Was the Big Bang Really the Beginning?
Most physicists tend to think of the Big Bang as really being the beginning of the physical universe, and with it, the beginning of time itself. This idea of a “beginning of time” is hard to grasp. The mind wants to ask, “What happened before the Big Bang?” In the standard Big Bang model that question is meaningless: there was no time before the Big Bang, and thus no such thing as “before” the Big Bang. Perhaps an analogy will help. What lies to the north of the North Pole? Nothing. The highest latitude that it makes sense to talk about is 90 degrees. There is no such place as 91 degrees latitude. Latitude runs out at the North Pole. Let us call the moment of the Big Bang t = 0. Then there are no negative times; the time coordinate simply runs out at t = 0. The point is that time is not some absolute thing that exists whether there is a universe or not, just as latitude does not exist unless there is a globe. Time, like space, is a measure of the intervals between things and events in the physical universe, just as latitude is a measure of intervals on the earth’s surface. This, at least, is what time means to a physicist. One cannot talk about the time between events if there is no universe and therefore are no events.
As hard as this idea is to grasp, it was grasped 1,600 years ago by St. Augustine. In a celebrated chapter of his Confessions, he reflected deeply upon the nature of time. The beginning of his reflections was the question, “What happened before God created the heavens and the earth?” This question was posed as a trap by pagan opponents of Christianity and Judaism. Why, they asked, did God wait around an infinite length of time before creating the world?1 St. Augustine began by pointing out that time itself is merely an aspect of the created world: “There can be no time without creation.”2 Therefore, he argued, time itself, no less than the universe, is something created: “What times could there be that are not made by you, [O God]?”3 Remarkably, he even grasped that there was no time before the universe began: “You [O Lord] made that very time, and no time could pass by before you made those times. But if there was no time before heaven and earth, why do they ask what you did ‘then’? There was no ‘then,’ where there was no time.”4 This great thinker grasped a point that was not fully appreciated until the coming of twentieth-century developments in physics. Many of St. Augustine’s statements about time have a strangely modern sound and seem pregnant with meaning to scientists who think about relativity. Indeed, the Confessions is sometimes quoted in technical papers on quantum cosmology,5 and Bertrand Russell praised St. Augustine for what he called his “admirable relativistic theory of time.”6 (It is relativistic in a certain sense, but not in the full technical sense of the theory of relativity.)
It should be emphasized that this modern discovery of a beginning of time was a vindication for Jewish and Christian thought.7 While religious thinkers, like Augustine, spoke of a beginning to time, and while this concept was enshrined in Christian doctrine, no one until the twentieth century could make scientific sense out of such an idea. How could time have a beginning? It not only seemed absurd, but was, quite literally, unimaginable. Unimaginable, and yet, at least in the standard cosmology of today, true.
Even though the Big Bang, in standard cosmological theory, is the beginning of time, it is important to realize that alternative, very speculative cosmological scenarios have been proposed in which things did happen before the Big Bang. I will briefly explain the basic ideas behind three of these scenarios: the bouncing universe, baby universes, and eternal inflation. It is not essential for the discussions that will come later to read these sections, and so some readers may wish to skip directly to the next chapter. However, the ideas explained in the rest of this chapter have some interest of their own, and are not without relevance to some points made later in the book. Before explaining the basic ideas of such speculative scenarios as the bouncing universe, baby universes, and eternal inflation, I have to explain some of the possibilities that exist within the conventional or standard cosmological model. In particular, in the standard cosmological model does the universe have finite size or infinite size? Will it stop expanding at some point, or will it expand forever? These are the questions I will deal with in the next section.
THE UNIVERSE IN THE STANDARD BIG BANG MODEL
Homogeneity and Isotropy
In most theoretical discussions of cosmology the universe is assumed to be at least approximately “homogeneous and isotropic.” “Homogeneous” means that the universe looks the same from any place in it. More precisely, if one considers any particular time in the history of the universe, then at that time physical conditions, such as the temperature, the density of matter, or the curvature of space, will be the same at all points of space. “Isotropic” means that the universe looks the same in every direction.
There are two reasons why cosmologists often assume the universe to be homogeneous and isotropic. The first is that it greatly simplifies matters for them. If at a given time the density of matter is the same everywhere in the universe, it can be specified by just one number, “the matter density of the universe.” The same thing is true for other physical quantities, such as the curvature of space, or the temperature. The second reason that they make this assumption is that the universe is in fact quite homogeneous and isotropic on large scales. It is true that on what cosmologists consider “small” scales, such as the scale of the solar system or even that of the Milky Way, the universe is not at all homogeneous and isotropic. Conditions inside the Sun, for example, are very different from those on Earth. And conditions within the solar system are very different from those in interstellar space. However, if one considers distances much, much greater than the size of galaxies, the universe does indeed appear quite uniform. Once one averages over such small details as stars, planets, galaxies, and clusters of galaxies, the universe does appear reasonably homogeneous and isotropic. For the rest of the discussion in this section, I will be considering only idealized models of the universe in which it is assumed to be perfectly homogeneous and isotropic.
The Curvature of Space
The first thing we will consider is the curvature of space. If we are looking at a two-dimensional space, or surface, we know intuitively what it means for it to be curved. For example, the surface of a sphere is curved. By contrast, a plane is flat. But what does it mean to say that a three-dimensional volume of space is “curved” or “flat”? Here we cannot appeal directly to intuition, because human beings are not equipped to visualize curved spaces of more than two dimensions. But we can get some idea of what is meant in the following way.
If we draw two lines that are going in the same direction on a flat plane—i.e., “parallel lines”—they will never meet. They will always remain the same distance apart. If, however, we draw two lines on a sphere that start off going in the same direction, they will not remain the same distance apart, they will draw closer and closer together. (For example, if two lines on a globe start at the equator and go due north, they begin by going in the same direction, but as they are extended northward they get closer together until they intersect at the North Pole.) Are there surfaces where two lines that begin by going in the same direction end up getting farther apart? Yes. Consider, for example, the end of a trumpet, where it flares out. If two lines were drawn on the trumpet so that they began by going in the same direction, the flaring of the trumpet would cause these lines to splay out from each other and diverge. This behavior of “parallel” lines can be used to define what we mean by curvature. When parallel lines always stay a fixed distance apart, we say that the surface has zero curvature, i.e., it is flat. When they always end up converging, as on a sphere, we say that the surface has positive curvature. And when they always end up diverging, as on a trumpet-shaped surface, we say that the surface has negative curvature. The more quickly the lines converge or diverge, the greater the curvature is said to be.
This can all be made very precise mathematically. In fact, this is how mathematicians think about curvature; and the beauty of it is that the same ideas can be used to explain what we mean by three-dimensional spaces being curved. If a three-dimensional space is such that when two lines start off going in the same direction they always end up moving closer together, we say that the space is positively curved; if they always end up moving farther apart, we say that it is negatively curved; and if they always remain a fixed distance apart, we say that the space is “flat.”
Now, a two-dimensional surface can certainly be curved more in one place than another—like the surface of the earth, which has flat places and hills and valleys. Or it can have exactly the same curvature everywhere, like a perfect sphere. The same possibilities hold for spaces of higher dimensionality. In particular, the three-dimensional space of our universe could vary in curvature from place to place. However, if the universe were perfectly homogeneous and isotropic, as we are idealizing it to be, it would have to have exactly the same curvature everywhere. There are then three possibilities: (1) it has the same positive curvature everywhere (analogous to a sphere), (2) it has zero curvature everywhere (like a flat plane), or (3) it has the same negative curvature everywhere.
Open and Closed Universes
Just as a sphere has a finite surface area, so too does a universe whose space has the same positive curvature everywhere have a finite volume of space. Such a universe is called spatially “closed.” But a “flat universe” with zero curvature everywhere and a universe with the same negative curvature everywhere each have an infinite volume of space and are spatially “open.”
Is our actual universe open or closed? No one knows. As of now, the data are consistent with its being “flat.” (Remember, we are talking about its behavior on extremely large scales. Near lumps of matter, like Earth, or the Sun, or a galaxy, matter will warp space. But on very large scales the universe appears to be quite flat.) The data are still quite crude, and do not allow us to tell whether the universe really has zero spatial curvature on the whole, or has instead a slight positive or negative curvature. We may never know whether the universe has a truly infinite or a vast but finite volume.
Many people who have heard that the universe is expanding think that this implies that the universe has a finite volume right now. After all, they reason, if the universe were already of infinite volume, it would make no sense to talk of its getting any bigger. Reasonable as this sounds, it is wrong. The universe can be infinite in size and yet be expanding. To understand this, let us think about two-dimensional analogies.
The surface of a sphere has a finite area. If the sphere expands, as the surface of a balloon does when it is inflated, then its surface area increases. Now consider an infinite flat plane. We can imagine that this plane is an infinite piece of graph paper and has grid lines drawn on it. We can further imagine that this infinite piece of graph paper is put into an infinitely large photocopying machine that is set to a magnification of 120 percent. The copy made by the machine will also be an infinitely large piece of graph paper, but the grid lines will all be increased in spacing by 120 percent. Any picture drawn on the original paper will also be scaled up by 120 percent. In a real and simple sense, we can say that the copy is 120 percent “larger” than the original, even though both have infinite area. Or, to be closer to the balloon analogy, we can imagine an infinite rubber sheet with grid lines or other figures drawn on it. The sheet can be stretched uniformly in every direction, so that the grid spacings and figures get ever larger, even though the sheet always has infinite area.
When cosmologists say that the universe is expanding they in no way mean to imply that it is finite in volume. The expansion makes objects that are very distant from each other grow farther apart—the whole universe scales up as if by a cosmic copying machine that is making ever larger copies. But we have no idea at present whether the universe is infinite or finite in extent—i.e., whether it is open or closed.
Whether the universe is open or closed is closely connected to how much mass or energy (Einstein tells us the two are equivalent) it contains. If the density of mass/energy in the universe has a certain “critical value,” then the space of the universe is flat, and therefore open. (We are assuming here as always that the universe is homogeneous and isotropic.) If the mass/energy density of the universe is larger than the critical value, then space has a positive curvature and is closed. If the mass/energy density is less than the critical value, the universe is open. What matters here is the total mass/energy, which includes both mass/energy in what we shall call “ordinary matter”—i.e., electrons, protons, atoms, particles of light, and so on—and the mass/energy associated with the “cosmological constant” Λ that we spoke of previously.
Will the Universe Expand Forever?
We know that the universe is presently expanding. Will that expansion last forever or will it at some point stop and even reverse? The future of the universe depends on how much mass/energy it has and what kind of mass/energy it is filled with. Ordinary matter tends to slow down the expansion of the universe. One can understand this in a simple intuitive way. Ordinary matter tends to attract other ordinary matter gravitationally, and so the mutual attraction of the ordinary matter in the universe acts to pull the universe together, i.e., resist its expansion. If the universe were filled with only ordinary matter its expansion would always be slowing down. In fact, if its density is more than the critical value we mentioned, then the expansion will eventually stop and reverse. The universe will then begin an irresistible collapse that will culminate in a “Big Crunch” that is the reverse of the Big Bang. Space and time itself will come to an end. So far, I have been discussing the case where all mass/energy in the universe is in the form of “ordinary” matter (and the universe is homogeneous and isotropic). In that case things are relatively simple, and there is a connection between whether the universe is open or closed (i.e., infinite in spatial volume or finite) and whether it will expand forever. If it is infinite in volume it will expand forever, whereas if it is finite in volume it will eventually collapse.
Things are very different and more complicated if (as seems to be the case) some of the mass/energy in the universe is in the form of “cosmological constant.” Then there are other possibilities. For example, one could have a universe that is closed (finite in volume) but expands forever. The reason that things are more complicated is that the cosmological constant, if it is positive, tends to cause a repulsion that makes the universe expand even faster, as mentioned before. In fact, this seems to be actually happening. Observations suggest that earlier in its history the expansion of the universe was slowing down, but that “recently,” in cosmologist’s terms, i.e., in the last several billion years, it has picked up again and is accelerating. The best evidence that we now have suggests the following things about our universe: (1) it is “flat” or nearly so, but we don’t know yet whether it has a tiny positive spatial curvature or a tiny negative one; therefore, (2) it may be infinite in volume or finite, we cannot yet tell which; and (3) its expansion is accelerating, suggesting that it will expand forever. (However, one can imagine possibilities in which the acceleration will stop and the universe eventually collapses.)
THE BOUNCING UNIVERSE SCENARIO
One can think of the expansion of the universe as following a trajectory, like a ball shot out of a cannon. (The cannon is the Big Bang.) If the universe is filled only with ordinary matter its mutual gravitational pull tends to slow the expansion down, just as the earth’s mass pulling on the cannonball tends to slow its ascent. If the density of matter in the universe is above some critical value, then the universe will eventually fall back upon itself. Similarly, in the cannonball analogy, if the mass of the earth is great enough (in relation to the cannonball’s height and speed of ascent), the cannonball will fall back down upon the earth. On the other hand, if the earth’s pull is not great enough, the cannonball will keep going up forever—it has “escape velocity.” In the same way, if the density of matter in the universe is subcritical, the universe will expand forever. This is all assuming that the universe is filled with only ordinary matter. A positive cosmological constant acts in a different way from ordinary matter, as we saw. It tends to accelerate the expansion of the universe. In the cannonball analogy, it would be as if the cannonball were jet-assisted.
The ball analogy very naturally suggests the following idea. If a ball falls back to earth it can bounce; so perhaps if the universe falls back upon itself in the Big Crunch it too can bounce. In other words, at the moment of the Big Crunch, matter—and space itself—might rebound and start expanding again. This expansion would look just like a new Big Bang. And eventually, this new expansion would also reach a maximum extent and the universe would begin to collapse again to another Big Crunch, followed by another rebound, and so on, perhaps forever.
This suggests the further idea that there may already have been an infinite number of such cycles of expansion and contraction in the past. If that was so, then the universe is “eternal” after all, and the Big Bang, rather than being the beginning of time, was only the commencement of the latest cycle. This idea is not at all unreasonable, and it is an interesting possibility, to which, quite naturally, some theoretical attention has been given. However, it faces several difficulties.
In the first place, given the laws of physics as we know them, it is not clear that the universe could bounce. Certainly, it would not if Einstein’s theory of gravity in its classical (i.e., non-quantum) form were used to calculate what happens at a Big Crunch. In 1969, Stephen Hawking and Roger Penrose proved mathematically that space-time at a Big Crunch becomes, in the mathematical jargon, “singular.” Specifically, the curvature of space-time becomes infinite, and “world-lines” come to an end. If this is true, then bounces do not happen. However, there may be ways that such a “singularity” might be avoided by nature. In particular, extremely close to the time of a Big Crunch—or Big Bang—(in fact, within 10-43 seconds of it) “quantum effects” are believed to be important. These may very well “soften” the singularity in some way—we will return to that idea later. But whether they would allow an actual bounce is not known, and in fact this will remain unanswerable until the correct theory that unifies Einstein’s theory of gravity with quantum theory is known.
Even if the universe does bounce, there is a problem with the idea that these bounces have extended back infinitely into the past. The Second Law of Thermodynamics suggests that the “entropy,” or the amount of disorder, of the universe will be greater with each successive bounce. The universe would not be born completely fresh in each bounce, so to speak, but would show its age. Given this, it would seem quite unlikely that the universe has already undergone an infinite number of bounces in the past.
Finally, present data indicate an expansion of the universe that is getting faster and faster, and therefore suggest that the expansion will go on forever rather than reversing and leading to a crunch or bounce. In any event, beyond all of these objections, which are very cogent, the bouncing universe idea simply has not helped physicists to solve any theoretical problems, and consequently it no longer receives a great deal of attention. (However, there has been a very interesting recent attempt to revive it.8)
So far, all three attempts to avoid a beginning that I have discussed—Einstein’s carefully adjusted cosmological constant, the Steady State Theory, and the bouncing universe scenario—were clearly motivated to a large extent by philosophical prejudice against the idea of a beginning; and all of them are either discredited now or strongly disfavored. However, more recent ideas like baby universes and eternal inflation are still possibilities, and at least some of them have better scientific motivation.
The baby universes idea is basically simple in concept: the universe splits. In the balloon analogy, one can picture a little part of the balloon being pinched off and forming another separate balloon. That little baby balloon could then eventually expand to enormous size. In this picture, the Big Bang could have been the event where our universe was pinched off from a larger one. One can envision a situation where this process of universes giving birth to other universes has been going on forever.
THE ETERNAL INFLATION SCENARIO
What Is Cosmological “Inflation”?
The first thing to do is explain the idea of “inflation” itself. This will also help us to understand a few points that will be discussed in later chapters. Inflation is one of the most important and beautiful ideas in modern cosmology. It was proposed in 1979 by Alan Guth to resolve a number of serious cosmological conundrums. These included the so-called “horizon problem” and “flatness problem.”
The horizon problem refers to the fact that the “cosmic background radiation” discovered by Penzias and Wilson is extremely uniform. It glows with almost exactly the same intensity in every part of the sky. To understand why this is puzzling, we must start by recalling what this radiation is. It is the afterglow of the primeval fireball. Most of this glow was given off when the universe was about three hundred thousand years old. After that point the fireball cooled and became relatively transparent. The cosmic background radiation that we now see is therefore reflecting conditions as they were early in the history of the universe. What it tells us is that the region of the universe that we are now able to observe was very homogeneous back then. More precisely, the density of matter, the temperature, and the pressure were uniform to a few parts in a hundred thousand.
At first this does not seem too strange. After all, if you are sitting in a room, the air in that room is also very uniform in density, temperature, and pressure. But the reason for that is that any pockets of higher pressure or temperature would quickly smooth themselves out by the flow of air and heat from one part of the room to another. Air will flow from regions of high pressure to regions of lower pressure, and heat will flow from hotter to colder. But such flows take time, and in the early universe there was not enough time for flows of heat and matter to produce the uniformity we now observe. The word horizon refers to how far one can see. The point is that when the universe was only three hundred thousand years old, any regions that were more than a three hundred thousand light-years apart could not “see” each other, because there had not been enough time for light to travel from one of those regions to the other. Not only could such regions not see each other, they could not influence each other in any way. They were, in cosmology jargon, outside each other’s “horizon.” And yet, they were somehow at almost exactly the same temperature, pressure, and density. This is the “horizon problem.”
The flatness problem has to do with the fact that space itself is much less curved than it has any right to be in the standard model of cosmology. As we have explained, “flat” here does not mean two-dimensional, it means lacking in curvature. Einstein tells us that matter, such as planets, stars, and galaxies, warps the space-time in its vicinity. However, if the universe is looked at on much larger scales of distance its space appears to have very little, if any, curvature. This fact long puzzled cosmologists.
The hypothesis of inflation resolves both the flatness problem and the horizon problem. The idea of inflation is that very early in its history—within a tiny fraction of a second after the Big Bang—the universe, or a least some large part of it, underwent a brief and extremely rapid period of expansion. Not the gradual expansion that is seen by astronomers today, but a sudden jump in size by an enormous factor in a tiny fraction of a second. This “inflationary phase” is imagined to have lasted only a very brief time, after which the more normal, gradual type of expansion that we see today is supposed to have resumed.
The way inflation solves the flatness problem is easy to understand. If we were to blow up a balloon to enormous size, its surface would become very flat, just as, because of its enormous size, Earth’s surface was for a long time thought to be flat. In the same way, if just after the Big Bang the universe was suddenly hugely expanded, space would exhibit very little curvature thereafter.
Inflation solves the horizon problem in a similar way. The universe may well have had a very non-uniform appearance shortly after the Big Bang. There may have been great variation in physical conditions such as temperature, pressure, and density from one place to another. But if one looked at a small-enough patch of space, conditions would have been uniform in that patch. What inflation is thought to have done is take one tiny little uniform patch of space and stretch it to such enormous size that it entirely contains the part of the universe that we can now see with the most powerful telescopes—the part, that is, which is within our horizon. That is why things look so uniform within our horizon.
This aspect of inflation is relevant to the discussions about “anthropic coincidences” in a later chapter. The important lesson that inflationary theories have taught us is that the sameness that characterizes the part of the universe that we can see may be a misleading indicator of the way things are throughout the whole universe. It is quite possible that the universe looks very different—not just in temperature or pressure, but in much more radical ways—in regions that are too far away for us to observe, even though things look remarkably uniform in the part we can observe.
This idea of the whole universe, or a very large part of it, suddenly increasing in size by a huge factor in a fraction of a second sounds bizarre, to say the least. Nevertheless, there are some very reasonable ideas for how this may have happened, based on well-established ideas in physics. For example, shortly after the Big Bang, the universe was filled with matter at high temperature and density. This matter could have undergone what is called a “phase transition.” Common examples of phase transitions from everyday life are the melting of ice and the boiling of water. Certain kinds of phase transitions in the early universe would have caused the “stress-energy” of matter, which appears in Einstein’s equations, to suddenly change in such a way as to cause space to inflate.
So, however bizarre it may seem, inflation is a very reasonable hypothesis from the viewpoint of modern physics. Two words of caution are nevertheless in order. First, many different inflationary scenarios have been proposed. Just to name a few broad categories, there have been “old inflation,” “new inflation,” “supersymmetric inflation,” “Kaluza-Klein inflation,” “extended inflation,” “chaotic inflation,” “open inflation,” and “hybrid inflation.” Some of these variants of inflation have been shown not to lead to a realistic picture of the universe, but many of them are still viable. Moreover, within each of these categories, many specific models have been invented. There is no standard theory of inflation. Second, while recent observations have provided very strong indirect evidence for inflation, the evidence is not yet such as to leave no room for doubt. But the evidence in favor of it is getting stronger all the time.
How Inflation Could Happen Eternally
The idea of “eternal inflation” was proposed by the physicist Andrei Linde in 1986. The basic idea can be explained using the by-now-familiar balloon analogy. Think of the universe as the surface of a giant balloon that is gradually expanding. One can imagine that small patches on this balloon are undergoing rapid “inflationary” expansion. If they do, they will grow to form huge blisters, as it were, on the fabric of space. In fact, these blisters can inflate to such a size that they are really themselves like large balloons. After a while, these blisters can stop their rapid inflation and begin to expand in a normal, gradual manner. However, small patches on those blisters may continue to inflate rapidly. In this way, each blister will develop huge inflating blisters on it. Eventually, these will stop inflating and expand normally, but when they do small patches of space on them may continue to inflate, forming blisters on blisters on blisters. This process can go on and on indefinitely. And, conceivably, it may have been going on forever. However, there are physical arguments that suggest that it cannot have been.9
Each such blister on the space of the universe can eventually grow to enormous size. The region of the universe that we inhabit and that we can observe with telescopes may be just a part of one of these patches that inflated. What we call the Big Bang may just have been the process by which a new blister formed and inflated to astronomical proportions.