Many Worlds in One: The Search for Other Universes (9 page)
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Authors: Alex Vilenkin
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We have assumed so far that the starting point for inflation was a small closed universe with a scalar field in the false vacuum, at the top of its energy hill.
But these assumptions are not necessary. We could instead have started with a small chunk of false vacuum in an infinite universe. Such a beginning would also lead to inflation, but in a somewhat unexpected way.
But these assumptions are not necessary. We could instead have started with a small chunk of false vacuum in an infinite universe. Such a beginning would also lead to inflation, but in a somewhat unexpected way.
Remember, false vacuum has a large tension, which is responsible for its repulsive gravity. If it fills the entire space, the tension is the same everywhere and has no physical effect other than gravitational. But if it is surrounded by true vacuum, the tension inside is not balanced by any force outside and causes the false vacuum chunk to shrink. You might think that tension would be counteracted by the repulsive gravity, but this is not what actually happens.
Analysis based on Einstein’s general relativity shows that the gravitational repulsion is purely internal. So, if you had a false-vacuum chunk for your lecture demonstration, objects would not fly away from it as in
Figure 1.1
. They would be attracted to it instead. Outside the false vacuum, the gravitational force is attractive as usual. So the force of tension causes the chunk to shrink, while its interior “wants” to expand because of the internal gravitational repulsion. The outcome depends on the size of the chunk.
Figure 1.1
. They would be attracted to it instead. Outside the false vacuum, the gravitational force is attractive as usual. So the force of tension causes the chunk to shrink, while its interior “wants” to expand because of the internal gravitational repulsion. The outcome depends on the size of the chunk.
If it is smaller than a certain critical size, the tension wins, and the chunk shrinks like a piece of stretched rubber. Then, after a few oscillations, it disintegrates into elementary particles.
If the size is bigger than critical, repulsive gravity wins and the false vacuum begins to swell. As it does so, it warps space, like a blown-up balloon. This effect is illustrated in
Figure 6.7
for a spherical false-vacuum region. Only two spatial dimensions are shown, so the spherical boundary of the region is represented by a circle. Tension pulls the boundary inward, toward the center of the sphere, and this has the effect of reducing the volume of false vacuum. But this reduction is totally negligible compared with the exponential expansion of the interior.
Figure 6.7
for a spherical false-vacuum region. Only two spatial dimensions are shown, so the spherical boundary of the region is represented by a circle. Tension pulls the boundary inward, toward the center of the sphere, and this has the effect of reducing the volume of false vacuum. But this reduction is totally negligible compared with the exponential expansion of the interior.
The inflating balloon is connected to the exterior space by a narrow “wormhole.” From outside, the wormhole is seen as a black hole, and observers in the exterior region can neither verify nor disprove that there is a huge inflating universe inside this black hole. Likewise, observers that will evolve in the inflating bubble universe will see only a tiny part of it and will never find out that their universe has a boundary and that there is another big universe beyond it.
Figure 6.7
.
An inflating false-vacuum balloon (dark) is connected to the exterior space by a “wormhole” and is seen as a black hole from the exterior region.
.
An inflating false-vacuum balloon (dark) is connected to the exterior space by a “wormhole” and is seen as a black hole from the exterior region.
Since the fate of the false-vacuum sphere depends so crucially on whether its radius is greater than critical, it is important to know what the critical radius actually is. The answer depends on the vacuum energy density: the larger the energy density, the smaller the critical radius. For the electroweak vacuum it turns out to be about 1 millimeter, and for the grand-unified vacuum it is 10 trillion times smaller. This is all that is needed to create a universe! Truly, the ultimate free lunch. Almost …
The Antigravity Stone
It would be more impressive if it flowed the other way.
—OSCAR WILDE, on Niagara Falls
T
he theory of inflation became a major topic of my research soon after that Wednesday seminar at Harvard in 1980, where I first heard about it. In fact, if I were more mystically inclined, I might have seen the writing on the wall even before Guth’s seminar. There were some clues pointing to repulsive gravity right where I work, at Tufts University.
he theory of inflation became a major topic of my research soon after that Wednesday seminar at Harvard in 1980, where I first heard about it. In fact, if I were more mystically inclined, I might have seen the writing on the wall even before Guth’s seminar. There were some clues pointing to repulsive gravity right where I work, at Tufts University.
Set on a gently sloping hill, amid shady elms, the Tufts campus exudes an air of grace and tranquility. As you climb the stairs up the hill to the heart of the campus, and walk past the ivy-covered Romanesque chapel, you may notice a peculiar monument. It is a sizable slab of granite, rising vertically from the ground, like an old tombstone. The inscription says:
THIS MONUMENT HAS BEEN
ERECTED BY THE
GRAVITY RESEARCH FOUNDATION,
ROGER W. BABSON FOUNDER.
IT IS TO REMIND STUDENTS OF
THE BLESSINGS FORTHCOMING
WHEN A SEMI-INSULATOR IS
DISCOVERED IN ORDER TO HARNESS
GRAVITY AS FREE POWER
AND REDUCE AIRPLANE ACCIDENTS.
1961
ERECTED BY THE
GRAVITY RESEARCH FOUNDATION,
ROGER W. BABSON FOUNDER.
IT IS TO REMIND STUDENTS OF
THE BLESSINGS FORTHCOMING
WHEN A SEMI-INSULATOR IS
DISCOVERED IN ORDER TO HARNESS
GRAVITY AS FREE POWER
AND REDUCE AIRPLANE ACCIDENTS.
1961
This is the notorious antigravity stone, the sign of my destiny.
Roger Babson, who also founded Babson College, was living proof that shrewd business judgment can peacefully coexist with far-out scientific ideas. He claimed it was by using Newton’s laws of mechanics that he predicted the stock market crash of 1929 and the Great Depression that followed. With Newton’s help, he managed to amass a great fortune, and in gratitude to Sir Isaac, he bought an entire room from Newton’s last residence in London as well as an apple tree that is a descendant of the famous tree at Newton’s family home in Lincolnshire. Legend has it that the fall of an apple from that tree inspired Newton to discover the law of gravity. And gravity, as you might have guessed, was a paramount theme in Babson’s universe.
Babson’s obsession with gravity dates back to his childhood, when his sister drowned in a river. He blamed gravity for her death and resolved to free humanity from its fatal pull. In his book
Gravity—Our Enemy No. 1
, Babson described the benefits to be derived from an insulator against gravity. It would reduce the weight of airplanes and increase their speed; it could even be used in the soles of shoes to lighten weight when walking. Babson’s lifelong friend, the famous inventor Thomas Edison, suggested to him that birds may have some antigravity stuff in their skin, and Babson promptly acquired a collection of some five thousand stuffed birds. It is not clear exactly what he did with them, but apparently this line of research did not result in any breakthrough.
Gravity—Our Enemy No. 1
, Babson described the benefits to be derived from an insulator against gravity. It would reduce the weight of airplanes and increase their speed; it could even be used in the soles of shoes to lighten weight when walking. Babson’s lifelong friend, the famous inventor Thomas Edison, suggested to him that birds may have some antigravity stuff in their skin, and Babson promptly acquired a collection of some five thousand stuffed birds. It is not clear exactly what he did with them, but apparently this line of research did not result in any breakthrough.
To his credit, Babson did put his money where his mouth was. He made gifts to several universities, Tufts included, to facilitate antigravity research. The only condition of the grant was that a monument with Babson’s inscription be erected on campus.
The wacky monument was a source of embarrassment for the Tufts administration and inspired numerous pranks by the students. It would occasionally disappear, only to reappear where it was least expected. Once it was found blocking the entrance of the trustees and the president at the commencement.
At one time it looked as if the stone had disappeared for good, but then it miraculously resurfaced ten years later. It turned out that a group of students had buried it somewhere on campus and then dug it out when they returned to Tufts for their class reunion. Gravity alone was clearly not enough to keep the stone in place, so it was finally cemented to the ground.
At one time it looked as if the stone had disappeared for good, but then it miraculously resurfaced ten years later. It turned out that a group of students had buried it somewhere on campus and then dug it out when they returned to Tufts for their class reunion. Gravity alone was clearly not enough to keep the stone in place, so it was finally cemented to the ground.
Since few scientists could claim they had an active program of research in antigravity, the Babson money proved rather difficult to get. It’s not that nobody tried: the university president, Jean Mayer, who was a nutritionist, argued unsuccessfully that weight loss was antigravity. After years of discussions and legal arguments, the money was eventually used to establish the Tufts Institute of Cosmology.
Figure 7.1
.
A triumphant Dr. Vitaly Vanchurin after his Ph.D. inauguration, surrounded by members of the Institute of Cosmology. Standing, from left to right: Larry Ford, Ken Olum, and the author. (Courtesy of Delia Schwartz-Perlov)
.
A triumphant Dr. Vitaly Vanchurin after his Ph.D. inauguration, surrounded by members of the Institute of Cosmology. Standing, from left to right: Larry Ford, Ken Olum, and the author. (Courtesy of Delia Schwartz-Perlov)
Like any self-respecting academic institution, our institute has its own unique ritual—an “inauguration” ceremony for cosmology Ph.D. recipients. After defending the dissertation, a new Ph.D. gets an apple dropped on his
head while kneeling in front of the antigravity stone. The apple comes from the hand of the thesis advisor and may then be eaten by the “inauguree.”
head while kneeling in front of the antigravity stone. The apple comes from the hand of the thesis advisor and may then be eaten by the “inauguree.”
By the time the Institute of Cosmology was established, Babson was long since dead and his Gravity Research Foundation had evolved into a respectable institution giving research grants on gravitation. Nobody really expected that Tufts cosmologists would work on antigravity, but strangely enough—they do. Much of the research at the institute is focused on false vacuum and its repulsive gravity, which certainly qualifies as antigravity. So I think Mr. Babson could not have found a better use for the money. We have not succeeded in reducing the number of airplane accidents though.
Runaway Inflation
In my opinion, the most plausible answer to what happened before inflation is—more inflation.
—ALAN GUTH
W
hat lies beyond our present horizon? That was the question that intrigued me from the early days of inflation. If we can see only a minuscule part of the universe, then what is the big picture—like the view of our planet that is revealed to space travelers as their spaceship leaves the Earth?
hat lies beyond our present horizon? That was the question that intrigued me from the early days of inflation. If we can see only a minuscule part of the universe, then what is the big picture—like the view of our planet that is revealed to space travelers as their spaceship leaves the Earth?
The theory of density perturbations provided some clues. According to this theory, the pattern of how galaxies are distributed in space is determined by quantum kicks experienced by the scalar field during inflation. This is a random process; so some regions of the same size as ours have more galaxies, and others have less. The reason we have the Milky Way galaxy right here, where we are, is that the scalar field at this location had a tiny kick backward, away from the true vacuum, so that it ended its roll down the energy hill a bit later than it did in the neighboring locales. This produced a small density enhancement, which later evolved into our galaxy. Similar little humps on the smooth density background gave rise to our neighbor Andromeda and to countless other galaxies within our horizon and beyond. This description of structure formation suggests that the remotest parts of
the universe look more or less the same as what we see around here. But I was beginning to suspect that something was missing from this picture.
the universe look more or less the same as what we see around here. But I was beginning to suspect that something was missing from this picture.
The effect of quantum kicks is very small because they are much weaker than the force due to the slope of the energy hill that drives the scalar field down. This explains why the field reaches the bottom everywhere at about the same time and only small density perturbations are produced. The question I was asking myself was, What happens when the field is near the top of the hill, where the slope is very small? There, it should be at the mercy of quantum kicks, which shove it at random one way and then the other. The universe resulting from inflation might then be far less orderly, and more erratic, than it first appeared.
Figure 8.1
. Mr. Field walks randomly on the flat portion of the hill and slides down when he gets to the steeper slope.
. Mr. Field walks randomly on the flat portion of the hill and slides down when he gets to the steeper slope.
To picture the behavior of the scalar field near the top of the hill, we shall use a politically incorrect but pertinent analogy. Let me introduce a gentleman, named Mr. Field, who had too much to drink and is now trying to maintain his vertical position. He has little control of his feet and no idea where he is heading, so he steps to the right or to the left completely at random. Mr. Field starts his promenade at the top of the hill, as in
Figure 8.1
. Since on average he steps to the right as frequently as he does to the left, he is not getting anywhere very fast. But after a large number of steps he will gradually drift away from the hilltop. Eventually, he will get to the steeper
part of the hill, where he will inevitably slip and finish the rest of the journey sliding downhill on his rear.
Figure 8.1
. Since on average he steps to the right as frequently as he does to the left, he is not getting anywhere very fast. But after a large number of steps he will gradually drift away from the hilltop. Eventually, he will get to the steeper
part of the hill, where he will inevitably slip and finish the rest of the journey sliding downhill on his rear.
The scalar field behavior during inflation is very similar. The field wanders aimlessly near the top of the energy hill, until it reaches a steeper slope; then it “rolls” down toward the end of inflation. On the flat portion near the top of the hill, the field variation is induced by quantum kicks and is totally random, while the roll down the slope is orderly and predictable, with quantum kicks introducing only a small disturbance. The time interval between successive quantum kicks is roughly equal to the doubling time of inflation. This means that Mr. Field takes about one step per doubling time. And since he makes many steps wandering around the flat hilltop, it follows that the false vacuum takes many doubling times to decay.
A particular sequence of steps that brings Mr. Field from the top of the hill to the bottom represents one possible history of the scalar field. But quantum kicks experienced by the field differ from one place to another, so the scalar field histories will also be different. Each quantum kick affects a small region of space. Its size is, roughly, the distance traveled by light during one doubling time of inflation; we shall call it a “kickspan.”
p
We can imagine a party of gentlemen in the same condition as Mr. Field, each representing the scalar field at some point in space. When two points are within a kickspan of one another, they experience the same quantum kicks; so the corresponding two gentlemen do all the steps in sync, like a pair of tap dancers. But the points are rapidly driven apart by the inflationary expansion of the universe, and when they get separated by more than a kickspan, the two gentlemen part company and start walking independently. Once this happens, the scalar field values at the two points start gradually drifting apart, while the distance between the points continues to be rapidly stretched by inflation.
p
We can imagine a party of gentlemen in the same condition as Mr. Field, each representing the scalar field at some point in space. When two points are within a kickspan of one another, they experience the same quantum kicks; so the corresponding two gentlemen do all the steps in sync, like a pair of tap dancers. But the points are rapidly driven apart by the inflationary expansion of the universe, and when they get separated by more than a kickspan, the two gentlemen part company and start walking independently. Once this happens, the scalar field values at the two points start gradually drifting apart, while the distance between the points continues to be rapidly stretched by inflation.
The smallness of density perturbations in our observable region tells us that all points in this region were still within a kickspan of one another when the scalar field was well on its way down the hill. That is why the effect of quantum kicks was very minor, and the field reached the bottom everywhere at about the same time. But if we could go to very large distances, far
beyond our horizon, we would see regions that parted our company when the field was still wandering near the hilltop. The scalar field histories in such regions could be very different from ours, and I wanted to know what the universe looks like on such superlarge scales.
beyond our horizon, we would see regions that parted our company when the field was still wandering near the hilltop. The scalar field histories in such regions could be very different from ours, and I wanted to know what the universe looks like on such superlarge scales.
Imagine a large party of jolly walkers starting off from the top of the hill. Each walker represents a remote region of the universe, so they all walk independently. If the flat portion of the hill is
N
steps long, then a typical random walker will cross it in about
N
2
steps. Roughly half of the walkers will do it faster and another half slower. For example, if the distance is 10 steps, it will take, on average, 100 steps for a random walker to cross it. So, after the first 100 steps, about half of the company will have reached their destination at the bottom, while the other half will still be enjoying the promenade. In another 100 steps, the number of remaining walkers will again be cut in half, and so on, until the last fellow finally slides downhill.
N
steps long, then a typical random walker will cross it in about
N
2
steps. Roughly half of the walkers will do it faster and another half slower. For example, if the distance is 10 steps, it will take, on average, 100 steps for a random walker to cross it. So, after the first 100 steps, about half of the company will have reached their destination at the bottom, while the other half will still be enjoying the promenade. In another 100 steps, the number of remaining walkers will again be cut in half, and so on, until the last fellow finally slides downhill.
But now, there is a crucial difference between the walkers and the inflating regions they represent. While a walker is wandering near the hilltop, the corresponding region undergoes exponential inflationary expansion. So the number of independently evolving regions rapidly multiplies. This is as if the walkers were to multiply as well. As I continued to think about this, the picture was gradually taking shape.
In a way, inflation is similar to the reproduction of bacteria. There are two competing processes: bacteria reproduce by division, and they are occasionally destroyed by antibodies. The outcome depends on which process is more efficient. If the bacteria are destroyed faster than they reproduce, they will quickly die out. Alternatively, if the reproduction is faster, bacteria will rapidly multiply (
Figure 8.2
).
Figure 8.2
).
In the case of inflation, the two rival processes are the false-vacuum decay and its “reproduction” due to the rapid expansion of inflating regions. The efficiency of decay can be characterized by a
half-life
q
—the time during which half of the false vacuum would decay if it were not expanding. (In
our random-walk analogy, this is the time it takes for the number of walkers to be reduced by half.) On the other hand, the efficiency of reproduction is characterized by the doubling time, during which the volume of inflating false-vacuum doubles. The false-vacuum volume will shrink if the half-life is shorter than the doubling time and will grow otherwise.
half-life
q
—the time during which half of the false vacuum would decay if it were not expanding. (In
our random-walk analogy, this is the time it takes for the number of walkers to be reduced by half.) On the other hand, the efficiency of reproduction is characterized by the doubling time, during which the volume of inflating false-vacuum doubles. The false-vacuum volume will shrink if the half-life is shorter than the doubling time and will grow otherwise.
Figure 8.2
.
The number of bacteria will rapidly grow if the bacteria reproduce faster than they are destroyed.
.
The number of bacteria will rapidly grow if the bacteria reproduce faster than they are destroyed.
But it follows from the discussion in the preceding section that the false-vacuum half-life is long compared with the doubling time. The reason is that in models of inflation the energy hill is rather flat and it takes many steps to cross it. Since each step of a random walker corresponds to one doubling time of inflation, it follows that the half-life must be much longer than the doubling time. Hence, false-vacuum regions multiply much faster than they decay. This means that inflation never ends in the entire universe and the volume of inflating regions keeps growing without bound!
At this very moment, some distant parts of the universe are filled with false vacuum and are undergoing exponential inflationary expansion. Regions like ours, where inflation has ended, are also constantly being produced. They form “island universes” in the inflating sea.
r
Because of inflation, the space between these islands rapidly expands, making room for more island
universes to form. Thus, inflation is a runaway process, which stopped in our neighborhood, but still continues in other parts of the universe, causing them to expand at a furious rate and constantly spawning new island universes like ours.
r
Because of inflation, the space between these islands rapidly expands, making room for more island
universes to form. Thus, inflation is a runaway process, which stopped in our neighborhood, but still continues in other parts of the universe, causing them to expand at a furious rate and constantly spawning new island universes like ours.
The energy of the decaying false vacuum ignites a hot fireball of elementary particles and triggers the formation of helium and all the subsequent events of the standard big bang cosmology. Thus, the end of inflation plays the role of the big bang in this scenario. If we make this identification, then we should not think of the big bang as a one-time event in our past. Multiple bangs went off before it in remote parts of the universe, and countless others will erupt elsewhere in the future.
s
s
Once this new worldview was clear in my mind, I could not wait to share it with other cosmologists. And who better could I choose as my first confidant but Mr. Inflation himself—Alan Guth, whose office at MIT was only a 20-minute drive away from Tufts. So I did just that—I drove to the famous institute for a meeting with Alan.
MIT occupies a monstrous conglomeration of buildings, where I have gotten hopelessly lost on many occasions. You may walk on the third floor of building 6 and suddenly discover that you are already on the fourth floor of building 16. I decided to play it safe and took the simplest, although the longest, way to my destination: through the main entrance (marked by a row of Corinthian columns and crowned with a green dome). I had to march all the way along what locals call the Infinite Corridor, then climb a few flights of stairs, and finally I was in Alan Guth’s office.
I told Alan about the random walk of the scalar field and how it could be described mathematically. But then, when I was in the middle of unveiling my new dazzling picture of the universe, I noticed that Alan was beginning to doze off. Years later, when I got to know Alan better, I learned that he is a very sleepy fellow. We organize a joint seminar for the Boston-area cosmologists, and at every seminar meeting Alan falls peacefully asleep a
few minutes after the talk begins. Miraculously, when the speaker is finished, he wakes up and asks the most penetrating questions. Alan denies any supernatural abilities, but not everybody is convinced. So, in retrospect, I should have continued the discussion. But at the time I was not aware of Alan’s magical powers and hastily retreated.
few minutes after the talk begins. Miraculously, when the speaker is finished, he wakes up and asks the most penetrating questions. Alan denies any supernatural abilities, but not everybody is convinced. So, in retrospect, I should have continued the discussion. But at the time I was not aware of Alan’s magical powers and hastily retreated.
The response I got from other colleagues was also less than enthusiastic. Physics is an observational science, they said, so we should refrain from making claims that cannot be observationally confirmed. We cannot observe other big bangs, nor can we observe distant inflating regions. They are all beyond our horizon, so how can we verify that they really exist? I was disheartened by such a cool reception and decided to publish this work by embedding it as a section in a paper on a different subject: I came to think that it did not deserve to have a full paper devoted to it.
1
1
To explain the idea of eternal inflation in the paper, I used the analogy of a drunk wandering near the top of a hill. In a couple of months I got a letter from the editor saying that my paper was accepted, except that the discussion of drunks “was not appropriate for an archival journal like the
Physical Review
” and I should replace it with a more suitable analogy. I heard of a similar incident that happened earlier to Sidney Coleman. He had a diagram in his paper that looked like a circle with a wiggly tail. Coleman referred to it as a “tadpole diagram.” Predictably, the editor complained that the term was inappropriate. “OK,” replied Coleman, “let us call it sperm diagram.” Following that, the original version of the paper was accepted without further comment. I briefly contemplated using Coleman’s tactic, but then decided against it and removed the drunk analogy altogether: I did not feel like picking a fight.
Physical Review
” and I should replace it with a more suitable analogy. I heard of a similar incident that happened earlier to Sidney Coleman. He had a diagram in his paper that looked like a circle with a wiggly tail. Coleman referred to it as a “tadpole diagram.” Predictably, the editor complained that the term was inappropriate. “OK,” replied Coleman, “let us call it sperm diagram.” Following that, the original version of the paper was accepted without further comment. I briefly contemplated using Coleman’s tactic, but then decided against it and removed the drunk analogy altogether: I did not feel like picking a fight.
I did not return to the theory of eternal inflation for nearly ten years. Except for one episode …
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