because protons and electrons have equal but opposite charges, their atomic unions are electrically neutral. And since a plasma of electrically neutral composites allows photons to slip through like a hot knife through butter, the formation of atoms allowed the cosmic fog to clear and the luminous echo of the big bang to be released. The primordial photons have been streaming through space ever since.
Well, with one important caveat. Although no longer knocked to and fro by electrically charged particles, the photons have been subject to one other important influence. As space expands, things dilute and cool, including photons. But unlike particles of matter, photons don’t slow down when they cool; being particles of light, they always travel at light speed. Instead, when photons cool their vibrational frequencies decrease, which means they change color. Violet photons will shift to blue, then to green, to yellow, to red, and then into the infrared (like those visible with night goggles), the microwave (like those that heat food by bouncing around your microwave oven), and finally into the domain of radio frequencies.
As Gamow first realized and as Alpher and his collaborator Robert Herman worked out with greater fidelity, all this means that if the big bang theory is correct, then space everywhere should now be filled with remnant photons from the creation event, streaming every which way, whose vibrational frequencies are determined by how much the universe has expanded and cooled during the billions of years since they were released. Detailed mathematical calculations showed that the photons should have cooled close to absolute zero, placing their frequencies in the microwave part of the spectrum. For this reason, they are called the cosmic microwave background radiation.
I recently reread the papers of Gamow, Alpher, and Herman that in the late 1940s announced and explained these conclusions. They are marvels of theoretical physics. The technical analyses involved require hardly more than a grounding in undergraduate physics, and yet the results are profound. The authors concluded that we are all immersed in a bath of photons, a cosmic heirloom bequeathed to us by the universe’s fiery birth.
With that buildup, you may find it surprising that the papers were ignored. This was mostly because they were written during an era dominated by quantum and nuclear physics. Cosmology had yet to make its mark as a quantitative science, so the physics culture was less receptive to what seemed like fringe theoretical studies. To some degree, the papers also languished because of Gamow’s unusually playful style (he once modified the authorship of a paper he was writing with Alpher to include his friend the future Nobel laureate Hans Bethe, just to make the paper’s byline—Alpher, Bethe, Gamow—sound like the first three letters of the Greek alphabet), which resulted in some physicists taking him less seriously than he deserved. Try as they might, Gamow, Alpher, and Herman could not interest anyone in their results, let alone persuade astronomers to devote the significant effort required to attempt to detect the relic radiation they predicted. The papers were quickly forgotten.
In the early 1960s, unaware of the earlier work, the Princeton physicists Robert Dicke and Jim Peebles went down a similar path and also realized that the big bang’s legacy should be the presence of a ubiquitous background radiation filling space.1 Unlike the members of Gamow’s team, however, Dicke was a renowned experimentalist and so didn’t need to persuade anyone to seek the radiation observationally. He could do it himself. Together with his students David Wilkinson and Peter Roll, Dicke devised an experimental scheme to capture some of the big bang’s vestigial photons. But before the Princeton researchers could put their plan to the test, they received one of the most famous telephone calls in the history of science.
While Dicke and Peebles had been calculating, the physicists Arno Penzias and Robert Wilson at Bell Labs, less than thirty miles from Princeton, had been struggling with a radio communications antenna (coincidentally, it was based on a design Dicke had come up with in the 1940s). No matter what adjustments they made, the antenna hissed with a steady, unavoidable background noise. Penzias and Wilson were convinced that something was wrong with their equipment. But then came a serendipitous chain of conversations. It began with a talk Peebles gave in February 1965 at Johns Hopkins University, which was attended by the Carnegie Institution radio astronomer Kenneth Turner, who mentioned the results he heard Peebles present to his MIT colleague Bernard Burke, who happened to be in touch with Penzias at Bell Labs. Hearing of the Princeton research, the Bell Labs team realized that their antenna was hissing for good reason: it was picking up the cosmic microwave background radiation. Penzias and Wilson called Dicke, who quickly confirmed that they had unintentionally tapped into the reverberation of the big bang.
The two groups agreed to publish their papers simultaneously in the prestigious Astrophysical Journal. The Princeton group discussed their theory of the background radiation’s cosmological origin, while the Bell Labs team reported, in the most conservative of language and with no mention of cosmology, the detection of uniform microwave radiation permeating space. Neither paper mentioned the earlier work of Gamow, Alpher, and Herman. For their discovery, Penzias and Wilson were awarded the 1978 Nobel Prize in physics.
Gamow, Alpher, and Herman were deeply dismayed, and in the years that followed struggled mightily to have their work recognized. Only gradually and belatedly has the physics community saluted their primary role in this monumental discovery.
The Uncanny Uniformity of Ancient Photons
During the decades since it was first observed, the cosmic microwave background radiation has become a crucial tool in cosmological investigations. The reason is clear. In a great many fields, researchers would give their eyeteeth to have an unfettered, direct glimpse of the past. Instead, they generally have to piece together a view of remote conditions on the basis of evidence from remnants—weathered fossils, decaying parchments, or mummified remains. Cosmology is the one field in which we can actually witness history. The pinpoints of starlight we can see with the naked eye are streams of photons that have been traveling toward us for a few years or a few thousand. The light from more distant objects, captured by powerful telescopes, has been traveling toward us far longer, sometimes for billions of years. When you look at such ancient light, you are seeing—literally—ancient times. Those primeval comings and goings transpired far away, but the apparent large-scale uniformity of the universe argues strongly that what was happening there was also, on average, happening here. In looking up, we are looking back.
The cosmic microwave photons allow us to make the most of this opportunity. No matter how technology may improve, the microwave photons are the oldest we can hope to see, because their elder brethren were trapped by the foggy conditions that prevailed during earlier epochs. When we examine the cosmic microwave background photons, we are glimpsing how things were nearly 14 billion years ago.
Calculations show that today there are about 400 million of these cosmic microwave photons racing through every cubic meter of space. Although our eyes can’t see them, an old-fashioned television set can. About 1 percent of the snow on a television that’s been disconnected from the cable signal and tuned to a station that’s ceased broadcasting is due to reception of the big bang’s photons. It’s a curious thought. The very same airwaves that carry reruns of All in the Family and The Honeymooners are infused with some of the universe’s oldest fossils, photons communicating a drama that played out when the cosmos was but a few hundred thousand years old.
The big bang model’s correct prediction that space would be filled with microwave background radiation was a triumph. During a mere three hundred years of scientific thought and technological progress, our species went from peering through rudimentary telescopes and dropping balls from leaning towers to grasping physical processes at work just after the universe was born. Nevertheless, further investigation of the data raised a pointed challenge. Ever more refined measurements of the radiation’s temperature, made not with television sets but with some of the most precise astronomical equipment ever built, showed that the radiation is thoroughly—uncannily—uniform across space. Regardless of where you point your detector, the temperature of the radiation is 2.725 degrees above absolute zero. The puzzle is to explain how such fantastic uniformity came to be.
Given the ideas presented in Chapter 2 (and my comment four paragraphs ago), I can imagine your saying, “Well, that’s just the cosmological principle at work: no location in the universe is special when compared with any other, so the temperature at each should be the same.” Fair enough. But remember that the cosmological principle was a simplifying assumption that physicists, including Einstein, invoked to make the mathematical analysis of the universe’s evolution tractable. Since the microwave background radiation is indeed uniform throughout space, it provides convincing observational evidence for the cosmological principle, and it strengthens our confidence in conclusions the principle helped reveal. But the radiation’s astounding uniformity shines a glaring spotlight on the cosmological principle itself. Reasonable though the cosmological principle may sound, what mechanism established the cosmos-wide uniformity that observations confirm?
Faster Than the Speed of Light
We’ve all had the mildly unsettling sensation of shaking someone’s hand and finding it steamy hot (not so bad) or clammy cold (definitely worse). But were you to hold on to that hand, you’d find that the modest temperature differential would quickly subside. When objects are in contact, heat migrates from the hotter to the colder, until their temperatures are equal. You experience this all the time. It’s why coffee left on your desk eventually comes to room temperature.
Similar reasoning would seem to explain the uniformity of the microwave background radiation. As with holding hands and standing coffee, the uniformity presumably reflects the familiar reversion of an environment to an overall common temperature. The sole novelty of the process is that the reversion is supposed to have taken place over cosmic distances.
In the big bang theory, however, the explanation fails.
For places or things to reach a common temperature, an essential condition is mutual contact. It may be direct, as with shaking hands, or, minimally, through an exchange of information so that conditions at distinct locations can become correlated. Only through such mutual influence can a shared, communal environment be achieved. A thermos is designed to prevent such interactions, thwarting the drive to uniformity and preserving temperature differences.
This simple observation highlights the problem with the naïve explanation of the cosmic temperature uniformity. Locations in space that are very far apart—say, one point way off to your right, so deep in the night sky that the first light it ever emitted has only just reached you, and a second, similar point way off to your left—have never interacted. Although you can see both, light from one still has an enormous distance to cover before it reaches the other. Thus, hypothetical observers situated at the distant left and right locations have yet to see each other, and since the speed of light sets the upper limit for how fast anything can travel, they’ve yet to interact in any way. To use the language of the previous chapter, they are beyond each other’s cosmic horizon.
This description makes the mystery manifest. You’d be floored if inhabitants of these distant locations spoke the same language and had libraries filled with the same books. With no contact, how could a common heritage have been established? You should be equally floored to learn that without any apparent contact, these widely separated regions share a common temperature, one that matches to an accuracy of better than four decimal places.
Years ago, when I first learned of this puzzle, I was floored. But on further thought, I became puzzled by the puzzle. How could two objects that were once close together—as we believe all things in the observable universe were at the time of the big bang—have separated so quickly that light emitted by one wouldn’t have time to reach the other? Light sets the cosmic speed limit, so how could the objects achieve a spatial separation greater than what light would have had time to traverse?
The answer highlights a point that’s often not adequately stressed. The speed limit set by light refers solely to the motion of objects through space. But galaxies recede from one another not because they are traveling through space—galaxies don’t have jet engines—but rather because space itself is swelling and the galaxies are being dragged along by the overall flow.2 And the thing is, relativity places no limit on how fast space can swell, so there is no limit on how fast galaxies that are being pushed apart by the swell recede from one another. The rate of recession between any two galaxies can exceed any speed, including the speed of light.
Indeed, the mathematics of general relativity shows that in the universe’s earliest moments, space would have swelled so fast that regions would have been propelled apart at greater than light speed. As a result, they would have been unable to exert any influence on one another. The difficulty then is to explain how nearly identical temperatures were established in independent cosmic domains, a puzzle cosmologists have named the horizon problem.
In 1979, Alan Guth (then working at the Stanford Linear Accelerator Center) came up with an idea that, with subsequent critical refinements made by Andrei Linde (then carrying out research at the Lebedev Physical Institute in Moscow), and by Paul Steinhardt and Andreas Albrecht (a professor-student duo who were then working at the University of Pennsylvania), is widely believed to solve the horizon problem. The solution, inflationary cosmology, relies on some subtle features of Einstein’s general relativity that I’ll describe in a moment, but its broad outline can be readily summarized.
The horizon problem afflicts the standard big bang theory because regions of space separate too quickly for thermal equality to be established. The inflationary theory resolves the problem by slowing the speed with which the regions were separating very early on, providing them ample time to come to the same temperature. The theory then proposes that after the completion of these “cosmic handshakes” there came a brief burst of enormously fast and ever-quickening expansion—called inflationary expansion—which more than compensated for the sluggish start, rapidly driving the regions to vastly distant positions in the sky. The uniform conditions we observe no longer pose a mystery, since a common temperature was established before the regions were rapidly driven apart.3 In broad strokes, that’s the essence of the inflationary proposal.*
Bear in mind, however, that physicists don’t dictate how the universe expands. As far as we can tell from our most refined observations, Einstein’s equations of general relativity do. The viability of the inflationary scenario thus depends on whether its proposed modification to the standard big bang expansion can emerge from Einstein’s mathematics. At first glance, this is far from obvious.
For example, I’m pretty sure that if you were to bring Newton up to date by giving him a five-minute primer on general relativity, explaining the outlines of warped space and the expanding universe, he’d find your subsequent description of the inflationary proposal preposterous. Newton would sternly maintain that regardless of fancy math and newfangled Einsteinian language, gravity is still an attractive force. And so, he would emphasize with a pound on the table, gravity acts to pull objects together, slowing any cosmic divergence. Expansion that starts out dawdling, then sharply quickens for a brief period, might solve the horizon problem, but it’s a fiction. Newton would declare that just as gravitational attraction implies that the speed of a batted baseball diminishes as the ball moves upward, it similarly implies that the cosmic expansion must slow over time. Sure, if the expansion drops all the way to zero and then turns into cosmic contraction, the implosion can speed up over time, much as the ball’s speed can increase when it starts its downward journey. But the speed of the outward spatial expansion can’t increase.
Newton’s making a mistake, but you can’t blame him. The burden lies with the cursory summary you gave him of general relativity. Don’t get me wrong. It’s understandable that, given only five minutes (one of which was spent explaining baseball), you focused on curved spacetime as the source of gravity. Newton himself had called attention to the fact that there was no known mechanism for transmitting gravity, and he always viewed that as a yawning hole in his own theory. Naturally, you wanted to show him Einstein’s resolution. But Einstein’s theory of gravity did much more than merely fill a gap in Newtonian physics. Gravity in general relativity differs in its essence from gravity in Newton’s physics, and in the present context, there is one feature that cries out for emphasis.
In Newton’s theory, gravity arises solely from an object’s mass. The bigger the mass, the bigger the object’s gravitational pull. In Einstein’s theory, gravity arises from an object’s mass (and energy) but also from its pressure. Weigh a sealed bag of potato chips. Weigh it again, but this time squeeze the bag so that the air inside is under higher pressure. According to Newton, the weight will be the same, because there’s been no change in mass. According to Einstein, the squeezed bag will weigh slightly more, because although the mass is the same there’s been an increase in pressure.4 In everyday circumstances we’re not aware of it, because for ordinary objects the effect is fantastically tiny. Even so, general relativity, and the experiments that have shown it to be correct, makes it perfectly clear that pressure contributes to gravity.
This deviation from Newton’s theory is critical. Air pressure, whether the air is in a bag of potato chips, an inflated balloon, or the room where you’re now reading, is positive, meaning that the air pushes outward. In general relativity, positive pressure, like positive mass, contributes positively to gravity, resulting in increased weight. But whereas mass is always positive, there are situations in which pressure can be negative. Think of a stretched rubber band. Rather than pushing outward, the rubber band’s straining molecules pull inward, exerting what physicists call negative pressure (or, equivalently, tension). And much as general relativity shows that positive pressure gives rise to attractive gravity, it shows that negative pressure gives rise to the opposite: repulsive gravity.
This would blow Newton’s mind. For him, gravity was only attractive. But your mind should remain intact: you’ve already encountered this strange clause in general relativity’s contract with gravity. Remember Einstein’s cosmological constant, discussed in the previous chapter? I declared there that by infusing space with a uniform energy, a cosmological constant generates repulsive gravity. But in that earlier encounter, I didn’t explain why this happens. Now I can. A cosmological constant not only endows the spatial fabric with a uniform energy determined by the constant’s value (the number on the third line of the apocryphal relativity tax form), but it also fills space with a uniform negative pressure (we will see why in a moment). And, as above, when it comes to the gravitational force each produces, negative pressure does the opposite of positive mass and positive pressure. It yields repulsive gravity.*
In Einstein’s hands, repulsive gravity was used for a single erroneous purpose. He proposed finely adjusting the amount of negative pressure that permeates space to ensure that the repulsive gravity produced would exactly counter the attractive gravity exerted by the universe’s more familiar material contents, yielding a static universe. As we’ve seen, he subsequently renounced this move. Six decades later, the developers of the inflationary theory proposed a kind of repulsive gravity that differed from Einstein’s version much as the finale of Mahler’s Eighth differs from the drone of a tuning fork. Rather than a moderate and steady outward push that would stabilize the universe, the inflationary theory envisions a gargantuan surge of repulsive gravity that’s astoundingly short and thunderingly intense. Regions of space had ample time before the burst to come to the same temperature, but then, riding the surge, covered the great distances necessary to reach their observed positions in the sky.
At this point, Newton would surely shoot you another disapproving look. Ever the skeptic, he would find another problem with your explanation. After catching up on the more intricate details of general relativity by racing through one of the standard textbooks, he would accept the strange fact that gravity can—in principle—be repulsive. But, he’d ask, what’s all this talk of negative pressure permeating space? It’s one thing to use the inward pull of a stretched rubber band as an example of negative pressure. It’s another to argue that billions of years ago, just around the time of the big bang, space was momentarily permeated by an enormous and uniform negative pressure. What thing, or process, or entity has the capacity to supply such a fleeting but pervasive negative pressure?
The genius of inflation’s pioneers was to provide an answer. They showed that the negative pressure required for an antigravity burst naturally emerges from a novel mechanism involving ingredients known as quantum fields. For our story, the details are crucial because the manner in which inflationary expansion comes about is central to the version of parallel universes it yields.
In Newton’s day, physics concerned itself with the motion of objects you can see—stones, cannonballs, planets—and the equations he developed closely reflected this focus. Newton’s laws of motion are a mathematical embodiment of how such tangible bodies move when they’re pushed, pulled, or shot through the air. For more than a century, this was a wonderfully fruitful approach. But in the early 1800s, the English scientist Michael Faraday initiated a transformation in thinking with the elusive but demonstrably powerful concept of the field.
Take a strong refrigerator magnet and place it an inch above a paper clip. You know what happens. The clip jumps up and sticks to the magnet’s surface. This demonstration is so commonplace, so thoroughly familiar, that it’s easy to overlook how bizarre it is. Without touching the paper clip, the magnet can make it move. How is this possible? How can an influence be exerted in the absence of any contact with the clip itself? These and a multitude of related considerations led Faraday to postulate that though the magnet proper does not touch the paper clip, the magnet produces something that does. That something is what Faraday called a magnetic field.
We can’t see the fields produced by magnets; we can’t hear them; none of our senses are attuned to them. But that reflects physiological limitations, nothing more. As a flame generates heat, so a magnet generates a magnetic field. Lying beyond the physical boundary of the solid magnet, the magnet’s field is a “mist” or “essence” that fills space and does the magnet’s bidding.
Magnetic fields are but one kind of field. Charged particles give rise to another: electric fields, such as those responsible for the shock you sometimes receive when you reach for a metal doorknob in a room with wall-to-wall wool carpeting. Unexpectedly, Faraday’s experiments showed that electric and magnetic fields are intimately related: he found that a changing electric field generates a magnetic field, and vice versa. In the late 1800s, James Clerk Maxwell put mathematical might behind these insights, describing electric and magnetic fields in terms of numbers assigned to each point in space; the numbers’ values reflect the field’s ability, at that location, to exert influence. Places in space where the magnetic field’s numerical values are large, for instance an MRI’s cavity, are places where metal objects will feel a strong push or pull. Places in space where the electric field’s numerical values are large, for instance the inside of a thundercloud, are places where powerful electrical discharges such as lightning may occur.
Maxwell discovered equations, which now bear his name, that govern how the strength of electric and magnetic fields varies from point to point in space and moment to moment in time. These very same equations govern the sea of rippling electric and magnetic fields, so-called electromagnetic waves, within which we’re all immersed. Turn on a cell phone, a radio, or a wireless computer, and the signals received represent a tiny portion of the thicket of electromagnetic transmissions silently rushing by and through you every second. Most stunning of all, Maxwell’s equations revealed that visible light itself is an electromagnetic wave, one whose rippling patterns our eyes have evolved to see.
In the second half of the twentieth century, physicists united the field concept with their burgeoning understanding of the microworld encapsulated by quantum mechanics. The result, quantum field theory, provides a mathematical framework for our most refined theories of matter and nature’s forces. Using it, physicists have established that in addition to electric and magnetic fields, there exists a whole panoply of others with names like strong and weak nuclear fields and electron, quark, and neutrino fields. One field that to date remains wholly hypothetical, the inflaton field, provides a theoretical basis for inflationary cosmology.*
Quantum Fields and Inflation
Fields carry energy. Qualitatively, we know this because fields accomplish tasks that require energy, such as causing objects (like paper clips) to move. Quantitatively, the equations of quantum field theory show us how, given the numerical value of a field at a particular location, to calculate the amount of energy it contains. Typically, the larger the value, the larger the energy. A field’s value can vary from place to place, but should it be constant, taking the same value everywhere, it would fill space with the same energy at every point. Guth’s critical insight was that such uniform field configurations fill space not only with uniform energy but also with uniform negative pressure. And with that, he found a physical mechanism to generate repulsive gravity.
To see why a uniform field yields negative pressure, think first about a more ordinary situation that involves positive pressure: the opening of a bottle of Dom Pérignon. As you slowly remove the cork, you can feel the positive pressure of the champagne’s carbon dioxide pushing outward, driving the cork from the bottle and into your hand. A fact you can directly verify is that this outward exertion drains a little energy from the champagne. You know those vapor tendrils you see near the bottle’s neck when the cork is out? They form because the energy expended by the champagne in pushing against the cork results in a drop in temperature, which, much as with your breath on a wintry day, causes surrounding water vapor to condense.
Now imagine replacing the champagne with something less festive but more pedagogical—a field whose value is uniform throughout the bottle. When you remove the cork this time, your experience will be very different. As you slide the cork outward, you make a little extra volume inside the bottle available for the field to permeate. Since a uniform field contributes the same energy at every location, the larger the volume the field fills, the greater the total energy the bottle contains. Which means that, unlike with champagne, the act of removing the cork adds energy to the bottle.
How could that be? Where would the energy come from? Well, think about what happens if the bottle’s contents, rather than pushing the cork outward, pull the cork inward. This would require you to pull on the cork to remove it, an exertion of effort that in turn would transfer energy from your muscles to the contents of the bottle. To explain the increase in the bottle’s energy we thus conclude that, unlike champagne, which pushes outward, a uniform field sucks inward. That’s what we mean by a uniform field’s resulting in a negative—not positive—pressure.
Although there’s no sommelier uncorking the cosmos, the same conclusion holds: if there’s a field—the hypothetical inflaton field—that has a uniform value throughout a region of space, it will fill that region not only with energy but also with negative pressure. And, as is now familiar, such negative pressure yields repulsive gravity, which drives an ever-quickening expansion of space. When Guth slotted into Einstein’s equations the likely numerical values for the inflaton’s energy and pressure consonant with the extreme environment of the early universe, the mathematics revealed that the resulting repulsive gravity would be stupendous. It would easily be many orders of magnitude stronger than the repulsive force Einstein envisioned years earlier when he dallied with the cosmological constant, and would propel a spectacular spatial stretching. That alone was exciting. But Guth realized there was an indispensable bonus.
The same reasoning that explains why a uniform field has negative pressure applies as well to a cosmological constant. (If the bottle contains empty space endowed with a cosmological constant, then when you slowly remove the cork the extra space you make available within the bottle contributes extra energy. The only source for this extra energy is your muscles, which therefore must have strained against an inward, negative pressure supplied by the cosmological constant.) And, as with a uniform field, a cosmological constant’s uniform negative pressure also yields repulsive gravity. But the vital point here is not the similarities, per se, but the manner in which a cosmological constant and a uniform field differ.
A cosmological constant is just that—a constant, a fixed number inserted on the third line of general relativity’s tax form that would generate the same repulsive gravity today as it would have billions of years ago. By contrast, the value of a field can change, and generally will. When you turn on your microwave oven, you change the electromagnetic field filling its interior; when the technician flips the switch on an MRI machine, he or she changes the electromagnetic field threading the cavity. Guth realized that an inflaton field filling space could behave similarly—turning on for a burst and then turning off—which would allow repulsive gravity to operate during only a brief window of time. That’s essential. Observations establish that if the blistering growth of space happened at all, it must have happened billions of years ago and then sharply dropped off to the statelier-paced expansion evidenced by detailed astronomical measurements. So an all-important feature of the inflationary proposal is that the era of powerful repulsive gravity be transient.
The mechanism for turning on and then shutting off the inflationary burst relies on physics that Guth initially developed but that Linde, and Albrecht and Steinhardt, refined substantially. To get a feel for their proposal, think of a ball—better still, think of nearly round Eric Cartman—perched precariously on one of South Park’s snow-covered mountains. A physicist would say that because of his position, Cartman embodies energy. More precisely, he embodies potential energy, meaning that he has pent-up energy that’s ready to be tapped, most easily by his tumbling downward, which would transform the potential energy into the energy of motion (kinetic energy). Experience attests, and the laws of physics make precise, that this is typical. A system harboring potential energy will exploit any opportunity to release that energy. In short, things fall.
The energy carried by a field’s nonzero value is also potential energy: it, too, can be tapped, resulting in an incisive analogy with Cartman. Just as the increase in Cartman’s potential energy as he climbs the mountain is determined by the shape of the slope—in flatter regions his potential energy varies minimally as he walks, because he gets hardly any higher, while in steeper regions his potential energy rises sharply—the potential energy of a field is described by an analogous shape, called its potential energy curve. Such a curve, as in Figure 3.1, determines how a field’s potential energy varies with its value.
Following inflation’s pioneers, let’s then imagine that in the earliest moments of the cosmos, space is uniformly filled with an inflaton field, whose value places it high up on its potential energy curve. Imagine further, these physicists urge us, that the potential energy curve flattens out into a gentle plateau (as in Figure 3.1), allowing the inflaton to linger near the top. Under these hypothesized conditions, what will happen?
Figure 3.1 The energy contained in an inflaton field (vertical axis) for given values of the field (horizontal axis).
Two things, both critical. While the inflaton is on the plateau, it fills space with a large potential energy and negative pressure, driving a burst of inflationary expansion. But, just as Cartman releases his potential energy by rolling down the slope, so the inflaton releases its potential energy by its value, throughout space, rolling to lower numbers. And as its value decreases, the energy and negative pressure it harbors dissipate, bringing an end to the period of blistering expansion. Just as important, the energy released by the inflaton field isn’t lost—instead, like a cooling vat of steam condensing into water droplets, the inflaton’s energy condenses into a uniform bath of particles that fill space. This two-step process—brief but rapid expansion, followed by energy conversion to particles—results in a huge, uniform spatial expanse that’s filled with the raw material of familiar structures like stars and galaxies.
Precise details depend on factors that neither theory nor observation has as yet determined (the initial value of the inflaton field, the exact shape of the potential energy slope, and so on)5 but in typical versions the mathematical calculations show that the inflaton’s energy would roll down the slope in a tiny fraction of a second, on the order of 10–35 seconds. And yet, during that brief span, space would expand by a colossal factor, perhaps 1030 if not more. These numbers are so extreme that they defy analogy. They imply that a region of space the size of a pea would be stretched larger than the observable universe in a time interval so short that the blink of an eye would overestimate it by a factor larger than a million billion billion billion.
However difficult it is to envision such a scale, what’s essential is that the region of space that spawned the observable universe was so small that it would easily have come to a uniform temperature before it was stretched into our grand cosmic expanse by the rapid burst. The inflationary expansion, and billions of years of subsequent cosmological evolution, resulted in this temperature cooling substantially, but the uniformity set in place early on dictates a uniform result today. This resolves the mystery of how the universe’s uniform conditions came to be. In inflation, a uniform temperature across space is inevitable.6
During the nearly three decades since its discovery, inflation has become a fixture of cosmological investigation. But to have an accurate picture of the research panorama, you should be aware that inflation is a cosmological framework, but it is not a specific theory. Researchers have shown that there are many ways to skin an inflationary cat, differing in details such as the number of inflaton fields supplying the negative pressure, the particular potential energy curves to which each field is subject, and so on. Fortunately, the sundry realizations of inflation have some implications in common, so we can draw conclusions even in the absence of a definitive version.
Among these, one first fully realized by Alexander Vilenkin of Tufts University and developed further by others, including most notably Linde, is of great importance.7 In fact, it’s the very reason I’ve spent the first half of this chapter explaining the inflationary framework.
In many versions of the inflationary theory, the burst of spatial expansion is not a onetime event. Instead, the process by which our region of the universe formed—rapid stretching of space, followed by a transition to a more ordinary, slower expansion, together with the production of particles—may happen over and over again at various far-flung locations throughout the cosmos. From a bird’s-eye view, the cosmos would appear riddled with innumerable widely separated regions, each being the aftermath of a portion of space transitioning out of the inflationary burst. Our realm, what we have always thought of as the universe, would then be but one of these numerous regions, floating within a vastly larger spatial expanse. If intelligent life exists in the other regions, those beings would just as surely have thought their universe to be the universe, too. And so inflationary cosmology steers us headlong into our second variation on the theme of parallel universes.
To grasp how this Inflationary Multiverse comes about, we need to engage two complications that my Cartman analogy glossed over.
First, the image of Cartman perched high on a mountaintop offered an analogy to an inflaton field harboring significant potential energy and negative pressure, poised to roll to lower values. But whereas Cartman is perched on a single mountaintop, the inflaton field has a value at each point in space. The theory posits that the inflaton field starts off with the same value at each location within an initial region. And so we’d achieve a more faithful rendering of the science if we imagine something a little odd: numerous Cartman clones perched on numerous, closely packed, identical mountaintops throughout a spatial expanse.
Second, we’ve so far barely touched on the quantum aspect of quantum field theory. The inflaton field, like everything else in our quantum universe, is subject to quantum uncertainty. This means that its value will undergo random quantum jitters, momentarily rising a little here and dropping a little there. In everyday situations, quantum jitters are too small to notice. But calculations show that the larger the energy an inflaton has, the greater the fluctuations it will experience from quantum uncertainty. And since the inflaton’s energy content during the inflationary burst was extremely high, the jitters in the early universe were big and dominant.8
We should thus not only picture a platoon of Cartmans perched high on identical mountaintops; we should also imagine that they are all subject to a random series of tremors—strong here, weak there, very strong way over there. With this setup, we can now determine what will happen. Different Cartman clones will stay perched on their mountaintops for different durations. In some locations, a strong tremor knocks most Cartmans down their slopes; in other locations, a mild tremor coaxes only a few to tumble down; in others still, some Cartmans may have started to roll down until a strong tremor knocked them back up. After a while, the terrain will be divided into a random assortment of domains—much as the United States is divided into states—in some of which no Cartmans are left on mountaintops, while in others many Cartmans remain securely perched.
The random nature of quantum jitters yields a similar conclusion for the inflaton field. The field begins high up on its potential energy slope at every point in a region of space. The quantum jitters then act like tremors. Because of this, as illustrated in Figure 3.2, the expanse of space rapidly divides into domains: in some, quantum jitters cause the field to topple down the slope, while in others it remains high.
So far, so good. But now stay with me closely; here’s where cosmology and Cartmans differ. A field that’s perched high up on its energy curve affects its environment far more significantly than a similarly perched Cartman does. From our familiar refrain—a field’s uniform energy and negative pressure generate repulsive gravity—we recognize that the region the field permeates expands at a fantastic rate. This means that the inflaton field’s evolution across space is driven by two opposing processes. Quantum jitters, by tending to knock the field off its perch, decrease the amount of space suffused with high field energy. Inflationary expansion, by rapidly enlarging those domains in which the field remains perched, increases the volume of space suffused with high field energy.
Which process wins?
In the vast majority of proposed versions of inflationary cosmology, the increase occurs at least as quickly as the decrease. The reason is that an inflaton field that can be knocked off its perch too quickly typically generates too little inflationary expansion to solve the horizon problem; in cosmologically successful versions of inflation, the increase thus wins over the decrease, ensuring that the total volume of space in which the field’s energy is high increases over time. Recognizing that such field configurations yield yet further inflationary expansion, we see that once inflation begins it never ends.
Figure 3.2 Various domains in which the inflaton field has dropped down the slope (darker gray) or remains high (lighter gray).
It’s like the spread of a viral pandemic. To eradicate the threat, you need to wipe out the virus faster than it can reproduce. The inflationary virus “reproduces”—a high field value generates rapid spatial expansion and thus infuses a yet larger domain with that same high field value—and it does so faster than the competing process eliminates it. The inflationary virus effectively resists eradication.9
Swiss Cheese and the Cosmos
Collectively, these insights show that inflationary cosmology leads to a vastly new picture of reality’s expanse, one that can be grasped most easily with a simple visual aid. Think of the universe as a gigantic block of Swiss cheese, with the cheesy parts being regions where the inflaton field’s value is high and the holes being regions where it’s low. That is, the holes are regions, like ours, that have transitioned out of the superfast expansion and, in the process, converted the inflaton field’s energy into a bath of particles, which over time may coalesce into galaxies, stars, and planets. In this language, we’ve found that the cosmic cheese acquires more and more holes because quantum processes knock the inflaton’s value downward at a random assortment of locations. At the same time, the cheesy parts stretch ever larger because they’re subject to inflationary expansion driven by the high inflaton field value they harbor. Taken together, the two processes yield an ever-expanding block of cosmic cheese riddled with an ever-growing number of holes. In the more standard language of cosmology, each hole is called a bubble universe (or a pocket universe).10 Each is an opening tucked within the superfast stretching cosmic expanse (Figure 3.3).
Don’t let the descriptive but diminutive-sounding “bubble universe” fool you. Our universe is gigantic. That it may be a single region embedded within an even larger cosmic structure—a single bubble in an enormous block of cosmic cheese—speaks to the fantastic expanse, in the inflationary paradigm, of the cosmos as a whole. And this goes for the other bubbles too. Each would be as much a universe—a real, gigantic, dynamic expanse—as ours.
Figure 3.3 The Inflationary Multiverse arises when bubble universes continually form within an ever-expanding spatial environment permeated by a high-valued inflaton field.
There are versions of the inflationary theory in which inflation is not eternal. By fiddling with details such as the number of inflaton fields and their potential energy curves, clever theorists can arrange things so that the inflaton would, in due course, be knocked off its perch everywhere. But these proposals are the exception rather than the rule. Garden-variety inflationary models yield a gargantuan number of bubble universes carved into an eternally expanding spatial expanse. And so, if the inflationary theory is on the mark, and if, as many theoretical investigations conclude, its physically relevant realization is eternal, the existence of an Inflationary Multiverse would be an inevitable consequence.
Back in the 1980s, when Vilenkin realized the eternal nature of inflationary expansion and the parallel universes to which it would give rise, he excitedly visited Alan Guth at MIT to tell him about it. Midway through the explanation, Guth’s head drooped forward: he’d fallen asleep. This was not necessarily a bad sign; Guth is famous for nodding off during physics seminars—he’s caught a few winks during talks I’ve given—then opening his eyes midway through to ask the most insightful of questions. But the broader physics community was no more enthusiastic than Guth was, so Vilenkin shelved the idea and moved on to other projects.
Sentiment today is very different. When Vilenkin was first thinking about the Inflationary Multiverse, the evidence in direct support of the inflationary theory itself was thin. So, to the few who paid any attention at all, ideas about inflationary expansion yielding a vast collection of parallel universes seemed like speculation piled upon speculation. But in the years since, the observational case for inflation has grown much stronger, once again thanks largely to precise measurements of the microwave background radiation.
Even though the observed uniformity of the microwave background radiation was one of the prime motivations for developing the inflationary theory, early proponents realized that rapid spatial expansion would not render the radiation perfectly uniform. Instead, they argued that quantum mechanical jitters stretched large by the inflationary expansion would overlay the uniformity with minuscule temperature variations, like tiny ripples on the surface of an otherwise smooth pond. This has proved to be a spectacular and enormously influential insight.* Here’s how it goes.
Quantum uncertainty would have caused the value of the inflaton field to jitter. Indeed, if the inflationary theory is correct, the burst of inflationary expansion stopped here because a large and lucky quantum fluctuation, nearly 14 billion years ago, knocked the inflaton off its perch in our vicinity. Yet there’s more to the story. As the inflaton’s value rolled down its slope headlong toward the point of bringing inflation in our bubble universe to a close, its value would still have been subject to quantum jitters. The jitters, in turn, would have made the inflaton’s value a little higher here and a little lower there, like the wavy surface of an unfurled sheet as it descends to your mattress. This would have produced slight variations in the energy the inflaton harbored across space. Normally, such quantum variations are so tiny and happen over such minuscule scales that they are irrelevant over cosmological distances. But inflationary expansion is anything but normal.
The expansion of space is so rapid, even during the transition out of the inflationary phase, that the microscopic would have been stretched to the macroscopic. And much as a tiny message scribbled on a deflated balloon becomes easier to read when air stretches the balloon’s surface, so the influence of quantum jitters becomes visible when inflationary expansion stretches the cosmic fabric. More particularly, minute energy differences caused by quantum jitters are stretched into temperature variations that become imprinted in the cosmic microwave background radiation. Calculations show that the temperature differences wouldn’t exactly be huge, but could be as large as a thousandth of a degree. If the temperature is 2.725 K in one region, the stretched-out quantum jitters would result in its being a touch colder, say 2.7245 K, or a touch hotter, 2.7255 K, at nearby regions.
Painstakingly precise astronomical observations have sought these temperature variations. They’ve found them. Just as the theory predicted, they measure about a thousandth of a degree (see Figure 3.4). More impressive still, the tiny temperature differences fit a pattern on the sky that is explained spot-on by the theoretical calculations. Figure 3.5 compares theoretical predictions of how the temperature should vary as a function of the distance between two regions (measured by the angle between their respective lines of sight when viewed from earth) with the actual measurements. The agreement is stunning.
The 2006 Nobel Prize in Physics was awarded to George Smoot and John Mather, who led more than a thousand researchers on the Cosmic Background Explorer team in the early 1990s to the first detection of these temperature differences. During the past decade, every new and more accurate measurement, yielding data such as those in Figure 3.5, has resulted in yet more precise verification of the predicted temperature variations.
These works have capped a thrilling story of discovery that began with the insights of Einstein, Friedmann, and Lemaître, was pushed sharply forward by the calculations of Gamow, Alpher, and Herman, was reinvigorated by the ideas of Dicke and Peebles, was shown relevant by the observations of Penzias and Wilson, and has now culminated in the handiwork of armies of astronomers, physicists, and engineers whose combined efforts have measured a fantastically minute cosmic signature that was set in place billions of years ago.
On a more qualitative level, we should all be thankful for the blotches in Figure 3.4. At the close of inflation in our bubble universe, regions with slightly more energy (equivalently, via E = mc2, regions with slightly more mass) exerted a slightly stronger gravitational pull, attracting more particles from their surroundings and thus growing larger. The larger aggregate, in turn, exerted an even stronger gravitational pull, thus attracting yet more matter and growing larger still. In time, this snowball effect resulted in the formation of clumps of matter and energy that, over billions of years, evolved into galaxies and the stars within them. In this way, inflationary theory establishes a remarkable link between the largest and smallest structures in the cosmos. The very existence of galaxies, stars, planets, and life itself derives from microscopic quantum uncertainty amplified by inflationary expansion.
Figure 3.4 The enormous spatial expansion in inflationary cosmology stretches quantum fluctuations from the microscopic to the macroscopic, resulting in observable temperature variations in the cosmic microwave background radiation (the darker splotches are slightly colder than the lighter ones).
Figure 3.5 The pattern of temperature differences in the cosmic microwave background radiation. Temperature variation is the vertical axis; the separation between two locations (measured by the angle between their respective lines of sight when viewed from earth—larger angles to the left, smaller angles to the right) is the horizontal axis.11 The theoretical curve is solid; the observational data are given by the circles.
Inflation’s theoretical underpinnings may be rather tentative: the inflaton, after all, is a hypothetical field whose existence has yet to be demonstrated; its potential energy curve is posited by researchers, not revealed by observation; the inflaton must somehow start at the top of its energy curve across a region of space; and so on. Despite all that, and even if some details of the theory are not quite right, the agreement between theory and observation has convinced many that the inflationary scheme taps into a deep truth about cosmic evolution. And since a great many versions of inflation are eternal, yielding an ever-growing number of bubble universes, theory and observation combine to make an indirect yet compelling case for this second version of parallel worlds.
Experiencing the Inflationary Multiverse
In a Quilted Multiverse, there’s no sharp divide between one parallel universe and another. All are part of a single spatial expanse whose overall qualitative features are similar from region to region. The surprise lies in the details. Most of us wouldn’t expect worlds to repeat; most of us wouldn’t expect, every so often, to encounter versions of ourselves, our friends, our families. But if we could journey sufficiently far, that’s what we would find.
In an Inflationary Multiverse, the member universes are sharply divided. Each is a hole in the cosmic cheese, separated from the others by domains in which the inflaton’s value remains high. Since such intervening regions are still undergoing inflationary expansion, the bubble universes are rapidly driven apart, with a speed of recession proportional to the amount of swelling space between them. The farther apart they are, the greater the expansion’s speed; the ultimate result is that distant bubbles move apart faster than the speed of light. Even with unlimited longevity and technology, there’s no way to cross such a divide. There’s no way to even send a signal.
All the same, we can still imagine a voyage to one or more of the other bubble universes. On such a journey, what would you find? Well, because each bubble universe results from the same process—the inflaton is knocked from its perch, yielding a region that drops out of the inflationary expansion—they are all governed by the same physical theory and so are all subject to the same set of physical laws. But, much as the behavior of identical twins can differ profoundly as a result of environmental differences, identical laws can manifest themselves in profoundly different ways in different environments.
Imagine, for example, that one of the other bubble universes looks much like ours, dotted by galaxies containing stars and planets, but with one essential difference. Permeating the universe is a magnetic field, thousands of times stronger than that created in our most advanced MRI machines, and one that can’t be switched off by a technician. Such a powerful field would affect the way a great many things behave. Not only would objects containing iron have a nasty habit of flying off in the direction of the field, but even basic properties of particles, atoms, and molecules would shift. A sufficiently strong magnetic field would so disrupt cellular function that life as we know it couldn’t take hold.
Yet just as the physical laws operating inside an MRI are the very same laws that operate outside, so the fundamental physical laws operating in this magnetic universe would be the same as ours. The discrepancies in experimental results and observable features would be due solely to an aspect of the environment: the strong magnetic field. Talented scientists in the magnetic universe would in time tease out this environmental factor and home in on the same mathematical laws we’ve discovered.
Over the past forty years, researchers have built a case for a similar scenario right here in our own universe. The most lauded theory of fundamental physics, the Standard Model of particle physics, posits that we are immersed in an exotic mist called the Higgs field (named after the English physicist Peter Higgs, who with important contributions from Robert Brout, François Englert, Gerald Guralnik, Carl Hagen, and Tom Kibble pioneered this idea in the 1960s). Both Higgs fields and magnetic fields are invisible and hence can fill space without directly revealing their presence. However, according to modern particle theory, a Higgs field camouflages itself far more fully. As particles move through a uniform, space-filling Higgs field, they don’t speed up, they don’t slow down, they are not coaxed to follow particular trajectories, as some would in the presence of a strong magnetic field. Instead, the theory claims, they’re influenced in ways more subtle and profound.
As fundamental particles burrow through a Higgs field, they acquire and maintain the mass that experiments have revealed them to possess. According to this idea, when you push against an electron or quark in an effort to change its speed, the resistance you feel comes from the particle’s “rubbing” against the molasses-like Higgs field. It’s this resistance that we call the particle’s mass. Were you to remove the Higgs field from some region, particles passing through would suddenly become massless. Were you to double the value of the Higgs field in another region, particles passing through would suddenly have twice their usual mass.*
Such human-induced changes are hypothetical, because the energy required to substantially modify a Higgs field’s value in even a small region of space is enormously beyond what we can muster. (The changes are also hypothetical because the existence of the Higgs fields is still up in the air. Theorists eagerly anticipate highly energetic collisions between protons at the Large Hadron Collider chipping off small chunks of the Higgs field—Higgs particles—that may be detected in the coming years.) But in many versions of inflationary cosmology, a Higgs field would naturally have different values in different bubble universes.
A Higgs field, much like an inflaton field, has a curve that records the amount of energy it contains for various values it can assume. An essential difference from the inflaton field’s energy curve, though, is that the Higgs typically settles not at the value 0 (as in Figure 3.1), but rather rolls to one of the troughs illustrated in Figure 3.6a. Picture, then, an early stage in each of two bubble universes, ours and another. In both, the hot, tempestuous frenzy causes the value of the Higgs field to undulate wildly. As each universe expands and cools, the Higgs field calms and its value rolls toward one of the troughs in Figure 3.6a. In our universe, the Higgs field’s value settles down in, say, the left trough, giving rise to the particle properties familiar from experimental observation. But in the other universe, the Higgs’ motion may result in its value settling down in the right trough. If it did, that universe would have properties substantially different from ours. Although the underlying laws in both universes would be the same, the masses and various other properties of particles would not.
Even a modest difference in particle properties would have weighty consequences. If the electron mass in another bubble universe were a few times larger than it is here, electrons and protons would tend to merge, forming neutrons and thus preventing the widespread production of hydrogen. The fundamental forces—the electromagnetic force, the nuclear forces, and (we believe) gravity—are also communicated by particles. Change the particle properties and you drastically change the properties of the forces. The heavier a particle, for example, the more sluggish its motion and so the shorter the distance over which the corresponding force is transmitted. The formation and stability of atoms in our bubble universe rely on the properties of the electromagnetic and nuclear forces. If you substantially modify those forces, atoms will fall apart or, more likely, not coalesce in the first place. An appreciable change to the properties of particles would thus disrupt the very processes that give our universe its familiar features.
Figure 3.6 (a) A potential energy curve for a Higgs field that has two troughs. The familiar features of our universe are associated with the field settling down in the left trough; in another universe, however, the field can settle down in the right trough, yielding different physical features. (b) A sample potential energy curve for a theory with two Higgs fields.
Figure 3.6a illustrates only the simplest case, in which there is a single species of Higgs field. But theoretical physicists have explored more complicated scenarios involving multiple Higgs fields (we will shortly see that such possibilities naturally emerge from string theory), which translate into an even richer set of distinct bubble universes. An example with two Higgs fields is illustrated in Figure 3.6b. As before, the various troughs represent Higgs field values that one or another bubble universe could settle into.
Permeated by such unfamiliar values of various Higgs fields, these universes would differ from ours considerably, as schematically illustrated in Figure 3.7. This would make a journey through the Inflationary Multiverse a perilous undertaking. Many of the other universes would not be places you’d want high on your itinerary, because the conditions would be incompatible with the biological processes essential to survival, giving new meaning to the saying that there’s no place like home. In the Inflationary Multiverse, our universe could well be an island oasis in a gigantic but largely inhospitable cosmic archipelago.
Figure 3.7 Because fields can settle down to different values in different bubbles, the universes in the Inflationary Multiverse can have different physical features, even though the universes are all governed by the same fundamental physical laws.
Universes in a Nutshell
Because of their fundamental differences, the Quilted and Inflationary Multiverses might appear unrelated. The quilted variety emerges if the extent of space is infinite; the inflationary variety emerges from eternal inflationary expansion. Yet, there is a deep and wonderfully satisfying connection between them, one that brings the discussion in the previous two chapters full circle. The parallel universes arising from inflation generate their quilted cousins. The process has to do with time.
Of the many strange things Einstein’s work revealed, the fluidity of time is the hardest to grasp. Whereas everyday experience convinces us that there is an objective concept of time’s passage, relativity shows this to be an artifact of life at slow speeds and weak gravity. Move near light speed, or immerse yourself in a powerful gravitational field, and the familiar, universal conception of time will evaporate. If you’re rushing past me, things I insist happened at the same moment will appear to you to have occurred at different moments. If you’re hanging out near the edge of a black hole, an hour’s passage on your watch will be monumentally longer on mine. This isn’t evidence of a magician’s trickery or a hypnotist’s deception. The passage of time depends on the particulars—trajectory followed and gravity experienced—of the measurer.12
When applied to the entire universe, or to our bubble in an inflationary setting, this immediately raises a question: How does such malleable, custom-made time comport with the notion of an absolute cosmological time? We freely speak of the “age” of our universe, but given that galaxies are moving rapidly relative to one another, at speeds dictated by their various separations, doesn’t the relativity of time’s passage create a nightmarish accounting problem for any would-be cosmic timekeeper? More pointedly, when we speak of our universe being “14 billion years old,” are we using a particular clock to measure that duration?
We are. And a careful consideration of such cosmic time reveals a direct link between parallel universes of the inflationary and quilted varieties.
Every method we use to measure time’s passage involves an examination of change that occurs to some particular physical system. Using a common wall clock, we examine the change in position of its hands. Using the sun, we examine the change in its position in the sky. Using carbon 14, we examine the percentage of an original sample that’s undergone radioactive decay to nitrogen. Historical precedent and general convenience have led us to use the rotation and revolution of the earth as physical referents, giving rise to our standard notions of “day” and “year.” But when we’re thinking on cosmic scales, there is another, more useful, method for keeping time.
We’ve seen that inflationary expansion yields vast regions whose properties on average are homogeneous. Measure the temperature, pressure, and average density of matter in two large but separate regions within a bubble universe, and the results will agree. The results can change over time, but the large-scale uniformity ensures that, on average, the change here is the same as the change there. As an important case in point, the mass density in our bubble universe has steadily decreased over our multibillion-year history, thanks to the relentless expansion of space, but because the change has occurred uniformly, our bubble’s large-scale homogeneity has not been disrupted.
This proves important because just as the steadily decreasing amount of carbon 14 in organic matter provides a means of measuring time’s passage on earth, so the steadily decreasing mass density provides a means of measuring time’s passage across space. And because the change has happened uniformly, mass density as a marker of time’s passage provides our bubble universe with a global standard. If everyone diligently calibrates their watches to the average mass density (and recalibrates after trips to black holes, or periods of travel at near light speed), the synchronicity of our timepieces across our bubble universe will be maintained. When we speak of the age of the universe—the age of our bubble, that is—it is on such cosmically calibrated watches that we imagine time’s passage being measured; it is only with respect to them that cosmic time is a sensible concept.
In the earliest era of our bubble universe, the same reasoning would have applied with one change of detail. Ordinary matter had yet to form, so we can’t speak of the average mass density in space. Instead, the inflaton field carried our universe’s storehouse of energy—energy that would shortly be converted into familiar particles—so we need to envisage setting our clocks by the density of the inflaton field’s energy.
Now, the inflaton’s energy is determined by its value, as summarized by its energy curve. To determine what time it is at a given location in our bubble, we therefore need to determine the value of the inflaton at that location. Then, just as two trees are the same age if they have the same number of tree rings, and just as two samples of glacial sediment are the same age if they have the same percentage of radioactive carbon, two locations in space are passing through the same moment in time when they have the same value of the inflaton field. That’s how we set and synchronize clocks in our bubble universe.
The reason I’ve brought all this up is that when applied to the cosmic Swiss cheese of the Inflationary Multiverse, these observations yield a strikingly counterintuitive implication. Much as Hamlet famously declares, “I could be bounded in a nutshell, and count myself a king of infinite space,” each of the bubble universes appears to have finite spatial extent when examined from the outside, but infinite spatial extent when examined from the inside. And that’s a marvelous realization. Infinite spatial extent is just what we need for quilted parallel universes. So we can meld the Quilted Multiverse into the inflationary story.
The extreme disparity between the outsider’s and insider’s perspectives arises because they have vastly different conceptions of time. Although the point is far from obvious, we’ll now see that what appears as endless time to an outsider appears as endless space, at each moment of time, to an insider.13
Space in a Bubble Universe
To grasp how this comes about, imagine that Trixie, floating within a rapidly expanding inflaton-filled region of space, is observing the formation of a nearby bubble universe. Focusing her inflaton-meter on the growing bubble, she is able to directly track its changing inflaton field value. Although the region—the hole in the cosmic cheese—is three-dimensional, it’s simpler to examine the field along a one-dimensional cross section across its diameter, and as Trixie does so she records the data in Figure 3.8a. Each higher row shows the inflaton’s value at a successive moment in time, from Trixie’s perspective. And as is apparent from the figure, Trixie sees the bubble universe—represented in the figure by the lighter locations where the inflaton’s value has dropped—grow ever larger.
Now imagine that Norton is also examining this very same bubble universe, but from the inside; he’s hard at work making detailed astronomical observations with his own inflaton-meter. Norton, unlike Trixie, adheres to a notion of time that’s calibrated by the value of the inflaton. This is key to the conclusion we’re chasing, so I need you to buy into it fully. Imagine, if you will, that everyone in the bubble universe wears a watch that measures and displays the inflaton’s value. When Norton throws a dinner party, he instructs the guests to show up at his house when the inflaton’s value is 60. Since everyone’s watch is calibrated to the same, uniform standard—the inflaton field’s value—the party goes off without a hitch. Everyone shows up at the same moment because everyone is attuned to the same concept of synchronicity.
Figure 3.8a Each row chronicles the inflaton’s value at one moment of time from an outsider’s perspective. Higher rows correspond to later moments. The columns denote positions across space. A bubble is a region of space that stops inflating because of a drop in the inflaton’s value. The lighter entries denote the value of the inflaton field within the bubble. From the perspective of the outside observer, the bubble grows ever larger.
With this understanding, it’s a simple matter for Norton to work out the size of the bubble universe at any given moment of his time. In fact, it’s child’s play: all Norton has to do is paint by numbers. By connecting all points that have the same numerical value for the inflaton field, Norton can delineate all locations within the bubble at a single moment of time. His time. Insider’s time.
Norton’s drawing in Figure 3.8b says it all. Each curve, connecting points with the same inflaton-field value, represents all of space at a given moment of time. As the figure makes clear, each curve extends indefinitely far, which means that the size of the bubble universe, according to its inhabitants, is infinite. This reflects that endless outsider time, experienced by Trixie as the endless number of rows in Figure 3.8, appears as endless space, at each moment of time, according to an insider like Norton.
That’s a powerful insight. In Chapter 2, we found that the Quilted Multiverse was contingent upon space being infinitely large, something that, as we discussed there, might or might not be the case. Now we see that each bubble within the Inflationary Multiverse is spatially finite from the outside but spatially infinite from the inside. If the Inflationary Multiverse is real, then the inhabitants of a bubble—us—would thus be members not only of the Inflationary Multiverse but of the Quilted Multiverse, too.14
Figure 3.8b The same information as in Figure 3.8a is organized differently by someone within the bubble. Inflaton values that agree correspond to identical moments, so the curves drawn sweep through all those points in space that exist at the same moment in time. Smaller inflaton values correspond to later moments. Note that the curves could be extended infinitely far, so from an insider’s perspective, space is infinite.
When I first learned of the Quilted and Inflationary Multiverses, it was the inflationary variety that struck me as more plausible. Inflationary cosmology resolves a number of long-standing puzzles while yielding predictions that match up well with observations. And by the reasoning we’ve recounted, inflation is naturally a process that never ends; it produces bubble universes upon bubble universes, of which we inhabit but one. The Quilted Multiverse, on the other hand, by having its full force when space is not just large but truly infinite (you might have repetition in a large universe, but you are guaranteed repetition in an infinite one), seemed avoidable: it might be the case, after all, that the universe has finite size. But we now see that eternal inflation’s bubble universes, when properly analyzed from the viewpoint of their inhabitants, are spatially infinite. Inflationary parallel universes beget quilted ones.
The best available cosmological theory for explaining the best available cosmological data leads us to think of ourselves as occupying one of a vast inflationary system of parallel universes, each of which harbors its own vast collection of quilted parallel universes. Cutting-edge research yields a cosmos in which there are not only parallel universes but parallel parallel universes. It suggests that reality is not only expansive but abundantly expansive.
*Equivalently, superfast accelerated expansion means that today’s distant regions would have been much closer together in the early universe than is suggested by the traditional big bang theory—ensuring that a common temperature could be established before the burst separated them.
*You might think that negative pressure would pull inward and thus be at odds with repulsive—outward-pushing—gravity. Actually, uniform pressure, regardless of its sign, doesn’t push or pull at all. Your eardrums pop only when there is nonuniform pressure, lower on one side than the other. The repulsive push I’m describing here is the gravitational force generated by the presence of the uniform negative pressure. This is a difficult but essential point. Again, whereas the presence of positive mass or positive pressure generates attractive gravity, the presence of negative pressure generates the less familiar repulsive gravity.
*The rapid expansion of space is called inflation, but following the historical pattern of invoking names that end in “on” (electron, proton, neutron, muon, etc.), when physicists refer to the field driving inflation, they drop the second “i.” Hence, inflaton field.
*Among those who played a leading role in this work were Viatcheslav Mukhanov, Gennady Chibisov, Stephen Hawking, Alexei Starobinsky, Alan Guth, So-Young Pi, James Bardeen, Paul Steinhardt, and Michael Turner.
*I stress fundamental particles, like electrons and quarks, because for composite particles, like protons and neutrons (each made from 3 quarks), much of the mass arises from interactions between the constituents (the energy carried by gluons of the strong nuclear force, which bind the quarks inside protons and neutrons, contributes most of the mass of these composite particles).