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Authors: Alex Vilenkin
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The Inflationary Universe
An invasion of armies can be resisted, but not an idea whose time has come.
—VICTOR HUGO
S
uppose one day you receive a radio message from a distant galaxy saying “Elvis lives.” You point your antenna to a different galaxy, and to your surprise you get an identical message! Mystified, you turn the antenna from one galaxy to another, but the same message keeps coming to you from all over the sky. One conclusion that you draw is that the universe is full of Elvis fans; the other is that they are in communication with one another. How else would they come up with identical messages?
uppose one day you receive a radio message from a distant galaxy saying “Elvis lives.” You point your antenna to a different galaxy, and to your surprise you get an identical message! Mystified, you turn the antenna from one galaxy to another, but the same message keeps coming to you from all over the sky. One conclusion that you draw is that the universe is full of Elvis fans; the other is that they are in communication with one another. How else would they come up with identical messages?
Silly as it is, this example closely resembles the situation we observe in our universe. The intensity of the microwave radiation coming to us from all directions in the sky is the same, with a very high degree of accuracy, which indicates that the density and temperature of the universe were highly uniform at the time when the radiation was emitted. This observation suggests that there was some interaction between the radiation-emitting regions that led to equilibration of densities and temperatures. The problem is, however, that the time elapsed since the big bang is too short for such an interaction to have occurred.
The crux of the problem is that physical interactions cannot propagate faster than the speed of light. The distance traveled by light since the big bang, about 40 billion light-years, is the
horizon distance
. It puts a limit on how far we can see in the universe and gives the maximum range over which communications could be established. The cosmic radiation that we now observe was emitted shortly after the big bang and comes to us from distances approximately equal to the horizon. Now, consider the radiation coming from two opposite directions in the sky (
Figure 5.1
). The regions where this radiation was emitted are now separated by twice the horizon distance, and thus could not possibly interact. In particular, they could not exchange heat to equalize their temperature.
horizon distance
. It puts a limit on how far we can see in the universe and gives the maximum range over which communications could be established. The cosmic radiation that we now observe was emitted shortly after the big bang and comes to us from distances approximately equal to the horizon. Now, consider the radiation coming from two opposite directions in the sky (
Figure 5.1
). The regions where this radiation was emitted are now separated by twice the horizon distance, and thus could not possibly interact. In particular, they could not exchange heat to equalize their temperature.
At earlier times the two regions were closer to one another, and you might think this could have helped them to equilibrate. But actually at early times the difficulty is even more severe. The reason is that as we go back in time, the horizon distance shrinks even faster than the separation between the regions. At the time of last scattering, when the radiation was emitted, the observable part of the universe was fragmented into thousands of small regions that could not “talk” to one another. We are thus driven to the conclusion that no physical process could make the fireball uniform if it was not uniform to begin with.
Figure 5.1
. Cosmic radiation coming from opposite directions in the sky originated in regions that are now separated by twice the horizon distance.
. Cosmic radiation coming from opposite directions in the sky originated in regions that are now separated by twice the horizon distance.
This mysterious feature of the big bang is often referred to as the
horizon problem
. The only explanation we can give to the remarkable uniformity of density and temperature in the early universe is that this is how the infant universe emerged from the big bang. Logically, there is nothing wrong with
this “explanation.” The physical conditions at the singularity are undetermined, so one can postulate any physical state immediately after the big bang. But one cannot help feeling that this does not explain anything at all.
horizon problem
. The only explanation we can give to the remarkable uniformity of density and temperature in the early universe is that this is how the infant universe emerged from the big bang. Logically, there is nothing wrong with
this “explanation.” The physical conditions at the singularity are undetermined, so one can postulate any physical state immediately after the big bang. But one cannot help feeling that this does not explain anything at all.
Another puzzling feature of the big bang is the precarious balance between the power of the blast that sent all particles rushing away from one another and the force of gravity that slows the expansion down. If the density of matter in the universe were a bit higher, its gravitational pull would be strong enough to halt the expansion and the universe would eventually recollapse. If it were a bit lower, the universe would continue expanding forever. The observed density is within a few percentage points of the critical density, at the borderline between the two regimes. This is very peculiar and calls for an explanation.
The problem is that in the course of cosmic evolution the universe tends to be quickly driven away from the critical density. If, for example, we start 1 percent above the critical density at 1 second A.B., then in less than a minute we would get to twice the critical density and in a little over 3 minutes the universe would already have collapsed. Similarly, if we start 1 percent below the critical density, then in 1 year the density would be 300,000 times smaller than critical. In such a low-density universe, stars and galaxies would never form; there would be nothing but dilute, featureless gas. In order to have a nearly critical density at the present cosmic age of 14 billion years, the initial density has to be fine-tuned with a surgical accuracy. A calculation shows that at 1 second the density had to be equal to critical within 0.00000000000001 percent.
A closely related issue is the geometry of the universe. As we know from Friedmann, there is a connection between the density of the universe and its large-scale geometry. The universe is closed if the density is above critical, open if it is below critical, and flat if the density is exactly equal to critical. Thus, instead of asking why the density of the universe is so close to critical, we could just as well ask why its spatial geometry is so close to flat. That is why this fine-tuning puzzle is often called the
flatness problem
.
flatness problem
.
The horizon and flatness problems had been recognized since the 1960s, but had almost never been discussed—simply because no one had any idea as to what could be done about them. These problems could not be attacked without confronting an even greater puzzle that was looming behind them: What actually happened at the big bang? What was the nature of the force
that caused the cosmic blast and sent all particles flying away from one another? With no progress in that direction for nearly half a century, physicists grew accustomed to the thought that this was one of those questions that you never ask—either because it does not belong to physics or because physics is not yet ready to tackle it. It therefore came as a total surprise when in 1980 Alan Guth made his dramatic breakthrough, pointing the way to resolve the stubborn cosmological puzzles in one shot.
1
that caused the cosmic blast and sent all particles flying away from one another? With no progress in that direction for nearly half a century, physicists grew accustomed to the thought that this was one of those questions that you never ask—either because it does not belong to physics or because physics is not yet ready to tackle it. It therefore came as a total surprise when in 1980 Alan Guth made his dramatic breakthrough, pointing the way to resolve the stubborn cosmological puzzles in one shot.
1
Guth came up with the idea that it was repulsive gravity that blew the universe up. He suggested that the early universe contained some very unusual material, which produced a strong repulsive gravitational force. If you ever try to give a talk with this kind of idea, you had better have a piece of antigravity stuff in your pocket, or at least be prepared to give a very good reason why anybody should believe that it really exists. Luckily for Guth, he did not have to invent any magic material. The leading elementary particle theories had it already in stock: it was called
false vacuum
.
false vacuum
.
“Can you make no use of nothing, nuncle?”
“Why, no, boy; nothing can be made out of nothing.”
“Why, no, boy; nothing can be made out of nothing.”
—SHAKESPEARE,
King Lear
King Lear
Vacuum is empty space. It is often regarded as synonymous with “nothing.” That is why the idea of vacuum energy sounded so weird when Einstein first introduced it. But the physicist’s view of the vacuum has been drastically transformed, as a result of developments in particle physics over the last three decades. The study of the vacuum still continues, and the more we learn about it, the more complex and fascinating it becomes.
According to modern theories of elementary particles, vacuum is a physical object; it can be charged with energy and can come in a variety of different states. In physics terminology, these states are referred to as different vacua. The types of elementary particles, their masses, and their interactions are determined by the underlying vacuum. The relation between particles and the vacuum is similar to the relation between sound waves and
the material in which they propagate. The types of waves and the speed at which they travel vary in different materials.
the material in which they propagate. The types of waves and the speed at which they travel vary in different materials.
We live in the lowest-energy vacuum, the
true vacuum
.
2
Physicists have accumulated a great deal of knowledge about the particles that inhabit this type of vacuum and the forces acting between them. The strong
nuclear force
, for example, binds protons and neutrons in atomic nuclei; the
electromagnetic force
holds electrons in their orbits around nuclei in atoms; and the
weak force
is responsible for the interactions of elusive light particles called neutrinos. As their names suggest, the three types of forces have very different strengths, with the electromagnetic force intermediate between the strong and the weak.
true vacuum
.
2
Physicists have accumulated a great deal of knowledge about the particles that inhabit this type of vacuum and the forces acting between them. The strong
nuclear force
, for example, binds protons and neutrons in atomic nuclei; the
electromagnetic force
holds electrons in their orbits around nuclei in atoms; and the
weak force
is responsible for the interactions of elusive light particles called neutrinos. As their names suggest, the three types of forces have very different strengths, with the electromagnetic force intermediate between the strong and the weak.
The properties of elementary particles in other vacua may be completely different. We do not know how many vacua there are, but particle physics suggests that apart from our true vacuum, there are likely to be at least two more, both having more symmetry and less diversity among particles and their interactions. The first is the
electroweak
vacuum, in which the electromagnetic and weak interactions have the same strength and are manifested as parts of a single, unified force. Electrons in this vacuum have zero mass and are indistinguishable from neutrinos. They dash about at the speed of light and cannot be captured into atoms. No wonder we do not live in this type of vacuum.
electroweak
vacuum, in which the electromagnetic and weak interactions have the same strength and are manifested as parts of a single, unified force. Electrons in this vacuum have zero mass and are indistinguishable from neutrinos. They dash about at the speed of light and cannot be captured into atoms. No wonder we do not live in this type of vacuum.
The second is the
grand-unified
vacuum, where all three types of particle interactions are unified. Neutrinos, electrons, and quarks (of which protons and neutrons are made) are all interchangeable in this highly symmetric state. While the electroweak vacuum almost certainly exists, the grand-unified vacuum is more speculative. Particle theories that predict its existence are attractive from the theoretical point of view, but they are concerned with extremely high energies, and observational evidence for these theories is scant and rather indirect.
grand-unified
vacuum, where all three types of particle interactions are unified. Neutrinos, electrons, and quarks (of which protons and neutrons are made) are all interchangeable in this highly symmetric state. While the electroweak vacuum almost certainly exists, the grand-unified vacuum is more speculative. Particle theories that predict its existence are attractive from the theoretical point of view, but they are concerned with extremely high energies, and observational evidence for these theories is scant and rather indirect.
Each cubic centimeter of the electroweak vacuum carries a huge energy and, by Einstein’s mass-energy relation, a huge mass, approximately 10 million trillion tons (roughly the mass of the Moon). When faced with such colossal numbers, physicists resort to a shorthand power-of-ten notation. A trillion is 1 followed by 12 zeros; it is written as 10
12
. Ten million trillion is 1 with 19 zeros; hence, the mass density of electroweak vacuum is 10
19
tons per cubic centimeter. In a grand-unified vacuum, the mass density is still
higher, by a whopping factor of 10
48
. Needless to say, these vacua have never been synthesized in a laboratory: this would require energies far in excess of the present technological capabilities.
12
. Ten million trillion is 1 with 19 zeros; hence, the mass density of electroweak vacuum is 10
19
tons per cubic centimeter. In a grand-unified vacuum, the mass density is still
higher, by a whopping factor of 10
48
. Needless to say, these vacua have never been synthesized in a laboratory: this would require energies far in excess of the present technological capabilities.
In contrast to these enormous energies, the energy of the normal, true vacuum is minuscule. For a long time it was thought to be exactly zero, but recent observations indicate that our vacuum has a small positive energy, which is equivalent to the mass of three hydrogen atoms per cubic meter. The significance of this finding will become clear in Chapters 9, 12, and 14.
High-energy vacua are called “false” because, unlike our true vacuum, they are unstable. After a brief period of time, typically a small fraction of a second, a false vacuum decays, turning into the true vacuum, and its excess energy is released in a fireball of elementary particles. We shall delve into the details of the vacuum decay process in the following chapter.
If vacuum has energy, then we know from Einstein that it should also have tension.
3
And, as we discussed in Chapter 2, tension has a repulsive gravitational effect. In the case of a vacuum, the repulsion is three times stronger than the attractive gravity caused by the mass, and the net effect is a strong repulsive force. Einstein used this antigravity of the vacuum to balance the gravitational pull of ordinary matter in his static model of the world. He found that the balance is achieved when the mass density of matter is twice that of the vacuum. Guth had a different plan: instead of balancing the universe, he wanted to blow it up. So he allowed the repulsive gravity of false vacuum to reign unopposed.
3
And, as we discussed in Chapter 2, tension has a repulsive gravitational effect. In the case of a vacuum, the repulsion is three times stronger than the attractive gravity caused by the mass, and the net effect is a strong repulsive force. Einstein used this antigravity of the vacuum to balance the gravitational pull of ordinary matter in his static model of the world. He found that the balance is achieved when the mass density of matter is twice that of the vacuum. Guth had a different plan: instead of balancing the universe, he wanted to blow it up. So he allowed the repulsive gravity of false vacuum to reign unopposed.
What would happen if, at some early epoch, the space of the universe were in a false-vacuum state? If the matter density at that epoch were less than needed to balance the universe, then the repulsive gravity of the vacuum would have prevailed. This would cause the universe to expand—even if it did not expand to begin with.
To have a definite picture in mind, we shall assume that the universe is closed. Then it swells like an expanding balloon, as shown in
Figure 3.1
in Chapter 3. As the volume of the universe grows, the matter is diluted and
its mass density is reduced. But the mass density of false vacuum is a fixed constant; it always remains the same. Hence, very quickly the matter density becomes negligible, and we are left with a uniform, expanding sea of false vacuum.
Figure 3.1
in Chapter 3. As the volume of the universe grows, the matter is diluted and
its mass density is reduced. But the mass density of false vacuum is a fixed constant; it always remains the same. Hence, very quickly the matter density becomes negligible, and we are left with a uniform, expanding sea of false vacuum.
Figure 5.2
.
Alan Guth in his office at MIT. Guth is the proud winner of the 2005 contest for the messiest office, organized by
The Boston Globe
. (Photo by Larry Fink)
.
Alan Guth in his office at MIT. Guth is the proud winner of the 2005 contest for the messiest office, organized by
The Boston Globe
. (Photo by Larry Fink)
The expansion is driven by the false-vacuum tension, overcoming the attractive force of the vacuum mass density. Since neither of these quantities changes with time, the
expansion rate
remains constant as well. The expansion rate tells by what fraction the universe grows in a chosen unit of time (say, in 1 second). Its meaning is very similar to that of the inflation rate in economics: the percentage increase of prices in a year. In 1980, when Guth
gave his seminar at Harvard, the rate of economic inflation in the United States was 14 percent. If it remained fixed at that value, prices would double every 5.3 years. Similarly, a constant expansion rate of the universe implies that there is a fixed time in which the size of the universe doubles.
expansion rate
remains constant as well. The expansion rate tells by what fraction the universe grows in a chosen unit of time (say, in 1 second). Its meaning is very similar to that of the inflation rate in economics: the percentage increase of prices in a year. In 1980, when Guth
gave his seminar at Harvard, the rate of economic inflation in the United States was 14 percent. If it remained fixed at that value, prices would double every 5.3 years. Similarly, a constant expansion rate of the universe implies that there is a fixed time in which the size of the universe doubles.
The growth pattern with a constant doubling time is called exponential. It is known to build up very quickly to gigantic numbers. If a slice of pizza costs $1 now, then after 10 doubling cycles (53 years in our example) its price will be $1,024, and after 330 cycles it will be $10
100
. This stupendous number, 1 followed by 100 zeros, has a special name: a
googol
. Guth suggested that we adopt the term “inflation” in cosmology, using it to describe an exponential expansion of the universe.
100
. This stupendous number, 1 followed by 100 zeros, has a special name: a
googol
. Guth suggested that we adopt the term “inflation” in cosmology, using it to describe an exponential expansion of the universe.
The doubling time in a false-vacuum universe is unbelievably short. The higher the vacuum energy, the shorter the time. For the electroweak vacuum, the universe would expand by a googol in one-thirtieth of a microsecond, and for the grand-unified vacuum this expansion would happen 10
26
times faster. In this tiny fraction of a second, a region the size of an atom would be blown to dimensions much greater than the entire currently observable universe.
26
times faster. In this tiny fraction of a second, a region the size of an atom would be blown to dimensions much greater than the entire currently observable universe.
Since false vacuum is unstable, it eventually decays, and its energy ignites a hot fireball of particles. This event signals the end of inflation and the starting point of the usual cosmological evolution. We thus get an enormous, hot, expanding universe from a tiny initial seed. As an extra bonus, amazingly, the horizon and flatness problems of big bang cosmology disappear in this scenario.
The essence of the horizon problem is that the distances between some parts of the observable universe appear to have always been greater than the distance traveled by light since the big bang. This implies that these regions have never interacted with one another, and then it is hard to explain how they could reach nearly identical temperatures and densities. In the standard big bang theory, the distance traveled by light grows proportionally to the age of the universe, while the separation between the regions increases more slowly, because cosmic expansion is being slowed down by gravity. Regions that cannot interact now will be able to do so in the future, when the light-travel distance finally catches up with their separation. But at earlier times the light-travel distance fell even shorter of the mark, so that if the regions cannot interact at the present epoch, they were surely unable to
do so in the past. The root of the problem can thus be traced to the attractive nature of gravity, which causes the expansion to slow down with time.
do so in the past. The root of the problem can thus be traced to the attractive nature of gravity, which causes the expansion to slow down with time.
In a false-vacuum universe, however, gravity is repulsive; so instead of slowing down, expansion accelerates. Then the situation is reversed: regions that can exchange light signals will lose their ability to interact in the future. And more important, regions that are out of each other’s reach must have interacted in the past. The horizon problem has disappeared!
The flatness problem dissolves just as easily. It turns out that the universe is driven away from the critical density only if its expansion is slowing down. In the case of accelerated, inflationary expansion, the opposite is true: the universe is driven
toward
the critical density, and thus to flatness. Since inflation enlarges the universe by an enormous factor, we can see only a tiny part of it. This observable region appears to be flat, just as the surface of the Earth appears flat when you look at it from close by.
toward
the critical density, and thus to flatness. Since inflation enlarges the universe by an enormous factor, we can see only a tiny part of it. This observable region appears to be flat, just as the surface of the Earth appears flat when you look at it from close by.
In summary, a brief period of inflation makes the universe large, hot, uniform, and flat, setting just the right initial conditions for the standard big bang cosmology.
The theory of inflation was about to begin its conquest of the world. As for Guth himself, his days as a postdoc were over. He accepted a job offer from his alma mater, the Massachusetts Institute of Technology, where he has remained ever since.
This would be a nice happy ending to the story of inflation, except for one unfortunate problem: the theory did not work.
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