Even though Hawking has offered us an image of a self-contained Universe, with no boundaries and no edges, either in space or time, many people still wonder what might lie “outside” such a Universe. The analogy between the closed surface of the Universe and the closed surface of the Earth does, after all, encourage us to speculate that there might be other universes, just as there are other planets.

Within the framework of Hawking’s no-boundary Universe, any such other worlds would have to be embedded in some strange form of space which has more than the three dimensions we are used to: the surface of a sphere, after all, is actually a two-dimensional surface wrapped around in the third dimension, but space-time is four-dimensional; you always need at least one extra dimension to wrap up anything into a closed surface. But there is another model—or rather series of models—developed from the inflationary scenario which offers us another way to imagine many worlds coexisting, without having to try to wrap our brains around the higher geometries of five or more dimensions (four of space plus

one of time). Although Hawking himself has expressed reservations about the idea, which goes by the name of continual inflation, it is in fact based on his dramatic breakthrough discovery from 1974 that black holes explode.

Just after the Planck time, according to the inflationary scenario, the vacuum itself was in a “false” state, excited and full of energy, like supercooled water. When the false vacuum underwent a transition into its stable, lower-energy state, this energy went into the phenomenal burst of expansion that is known as inflation, creating the smooth Big Bang out of which the Universe as we know it has evolved. But suppose this transition did not happen everywhere at the same time.

Almost as soon as Alan Guth came up with the idea of inflation, researchers such as Alex Starobinsky and Andrei Linde realized that different regions of the primordial false vacuum might have made the transition into the low-energy state independently. The effect would be rather like unscrewing the cap of a bottle of fizzy drink— a myriad of bubbles would appear throughout the fluid, each corresponding to a stable vacuum expanding in its own way. Unlike the bubbles in your fizzy drink, though, each of these bubbles would carry on expanding, until all the fluid had gone and only bubbles remained.

This possibility raised serious technical problems for early versions of the inflationary scenario because, if two or more expanding bubbles were to merge, they would create disturbances that would spread right through both bubbles. If we lived in a Universe that had formed in this way, it would not be perfectly uniform, because these disturbances would leave their mark—for example, on the microwave background radiation.

There are ways around this problem. The notion that Hawking himself favors is that of “chaotic inflation,” in which the world beyond our Universe (the infinite “meta-universe”) is in a messy

state, with some regions expanding, some contracting, some hot and some cold. In such a chaotic meta-universe, there must inevitably be some regions just right for inflation to take place. We just happen, in this picture, to be in a Universe produced by a random fluctuation within the chaos.

But you don’t have to invoke chaos to explain our existence. Maybe we just happen to live in a bubble that hasn’t (yet!) merged with any of its neighbors (if this sounds like an extraordinary coincidence, it may not be, as we shall see later in this chapter). Or perhaps some law of physics prevents bubbles from forming very close together in the “fluid” of the false vacuum. This is where the proposal that Hawking Radiation might be involved comes in.

Hawking Radiation, as we saw in Chapter 9, is produced by the interplay of quantum effects and gravity at the horizon surrounding a black hole. But Hawking and his colleague Gary Gibbons, who shared an office with him in Cambridge in the late 1970s, realized that this kind of radiation must be produced wherever there is a horizon of this kind and that such horizons do not always surround black holes.

Because of the way the Universe expands, the more widely separated two regions are, the faster they recede from each other. So regions of space that are far enough apart can never “communicate” using light beams (or, indeed, anything else) because the space between them expands faster than light can travel. If light cannot travel from one region to another, then in effect there is a horizon which light cannot cross, separating the two regions of space as effectively as the horizon surrounding a black hole separates the inside from the outside.

Hawking and Gibbons showed that this kind of horizon will also produce radiation, just like the radiation at the horizon around a black hole, spreading out from the horizon into both regions of space. In the Universe as it is today, spread thin by expansion, the

effect of this radiation is tiny, but it could have played a much bigger role in the early stages of the expanding Universe. The expansion of the Universe is steadily slowing down, as the gravity of all the matter in the Universe tries to pull everything back together in a Big Crunch. So the expansion rate was much faster, and the effect of Hawking Radiation from horizons therefore more pronounced, when the Universe was younger. Long ago, even rapidly separating regions had not had time to move far and were much closer together.

The notion that radiation produced by horizons might affect the expansion of the Universe has been enthusiastically taken up and combined with the idea of inflation, by Richard Gott of Princeton University. Andrei Linde has also investigated it, but he has made less noise about the idea than the ebullient Gott.

It turns out that under the right conditions the Hawking Radiation produced in a volume of space filled with horizons of this kind can provide the energy that drives inflation and makes the Universe (or rather the meta-universe) expand super fast. The superfast expansion then creates more horizons, which in turn produce more radiation, driving the super-fast expansion in a self-sustaining continuing process of inflation. The bubbles of ordinary low-energy stable vacuum that form within this infinite sea of inflationary expansion grow at a slower rate, and so even if two bubbles form next to each other they will be kept apart by the rapid growth of the false vacuum of the meta-universe between them.

The “right” conditions for this process to work are mind-boggling. The temperature of the Hawking Radiation has to be about 10³¹ K, and the density of mass-energy in the false vacuum has to be an even more staggering 10⁹³ grams per cubic centimeter. And everywhere throughout this extraordinary, rapidly expanding false vacuum, bubbles of stable vacuum are forming and becoming universes in their own right.

In this scenario, there is not just one Universe but an infinity of universes, forever separated from one another by the impenetrable walls of the super-dense false vacuum. In a sense, such a concept is meaningless. The existence of other universes which we can never observe, and which can never have any interaction with our Universe, is a matter more suitable for discussion among philosophers than astrophysicists. But it turns out that there are more ways than one to make a universe and that in some scenarios universes can interact with one another, producing consequences of interest to everybody, not just to astrophysicists and philosophers.

With all this talk of superdensity and superenergy, and numbers like 10⁹³ grams per cubic centimeter being bandied about, it is natural to wonder how much mass-energy our entire bubble Universe contains (assuming, that is, that any of these scenarios have a grain of truth in them). The answer is perhaps even more startling—none at all! Let us leave the discussion of continual inflation to the philosophers and look again at Hawking’s no-boundary model of the Universe to see how this can possibly be true.

We are used to thinking of mass-energy chiefly in terms of lumps of matter: stars, planets, and so on. Each of them contributes its own amount of mc² to the total mass-energy of the Universe; but there is another, equally important contribution (exactly equally important, if Hawking’s ideas are correct). It comes from gravity. And there is a strange thing about gravitational energy—it is negative.

To understand what this means, physicists talk in terms of the gravitational energy of a hypothetical collection of particles. This is zero if the particles are dispersed to infinity, spread apart from one another as far as possible. But if the collection of particles falls together under the influence of gravity, perhaps eventually to make a star, it loses gravitational energy. Since the particles start with zero

energy, this means that by the time they have collected together to form a star or a planet they have negative energy. And if all the matter in the entire Universe could be collected together at a single point, its negative gravitational energy (-mc²) would exactly cancel out all the positive mass-energy (+mc²) of all the matter.

But that is exactly how we think the Universe did start out: with all its mass-energy concentrated in a point. The closed Universe scenarios actually describe a situation in which a point of zero energy becomes separated into matter with positive energy and gravity with negative energy, expands out to a certain size, and then collapses back into a point of zero energy again. At first the idea seems ridiculous. However, this is not some crackpot, lunatic-fringe theory, but a respectable cosmological idea, backed up by the equations of relativity.

The Universe, it seems, is the ultimate free lunch. And if the Universe contains zero energy, how much energy does it take to make a universe? Not a lot—certainly not very much compared with the amount of mc² contained in your body or the pages of this book. For according to Alan Guth and his colleague Edward Fahri, all you need is enough energy to squeeze some matter into forming a black hole. Then the new universe comes free—one universe free with every black hole. In a tour de force to rank with the great conjuring tricks, Guth and Fahri have shown that the two great threads of Hawking’s life’s work are really one and the same: black holes are big bangs.

In principle, the seeds of entire universes could be produced out of nothing at all, in a manner reminiscent of the way pairs of virtual particles can be produced out of nothing at all by quantum uncertainty (as we saw in Chapter 9). Such a baby universe would be in the form of a super-dense concentration of mass, smaller than a proton but containing no energy because the mass is balanced by negative gravitational energy. Of course, according to the ideas of

the 1970s and before, such tiny super-dense seeds would immediately collapse back into nothing under their own weight. But inflation provides a way to blast out such a seed to form an expanding universe before gravity can make it collapse. It would then take many billions of years for gravity first to halt the expansion and finally to make the universe disappear into a Big Crunch.

So do we really need the continually inflating false vacuum to make bubble universes pop up in infinite numbers? At first sight, this raises a worrying possibility. If a bubble universe can pop into existence out of the ordinary vacuum, what would happen if one burst into existence near us? Would we be overwhelmed by the expanding fireball of a Big Bang going on right next door? Fahri and Guth think that there is nothing to worry about. If such baby universes pop into existence spontaneously, or if they were created artificially, they would have no further interaction with our Universe once they had been born.

Remember that the seed of such a bubble universe must be self-contained, destined ultimately to collapse back in on itself; in other words, it must be a black hole. Fahri and Guth found that you could trigger this process of universe creation artificially, by squeezing a small amount of matter into a black hole at a temperature of about 10²⁴K (quite modest compared with conditions in the false vacuum). But they gave their scientific paper on the subject the tongue-in-cheek title “An Obstacle to Creating a Universe in the Laboratory,”¹ pointing out that although we have the technology (hydrogen bombs) to do half the job, releasing the energy required, we don’t yet have the ability to confine the energy released by hydrogen bombs within a black hole.

But it is not beyond the bounds of possibility that a civilization more advanced than our own might be able to confine the required energy in a small enough volume. What would happen then? To the people who created this energetic minihole, very little. The black

hole would simply form, spend billions of years evaporating through Hawking Radiation, and then disappear. But within the horizon of the hole things would be very different.

According to the calculations by the American team, conditions inside such an energetic minihole will sometimes be such as to trigger inflation. But when such a baby universe begins to expand, it does so not by bursting out of the minihole to engulf its surroundings in the space-time in which it was created, but by expanding in a set of directions which are all at right angles to each of the dimensions of the parent universe. And exactly the same thing will happen to baby universes that are produced by natural quantum fluctuations.

Because all the sets of dimensions are at right angles, the different universes never interact with one another once they have formed. But there is a crucial difference with the continual inflation idea, where the bubbles never interact at all. In the scenario sketched by Fahri and Guth (and studied by others, including Linde), one universe is created from another. In this picture, our Universe is the progeny of a previous universe; and it is even possible that our expanding bubble of space-time was created artificially in the equivalent of a laboratory in that parent universe. Science fiction writer David Brin is already working on the implications in a linked series of stories; we will leave further speculations along these lines to Brin and his colleagues while we try to explain the implications in terms of the spontaneous creation of baby universes.

It is hard to get a mental grip on the proliferation of dimensions that this implies. Every baby universe will contain its own vacuum, within which other quantum fluctuations can occur, producing yet more baby universes each with their own set of dimensions, with every set of dimensions at right angles to every other set. As usual, we have to fall back on an analogy in two dimensions, bent round a third, to get a picture of what is going on.

The helpful image is the old familiar one of the Universe represented by the skin of an expanding balloon. What we have to imagine now is that a tiny piece of that skin is pinched off, forming a little blister connected to the Universe by a narrow throat—the black hole. That little blister can now, in turn, expand to enormous size, while all that any resident of the parent universe sees is the tiny black hole throat in the fabric of space-time. And the whole process can repeat indefinitely, producing an infinite foam of bubbles, each one a universe in its own right. Quantum cosmology actually allows the possibility of creating not just one Universe but an infinite number of universes, out of nothing at all.

And this raises another question. At one level, physics operates by finding out the rules according to which the Universe operates and using them to make predictions about how systems will interact. We find, for example, that the speed of light has a certain value, and that this is the ultimate speed limit. That enables us (or at least it enabled Einstein) to work out how our view of the world changes when we move at high speed. But at another level some physicists puzzle over why the rules should have the precise form that we find.

Why, for example, is the speed of light 300,000 kilometers a second, rather than, say, 250,000 kilometers a second? Why does Planck’s constant have the precise value it has, and not one a little bigger or a little smaller? What would happen if gravity were weaker (or stronger)? And so on. We live in a world that seems to be just right for life-forms like us—which is in a way tautological, since obviously if the world were very different we would not be here to wonder about these things. But as far as anyone is yet able to tell, the rules of physics that came out of the era of inflation could have been different from the rules we know, either subtly different or dramatically different. Is it, then, just a coincidence that these rules have produced a Universe suitable for people like us to live in? The idea of an infinity of bubble universes, either formed

out of an eternally expanding false vacuum or pinched off from one another by the baby process, says that it is not—and explains other cosmic coincidences as well.

The idea of trying to understand the nature of the Universe in terms of the relationship between the laws of physics and ourselves is known as “anthropic cosmology.” It has a long history, but in its modern version it stems mainly from a revival of interest triggered by Martin Rees, of the University of Cambridge, in the 1970s and continuing to the present day.

Rees is an exact contemporary of Hawking. He was born on June 23, 1942, when Hawking was six months old. They were working for their Ph.D.s in Cambridge at the same time, and Rees became Plumian Professor of Astronomy and Experimental Philosophy in 1973, at the remarkably early age of thirty-one, just six years before Hawking became Lucasian Professor. He was elected a fellow of the Royal Society in 1979, five years after Hawking. But where Hawking has made his reputation by investigating in great detail one particular set of problems—the singularities and horizons around black holes and at the beginning of time— Rees is known and respected for the breadth of his work, ranging from quasars and pulsars to the influence of black holes on their surroundings, cosmology, and the nature of the dark matter that holds the Universe closed. When Rees turned his attention to anthropic cosmology and stirred the revival of serious interest in the subject by scientists in the 1970s and 1980s, for once Hawking was prepared to follow somebody else’s lead.

Rees has developed a particularly nice example of the nature of anthropic reasoning in cosmology. He has worked out in detail the evolution of a universe in which gravity is stronger than in our Universe, but every other rule of physics is the same. Galaxies, stars, and planets can all exist in this model universe, but they are all very

different from their counterparts in our Universe. In particular, everything is speeded up to such an extent that it is doubtful whether intelligence (which has taken more than four billion years to emerge on Earth) could ever evolve.

For the particular value of the strength of gravity chosen by Rees, each star has a mass about the same as that of an asteroid in our Solar System (much less than the mass of the Moon) and a diameter of about two kilometers. The typical lifetime of such a star is just one of our years, and it burns with a brightness one hundred-thousandth that of our Sun. The Earth has an average surface temperature of about 15°C, and a planet in this other universe, orbiting around its parent star at a distance roughly twice as great as the distance from the Earth to the Moon, would have a similar surface temperature. It would take about twenty of our days for the planet to orbit the star. So with the star itself having such a short lifetime, it would be burned out in just about 15 of the planet’s “years,” whereas the lifetime of our Sun is likely to be at least 10 billion of our years.

Life on the surface of such a planet would be short, in more ways than one. The biggest mountains on the tiny planet could be no more than 30 centimeters high, while the maximum mass of any creatures roaming its surface would be just one-thousandth of a gram—any bigger than this and their bodies would break if they fell over in the strong gravity of that world.

And all of these dramatic changes stem, remember, from making a change in just one of the constants of physics, the strength of gravity! It is possible to imagine very many changes that would ensure that the universe that emerged from the inflationary phase would be quite inhospitable for life-forms like us.

If ours is the only possible Universe, then the existence of the cosmic coincidences that permit our existence is a real puzzle. But if there are many possible universes, then there is a straightforward

explanation. Every different bubble universe may have its own laws of physics. In some cases, that will mean that the bubbles are held together very tightly by gravity and recollapse before life can evolve. In others, gravity may be so weak that material is never pulled together to form stars and planets at all. But there will be a range of possibilities—a range of universes—where stars, planets, and intelligences can evolve. The same argument applies to each and every one of the exact values of the laws and constants of physics.

If this picture is correct, it means that there may be an infinite number of universes in the meta-universe, and out of that infinite number life-forms like us will exist only in universes where the laws of physics are just right. The fact that we exist preselects, to some degree, the exact rules of physics that we will discover the Universe operates on. This idea is known, rather grandly, as the “anthropic principle,” a term coined by Bernard Carr, who worked with Rees on a seminal paper on the topic.

Of course, because the different universes can never communicate with one another, this is still largely a matter for the philosophers to debate. Except for one thing. Remember that the crucial ingredient of Hawking’s no-boundary model is the sum-over-histories quantum approach. When we mentioned this earlier, we rather glossed over the explanation of what, exactly, the different histories that were being “summed” were. Now we can set the record straight.

Instead of regarding all the different possible universes that could have emerged out of inflation, each with its own set of physical laws, as “real,” we can regard them as mathematical possibilities, like the many different paths that an electron can take from A to B. And using the sum-over-histories approach, Hawking shows not only that our Universe is one of the possible histories, but also that it is one of the most probable ones:

. . . [I]f all the histories are possible, then so long as we exist in one of the histories, we may use the anthropic principle to explain why the universe is found to be the way it is. Exactly what meaning can be attached to the other histories, in which we do not exist, is not clear.²

Nevertheless, using the “no-boundary” condition, Hawking and his colleagues have found that the Universe must start out with the maximum amount of irregularity allowed by quantum uncertainty and that inflation and the subsequent more leisurely expansion of the Universe then make these irregularities grow to become the clouds of gas that then contract to become galaxies of stars within the expanding Universe.

All of this is very much research at the cutting edge of science today. The choice of different variations on the theme—bubbles in a continually inflating false vacuum, baby universes, a choice of quantum histories—reflects not an inability of physicists to make up their minds but an attempt to push ahead on many different fronts, not yet knowing which (if any) will turn out to hold the most promise in the long term. But it is already clear that in the 1990s the basic premises underlying cosmological thinking changed dramatically from those of what we might call the “pre-Hawking” era. Thirty years ago it was generally accepted that our Universe was unique. Today, it seems to be generally accepted that, one way or another, it is just one among many. Is it any wonder that, when Hawking presented these ideas in a book in 1988, the book took the world by storm?