by Brian Greene
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
Eternal Inflation
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 coa
lesce 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.
Changing Perspectives
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.