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Authors: Alex Vilenkin
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Did the Universe Have a Beginning?
Whence all creation had its origin, … he, who surveys it all from highest heaven, he knows or maybe even he does not know.
—RIG-VEDA
A
ncient creation myths display wonderful ingenuity, but at the most fundamental level they have to choose one of two basic options: either the universe was created a finite time ago, or it has existed forever.
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ncient creation myths display wonderful ingenuity, but at the most fundamental level they have to choose one of two basic options: either the universe was created a finite time ago, or it has existed forever.
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Here is one of several scenarios offered in the sacred Hindu scripture, the Upanishads:
In the beginning this [world] was nonexistent. It became existent. It turned into an egg. The egg lay for the period of a year. Then it broke open … And what was born of it was yonder Aditya, the Sun. When it was born shouts of “Hurrah” arose, together with all beings and all objects of desire.
This idea looks simple enough, but unfortunately it has a serious flaw, which it shares with every other story of creation. The ancients were well aware of the problem; the Jain poet Jinasena wrote in the ninth century:
The doctrine that the world was created is ill-advised, and should be rejected.
If God created the world, where was he before creation? …
How could God have made the world without any raw material? If you say he made this first, and then the world, you are faced with an endless regression …
Thus the doctrine that the world was created by God makes no sense at all …
Know that the world is uncreated, as time itself is, without beginning and end … Uncreated and indestructible, it endures under the compulsion of its own nature.
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This critique applies equally well to every scenario of the cosmic origin—be it a creation by God, as in the story of the cosmic egg, or a “natural” creation, such as the big bang model of modern cosmology.
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According to the big bang theory, all the matter that we see around us came out of a hot cosmic fireball some 14 billion years ago. But where did the fireball come from? The theory of inflation has shown that an expanding fireball could arise out of a tiny false-vacuum nugget. But the question still remains: Where did that initial nugget originate? What happened before inflation?
For the most part, cosmologists were in no hurry to tackle this thorny issue. In fact, it appeared that a satisfactory answer could never be given. Whatever the answer is, one can always ask “And what happened before that?” This is the “endless regression” that Jinasena is referring to. However, in the 1980s, when the eternal inflation scenario was developed, it appeared to offer an attractive alternative.
An eternally inflating universe consists of an expanding “sea” of false vacuum, which is constantly spawning “island universes” like ours. Inflation is thus a never-ending process. It has ended in our own island universe, but will continue indefinitely in other remote regions. But if inflation is going to continue forever into the future, then perhaps it might have had no beginning in the past. We would then have an eternally inflating universe without a beginning and without an end; that would eliminate the perplexing problems associated with the cosmic origin. This picture is reminiscent of the
steady-state cosmology of the 1940s and ’50s. Some people found it very appealing.
steady-state cosmology of the 1940s and ’50s. Some people found it very appealing.
Apart from a steady state, there is another way for the universe to be eternal. And again, the Hindus figured this out a long time ago. The endless cycle of creation and destruction is symbolized by the dance of the god Shiva. “He rises from His rapture and, dancing, sends through inert matter pulsing waves of awakening sound.” The universe comes to life, but then “[i]n the fullness of time, still dancing, He destroys all forms and names by fire and gives new rest.”
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A parallel idea in scientific cosmology is that of an oscillating universe, which goes through a cycle of expansion and contraction. It was briefly popular in the 1930s, but then fell out of favor, because of apparent conflict with the second law of thermodynamics.
The second law requires that entropy, which is a measure of disorder, should grow in each cycle of cosmic evolution. If the universe had already gone through an infinite number of cycles, it would have reached the maximum-entropy state of thermal equilibrium. We certainly do not find ourselves in such a state. This is the “heat death” problem that I mentioned earlier.
The idea of an oscillating universe was abandoned for more than half a century, but in 2002 it was revived in a new guise by Paul Steinhardt and Neil Turok of Cambridge University. As in earlier models, they suggested that the history of the universe consists of an endlessly repeating cycle of expansion and contraction. Each cycle starts with a hot expanding fireball. It expands and cools down, galaxies form, and the vacuum energy comes to dominate the universe soon thereafter. At this point the universe starts expanding exponentially, with its size doubling every 10 billion years or so. After trillions of years of this super-slow inflation, the universe becomes very homogeneous, isotropic, and flat. Eventually the expansion slows down and then turns into contraction. The universe recollapses and immediately bounces back to start a new cycle. Part of the energy generated in the collapse goes to create a hot fireball of matter.
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Steinhardt and Turok argue that the problem of the beginning does not arise in their scenario. The universe has always been going through the same cycle, so there was no beginning. The problem of the heat death is also avoided, because the amount of expansion in a cycle is greater than the amount of contraction, so the volume of the universe is increased after each cycle. The entropy of our observable region is now the same as the entropy of a similar region in the preceding cycle, but the entropy of the entire universe has increased, simply because the volume of the universe is now greater. As time goes on, both the entropy and the total volume grow without bound. The state of maximum entropy is never reached, because there is no maximum entropy.
Thus, it appears that we have two possible models for an eternal universe without a beginning: one is based on eternal inflation and the other on cyclic evolution. However, it turns out that neither possibility can yield a complete description of the universe.
When a physicist wants to understand some phenomenon, the first thing she does is to maximally simplify it, stripping it down to the bare essentials. In the case of eternal inflation, we can strip away island universes, keeping only the inflating sea. In addition, we can assume that the universe is homogeneous and isotropic, as in Friedmann’s models. With these simplifications, Einstein’s equations for the inflating universe can be easily solved.
The solution has the geometry of a three-dimensional sphere, which contracts from a very large radius in the remote past. The contraction is slowed down by the repulsive gravity of the false vacuum, until the sphere stops for a moment and then starts to re-expand. The force of gravity now works in the direction of motion, so the sphere expands with acceleration. Its radius grows exponentially, with a doubling time determined by the energy density of the false vacuum.
bi
bi
The solution I have just described has been known since the early days of general relativity; it is called
de Sitter spacetime
—after the Dutch astronomer
Willem de Sitter, who discovered it in 1917. This spacetime is illustrated in
Figure 16.1
. Inflation begins in de Sitter spacetime only after the spherical universe has reached its minimum radius. But once started, the exponential expansion continues forever, so inflation is eternal to the future.
de Sitter spacetime
—after the Dutch astronomer
Willem de Sitter, who discovered it in 1917. This spacetime is illustrated in
Figure 16.1
. Inflation begins in de Sitter spacetime only after the spherical universe has reached its minimum radius. But once started, the exponential expansion continues forever, so inflation is eternal to the future.
If we were to allow the formation of island universes, they would collide and merge in the contracting part of spacetime. The islands would then quickly fill the entire space, the false vacuum would be completely eliminated, and the universe would continue collapsing to a big crunch. Thus, inflation cannot be extended into the infinite past. It must have had some sort of beginning.
We should keep in mind, however, that this conclusion is based on the maximally simplified model of inflation, which assumes a homogeneous and isotropic universe. In reality, the universe may well be very irregular—inhomogeneous and anisotropic—on scales much greater than the present horizon. Could it be, then, that the contracting phase of de Sitter spacetime is an artifact of the simplifying assumptions that we have made? Is it possible to avoid the beginning in a more general spacetime?
Figure 16.1
.
De Sitter spacetime, with two of the three spatial dimensions suppressed. Horizontal slices of the spacetime give “snapshots” of the universe at different moments of time. In a four-dimensional spacetime the slices would be three-dimensional spherical spaces.
.
De Sitter spacetime, with two of the three spatial dimensions suppressed. Horizontal slices of the spacetime give “snapshots” of the universe at different moments of time. In a four-dimensional spacetime the slices would be three-dimensional spherical spaces.
These doubts were put to rest only recently, in a paper I wrote in collaboration with Arvind Borde of Long Island University and Alan Guth. The theorem we proved in that paper is amazingly simple. Its proof does not go beyond high school mathematics, but its implications for the beginning of the universe are very profound.
Borde, Guth, and I studied what an expanding universe looks like from the point of view of different observers. We considered imaginary observers moving through the universe under the action of gravity and inertia and recording what they see. If the universe had no beginning, then the histories of all such observers should extend into the infinite past. We showed that this assumption leads to a contradiction.
To have a specific picture in mind, suppose there is an observer in every galaxy of our local region. Since the universe is expanding, each of these observers will see the others moving away. Galaxies may not exist in some regions of space and time, but we can still imagine the entire universe “sprinkled” with observers in such a way that all of them are moving away from one another.
bj
To give these observers some name, we shall call them “spectators.”
bj
To give these observers some name, we shall call them “spectators.”
Let us now introduce another observer who is moving relative to the spectators. We shall call him the space traveler. He is moving by inertia, with the engines of his spaceship turned off, and has been doing so for all eternity. As he passes the spectators, they register his velocity.
Since the spectators are flying apart, the space traveler’s velocity relative to each successive spectator will be smaller than his velocity relative to the preceding one. Suppose, for example, the space traveler has just zoomed by the Earth at the speed of 100,000 kilometers per second and is now headed toward a distant galaxy, about a billion light-years away. That galaxy is moving away from us at 20,000 kilometers per second, so when the space traveler catches up with it, the observers there will see him moving at 80,000 kilometers per second.
If the velocity of the space traveler relative to the spectators gets smaller and smaller into the future, it follows that his velocity should get larger and larger as we follow his history into the past. In the limit, his velocity should get arbitrarily close to the speed of light.
The key insight of my paper with Borde and Guth is that as we go into the past and approach past infinity by the clocks of the spectators, the time elapsed by the clock of the space traveler is still
finite
. The reason is that according to Einstein’s theory of relativity, a moving clock ticks slower, and the closer you get to the speed of light, the more slowly it ticks. As we go backward in time, the speed of the space traveler approaches the speed of light and his clock essentially comes to a halt. This is from the spectator’s point of view. But the space traveler himself does not notice anything unusual. For him, what spectators perceive as a frozen moment, stretched into eternity, is a moment like any other, which has to be preceded by earlier moments. Like the histories of the spectators, the space traveler’s history should extend into the infinite past.
finite
. The reason is that according to Einstein’s theory of relativity, a moving clock ticks slower, and the closer you get to the speed of light, the more slowly it ticks. As we go backward in time, the speed of the space traveler approaches the speed of light and his clock essentially comes to a halt. This is from the spectator’s point of view. But the space traveler himself does not notice anything unusual. For him, what spectators perceive as a frozen moment, stretched into eternity, is a moment like any other, which has to be preceded by earlier moments. Like the histories of the spectators, the space traveler’s history should extend into the infinite past.
The fact that the time elapsed by the space traveler’s clock is finite indicates that we do not have his full history. This means that some part of the past history of the universe is missing; it is not included in the model. Thus, the assumption that the entire spacetime can be covered by an expanding “dust” of observers has led to a contradiction, and therefore it cannot be true.
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A remarkable thing about this theorem is its sweeping generality. We made no assumptions about the material content of the universe. We did not even assume that gravity is described by Einstein’s equations. So, if Einstein’s gravity requires some modification, our conclusion will still hold. The only assumption that we made was that the expansion rate of the universe never gets below some nonzero value, no matter how small.
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This assumption should certainly be satisfied in the inflating false vacuum. The conclusion is that past-eternal inflation without a beginning is impossible.
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This assumption should certainly be satisfied in the inflating false vacuum. The conclusion is that past-eternal inflation without a beginning is impossible.
What about a cyclic universe? It has alternating periods of expansion and contraction. Can this help the universe to escape from the clutches of the theorem? The answer turns out to be no. An essential feature of the cyclic scenario, which allows it to avoid the heat-death problem, is that the volume of the universe increases in every cycle, so on average the universe is expanding. In my paper with Borde and Guth, we show that as a result of
this expansion, the space traveler’s velocity increases on average as we go back in time and still approaches the speed of light in the limit. Hence, the same conclusions apply.
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this expansion, the space traveler’s velocity increases on average as we go back in time and still approaches the speed of light in the limit. Hence, the same conclusions apply.
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It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape: they have to face the problem of a cosmic beginning.
Working with Alan Guth on a paper was a memorable experience. The idea of the proof emerged in e-mail exchanges between me, Alan, and Arvind, and the details were nailed down in two hours at the blackboard, when the three of us met in my Tufts office in August 2001. In about a month, we wrote a paper and submitted it to
Physical Review Letters
. I was amazed. What happened to Alan and his legendary procrastination? But I was not to be disappointed. In a few months, the editor sent us the report of a referee, asking us to clarify some points in the proof. And that is when the good old Alan returned in full glory. His e-mails started arriving at longer and longer intervals, with headings like “swamped at the moment” and “nothing done yet.” When he did find some time to work on the paper, he seems to have spent a fair fraction of it on issues such as whether we should thank “an anonymous referee” or “the anonymous referee” for his or her comments. He gave a detailed discussion of pros and cons for either version. Alan might have suspected that his editing of the paper was taking a bit too long, and at some point he wrote “I need to thank you guys for not shooting me.” In fairness, I should add that he spent some time on more substantive issues as well and that the drawn-out process of revising the paper resulted in its substantial improvement. The paper was finally published in April 2003.
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Physical Review Letters
. I was amazed. What happened to Alan and his legendary procrastination? But I was not to be disappointed. In a few months, the editor sent us the report of a referee, asking us to clarify some points in the proof. And that is when the good old Alan returned in full glory. His e-mails started arriving at longer and longer intervals, with headings like “swamped at the moment” and “nothing done yet.” When he did find some time to work on the paper, he seems to have spent a fair fraction of it on issues such as whether we should thank “an anonymous referee” or “the anonymous referee” for his or her comments. He gave a detailed discussion of pros and cons for either version. Alan might have suspected that his editing of the paper was taking a bit too long, and at some point he wrote “I need to thank you guys for not shooting me.” In fairness, I should add that he spent some time on more substantive issues as well and that the drawn-out process of revising the paper resulted in its substantial improvement. The paper was finally published in April 2003.
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