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Authors: Alex Vilenkin
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I went on to work on my other research interests, and at times it even appeared that I was cured of my strange obsession with unobservable worlds. But the truth was that the temptation to get a glimpse of the universe beyond the horizon did not go away. In 1986, when I could not resist it any
more, I developed a computer simulation of the eternally inflating universe, together with a graduate student, Mukunda Aryal.
more, I developed a computer simulation of the eternally inflating universe, together with a graduate student, Mukunda Aryal.
I am technologically challenged and have never written a single line of computer code. But I have a pretty good understanding of how computers think, and over the years I have supervised several major computational projects by graduate students. Since I cannot check the code (and I suspect that I would not enjoy that even if I could), I am wary of hidden dangers and always view the results with great suspicion. So I made Mukunda go through multiple checks and run the simulation for simple cases, where we knew the answers. Finally, when I was satisfied that everything worked fine, we turned to the real thing.
We started the simulation with a small region of false vacuum, represented by a light square area on the computer screen. After a while, the first dark islands of true vacuum made their appearance. These island universes grew rapidly in size, as their boundaries advanced into the inflating sea. But the inflating regions expanded even faster, so the gaps separating the island universes widened and new island universes formed in the newly created space.
2
2
The picture that emerged after we allowed the simulation to run for some time showed large island universes surrounded by smaller ones, which were surrounded by still smaller ones, and so forth, resembling an aerial view of an archipelago—a pattern known as a fractal to mathematicians.
Figure 8.3
is the result of a similar, but more sophisticated, simulation that I later developed with my students Vitaly Vanchurin and Serge Winitzki.
Figure 8.3
is the result of a similar, but more sophisticated, simulation that I later developed with my students Vitaly Vanchurin and Serge Winitzki.
Mukunda and I published the results of our simulation in the European journal
Physics Letters
.
3
My curiosity about the unobservable universe now satisfied, I moved on to other things. In the meantime, the subject was taken up by Andrei Linde.
Physics Letters
.
3
My curiosity about the unobservable universe now satisfied, I moved on to other things. In the meantime, the subject was taken up by Andrei Linde.
Linde is the hero of inflation, the person who saved the theory by inventing a flattened energy hill for the scalar field. Since 1983, he was developing the idea that the universe started in a state of primordial chaos. The scalar field in that state was varying wildly from one place to another. In some regions
it happened to be high up on the energy hill, and that’s where inflation took place.
it happened to be high up on the energy hill, and that’s where inflation took place.
Figure 8.3
.
Computer simulation of an eternally inflating universe. Island universes (dark) in the inflating false-vacuum background (light). The larger island universes are the older ones: they had more time to grow.
.
Computer simulation of an eternally inflating universe. Island universes (dark) in the inflating false-vacuum background (light). The larger island universes are the older ones: they had more time to grow.
Linde realized that it was not necessary for the field to start at the highest point of the energy landscape. It could also roll down from some other point on the slope. In fact, the energy hill might have no highest point and keep rising without limit (see
Figure 8.4
). Such a “topless” hill has a true vacuum at the bottom, but there is no definite location for the false vacuum. Its role can be played by any point on the slope where the field happens to be in the initial chaos, provided that it is high enough to allow sufficient roll-down time for inflation. Linde described these ideas in a paper called “Chaotic Inflation.”
Figure 8.4
). Such a “topless” hill has a true vacuum at the bottom, but there is no definite location for the false vacuum. Its role can be played by any point on the slope where the field happens to be in the initial chaos, provided that it is high enough to allow sufficient roll-down time for inflation. Linde described these ideas in a paper called “Chaotic Inflation.”
A few years later, Linde investigated the effect of quantum kicks on the scalar field in this scenario. Surprisingly, he found that they can also result in eternal inflation, even though the energy hill does not have a flat top. His key observation was that at higher elevations quantum kicks get stronger and can push the field up, against the downward force of the slope. So, if the field starts high up the hill, it pays little attention to the slope and undergoes
a random walk, as in the flat hilltop case. When it wanders into the lower terrain, where quantum kicks are weak, it rolls in an orderly way down to the true vacuum. The time it takes for this to happen is much longer than the inflationary doubling time; so inflating regions multiply faster than they decay, which results once again in eternal inflation.
a random walk, as in the flat hilltop case. When it wanders into the lower terrain, where quantum kicks are weak, it rolls in an orderly way down to the true vacuum. The time it takes for this to happen is much longer than the inflationary doubling time; so inflating regions multiply faster than they decay, which results once again in eternal inflation.
Figure 8.4
.
Scalar field rolls down the slope of a “topless” energy hill.
.
Scalar field rolls down the slope of a “topless” energy hill.
Here I should stop to clarify the terminological confusion that bedevils this subject. “Eternal inflation” is often confused with “chaotic inflation,” although the two are very different. “Chaotic” refers to a chaotic initial state and has nothing to do with the eternal character of inflation. Linde showed that chaotic inflation can also be eternal, but that’s where the connection ends. For clarity, in the rest of this book I will limit the discussion to the original inflation model with a flattened energy hill. Eternal inflation on a topless hill is similar.
Linde’s paper on eternal inflation was published three years after mine and was met with as much enthusiasm.
4
But his reaction was different. He stuck to his guns, continued this line of research, and gave numerous talks on the subject. Still, the physics community was not swayed by his efforts. It took nearly two decades before the fortunes of eternal inflation started to turn.
4
But his reaction was different. He stuck to his guns, continued this line of research, and gave numerous talks on the subject. Still, the physics community was not swayed by his efforts. It took nearly two decades before the fortunes of eternal inflation started to turn.
The Sky Has Spoken
What is now proved was once only imagined.
—WILLIAM BLAKE
T
he theory of inflation was little more than a speculative hypothesis when Alan Guth proposed it in 1980. But by the end of the 1990s it was well on its way to becoming one of the cornerstones of modern cosmology. New observational data were coming in, confirming the predictions of the theory, at times in a rather unexpected way.
he theory of inflation was little more than a speculative hypothesis when Alan Guth proposed it in 1980. But by the end of the 1990s it was well on its way to becoming one of the cornerstones of modern cosmology. New observational data were coming in, confirming the predictions of the theory, at times in a rather unexpected way.
The most straightforward prediction of inflation is that the observable region of the universe should have a flat, Euclidean geometry. The universe as a whole may well be spherical, or have a more complicated shape, but our horizon encompasses only a tiny part of it, so we cannot distinguish it from flat. As we discussed in Chapter 4, this statement is equivalent to saying that the average density of the universe should be equal to the critical density with a very high accuracy.
In the early days of inflation, astronomers viewed this prediction with a high degree of skepticism. Ordinary matter, consisting of protons, neutrons,
and electrons, adds up to only a few percent of the critical density. There is also a much larger amount of what is called
dark matter
, made up of some unknown particles. As its name suggests, the dark matter cannot be seen directly, but its presence is manifested by the gravitational pull it exerts on visible objects. Observations of how stars and galaxies move indicate that the mass in dark matter is about ten times greater than that in ordinary matter. Still, putting it all together, the total mass density of the universe comes out to be about 30 percent of the critical density, 70 percent short of the target.
and electrons, adds up to only a few percent of the critical density. There is also a much larger amount of what is called
dark matter
, made up of some unknown particles. As its name suggests, the dark matter cannot be seen directly, but its presence is manifested by the gravitational pull it exerts on visible objects. Observations of how stars and galaxies move indicate that the mass in dark matter is about ten times greater than that in ordinary matter. Still, putting it all together, the total mass density of the universe comes out to be about 30 percent of the critical density, 70 percent short of the target.
This is where things stood until 1998, when two independent teams announced a startling discovery.
1
They measured the brightness of supernova explosions in distant galaxies and used the data to figure out the history of cosmic expansion.
t
To their great surprise, they found that instead of being slowed down by gravity, the speed of expansion is actually accelerating. This finding suggests that the universe is filled with some gravitationally repulsive stuff. The simplest possibility is that the true vacuum, which we now inhabit, has a nonzero mass density.
u
As we know, vacuum is gravitationally repulsive, and if its density is greater than half the average density of matter, the net result is repulsion.
1
They measured the brightness of supernova explosions in distant galaxies and used the data to figure out the history of cosmic expansion.
t
To their great surprise, they found that instead of being slowed down by gravity, the speed of expansion is actually accelerating. This finding suggests that the universe is filled with some gravitationally repulsive stuff. The simplest possibility is that the true vacuum, which we now inhabit, has a nonzero mass density.
u
As we know, vacuum is gravitationally repulsive, and if its density is greater than half the average density of matter, the net result is repulsion.
The mass density of the true vacuum is what Einstein called the cosmological constant—the idea he denounced as his greatest blunder. It lay buried for nearly seventy years, but now it looks as though it was not such a bad idea after all. As we shall see later in this book, the sudden return of the cosmological constant led to a deep crisis in elementary particle physics. But for the theory of inflation it was a very welcome development. The mass density of the vacuum, evaluated from the rate of cosmic acceleration, amounts to about 70 percent of the critical density—precisely what is needed to make the universe flat!
This conclusion was later independently confirmed by observations of the cosmic microwave radiation. Rather than relying on Friedmann’s link
between the geometry of the universe and its density, the microwave observations probe the geometry directly—in essence, by measuring the sum of the angles in a huge narrow triangle with one vertex on Earth and the other two at the points of emission of microwaves arriving to us from two nearby directions in the sky. (The longer sides of this triangle have lengths of about 40 billion light-years.) In flat space, the angles should add up to 180 degrees, as you might remember from your geometry class at school. A greater value of the sum of three angles would indicate a closed universe of spherical geometry (see
Figure 9.1
), and a smaller value would point to an open universe with the geometry of a saddle. The microwave observations showed that the sum of the angles is in fact very close to the flat-space answer. These results can be re-expressed in terms of the densities, using Friedmann’s geometry-density relation. The most recent measurements then imply that the density of the universe is equal to the critical density with an accuracy of better than 2 percent—a spectacular success for inflationary cosmology.
between the geometry of the universe and its density, the microwave observations probe the geometry directly—in essence, by measuring the sum of the angles in a huge narrow triangle with one vertex on Earth and the other two at the points of emission of microwaves arriving to us from two nearby directions in the sky. (The longer sides of this triangle have lengths of about 40 billion light-years.) In flat space, the angles should add up to 180 degrees, as you might remember from your geometry class at school. A greater value of the sum of three angles would indicate a closed universe of spherical geometry (see
Figure 9.1
), and a smaller value would point to an open universe with the geometry of a saddle. The microwave observations showed that the sum of the angles is in fact very close to the flat-space answer. These results can be re-expressed in terms of the densities, using Friedmann’s geometry-density relation. The most recent measurements then imply that the density of the universe is equal to the critical density with an accuracy of better than 2 percent—a spectacular success for inflationary cosmology.
Figure 9.1
.
In a spherical universe, the sum of the angles in a triangle is greater than 180 degrees. The triangle in this figure has three right angles, which add up to 270 degrees.
.
In a spherical universe, the sum of the angles in a triangle is greater than 180 degrees. The triangle in this figure has three right angles, which add up to 270 degrees.
Another triumph of inflation has been the explanation of small-density perturbations, the tiny ripples that later evolved into galaxies. The theory of inflation makes a sharp prediction—that the magnitude of perturbations should be nearly the same on all astrophysical distance scales, from the typical interstellar distance (a few light-years) all the way to the entire visible universe. By the early 1990s the observers were ready to put this prediction to a test.
As we discussed in Chapter 4, the primordial ripples leave an imprint on the cosmic background radiation. This afterglow of the big bang was emitted more than 13 billion years ago and now comes to us from all directions in the sky. Ever since its discovery in the mid-1960s, cosmologists were aware that hidden in this radiation was an image of the early universe. However, the primordial non-uniformities are so small, only one part in 100,000, that for many years they were beyond the accuracy of the measurements, and all one could observe was a perfectly uniform background. The breakthrough occurred in 1992, with the launch of the Cosmic Background Explorer (COBE) satellite. COBE produced a full map of the sky, detecting radiation from every direction, and we were, for the first time, able to discern tiny variations in the intensity of the radiation.
The COBE map is like a photograph that is somewhat out of focus: it captures the gross features of the cosmic fireball, but finer details, smaller than about 7 degrees on the sky, are completely blurred. (For comparison, the Moon subtends an angle of about half a degree.) COBE was followed by a series of other experiments, of ever increasing accuracy. The most recent of these was another satellite mission, WMAP.
v
Its image of the fireball, shown in
Figure 4.2
, resolves features as small as one-fifth of a degree; it is thirty times sharper than COBE’s original map.
v
Its image of the fireball, shown in
Figure 4.2
, resolves features as small as one-fifth of a degree; it is thirty times sharper than COBE’s original map.
Step by step, as the data accumulated, the pattern of primordial ripples gradually emerged. And amazingly, it was in striking agreement with the predictions of inflation! These records of the hot early epoch were there in
the sky for billions of years, waiting to be discovered and deciphered. Now, finally, the sky has spoken.
the sky for billions of years, waiting to be discovered and deciphered. Now, finally, the sky has spoken.
In the years to come, the theory of inflation will face a succession of new observational tests. A physical theory can be supported by the data, but it can never be proved. On the other hand, a single well-established fact that contradicts the theory would be enough to disprove it. For example, inflation predicts that the density should be equal to the critical density with an accuracy of 1 in 100,000. So, if some future experiment discovers a greater deviation from the critical density, inflation will be in trouble.
2
2
The next-generation microwave background missions include the Planck satellite,
w
which will further improve the image resolution, and the ground-based Clover and QUIET observatories. Clover and QUIET will accurately measure the orientation of the electric field, or
polarization
, of the microwaves. The polarization pattern is sensitive to the presence of gravitational waves—tiny vibrations of spacetime geometry. This effect can be used to test yet another prediction of inflation: we should be bathing in gravitational waves with a very wide spectrum of lengths, ranging from less than the size of the solar system up to the largest observable scales.
3
The amplitude of the waves is determined by the energy of the false vacuum that drives inflation : the higher the vacuum energy, the larger the waves. Thus, if Clover detects gravitational waves, we should be able to deduce the energy of the false vacuum that drove the inflationary expansion.
4
This would be an important step in our understanding of inflation and of its connection with the physics of the microworld.
w
which will further improve the image resolution, and the ground-based Clover and QUIET observatories. Clover and QUIET will accurately measure the orientation of the electric field, or
polarization
, of the microwaves. The polarization pattern is sensitive to the presence of gravitational waves—tiny vibrations of spacetime geometry. This effect can be used to test yet another prediction of inflation: we should be bathing in gravitational waves with a very wide spectrum of lengths, ranging from less than the size of the solar system up to the largest observable scales.
3
The amplitude of the waves is determined by the energy of the false vacuum that drives inflation : the higher the vacuum energy, the larger the waves. Thus, if Clover detects gravitational waves, we should be able to deduce the energy of the false vacuum that drove the inflationary expansion.
4
This would be an important step in our understanding of inflation and of its connection with the physics of the microworld.
As the new data were coming in, my thoughts were going back to my neglected brainchild, the theory of eternal inflation. The main objection against it was that it was concerned with the universe beyond our horizon, which is not accessible to observation. But if the theory of inflation is supported by the data in the observable part of the universe, shouldn’t we also believe its conclusions about the parts that we cannot observe?
If I drop a stone into a black hole, I can use general relativity to describe how it falls toward the center and how it is crushed and vaporized by immense gravitational forces. None of this can be observed from the outside, because neither light nor any other signal can escape from the black hole interior. And yet very few physicists would question the accuracy of my description. We have every reason to believe that general relativity applies inside black holes just as much as it does outside. The same case could now be made for the theory of inflation. We should try to extract from this theory as much as it will tell us about the grand design of the universe, its origin, and its ultimate fate.
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