The Universe Within

by Neil Turok

  Dark matter may consist of an unknown type of particle that does not interact with light or with ordinary matter. The only way to see these particles would be through their gravity. In the 1980s, astronomers found more evidence for dark matter by observing the bending of light by gravitational fields. This effect is called “gravitational lensing” and is similar to the effect water has on light passing through it. Although water is perfectly transparent, you can tell that it is there because it bends the light and distorts the image of whatever is behind it. If you’re in the bathtub and hold your hand up and look at the water droplets on the ends of your fingers, you’ll see a distorted image of the room behind every drop. Astronomers have found similarly distorted images of distant galaxies behind galaxy clusters. And by figuring out how the light was bent, they can reconstruct the distribution of the dark matter within the clusters.

  In the evolution of the universe, dark matter would have played a very important role, assisting the formation of galaxies by providing an extra gravitational pull. In many ways, dark matter forms a kind of cosmic backbone, holding the other matter together in the universe. Dark matter’s gravitational pull lowered the minimal level of density variations required in the early plasma to form galaxies by today, bringing it down to one part in a hundred thousand. It was very hard to see how galaxies could have formed from density variations any smaller than that. So as COBE reached this crucial sensitivity level, it was also reaching the smallest level of variations that could possibly have formed our current universe’s structure.

  Fortunately, the milky patches Smoot showed me turned out to be real. The temperature across the sky really does vary by a part in a hundred thousand, and in an incredibly simple way. The observations matched precisely expectations from inflationary theories like those discussed in the workshop I’d attended in Cambridge in 1982. When DMR’s result was announced a decade later, Stephen Hawking was quoted as saying the finding was the greatest discovery of the twentieth century, and perhaps of all time. Although his comment was hyperbolic, there was good reason to be excited.

  AS MEASUREMENTS OF THE universe became far more accurate and extended to a greater and greater volume, it became possible to envisage using the entire visible universe as a giant laboratory. The big bang is the ultimate high-energy experiment. We and everything around us are its consequence. So understanding the very early universe allows us to probe physics at the shortest distances and the very highest energies. Equally, looking at today’s universe allows us to probe the largest distances and the very lowest energies. And in this probing, cosmology made another of the greatest discoveries of twentieth-century physics, the full implications of which we are still struggling to understand.

  I have already mentioned Einstein’s earliest cosmological model and how it included the cosmological term. The model was a failure, but the idea of the cosmological term was a good one. In fact, it was Lemaître who persisted with it, arguing that it was a plausible addition to Einstein’s theory and should be thought of as a special, simple kind of matter that could be expected to be present in the universe. Later on, it was realized that the cosmological term represents the energy per unit volume of empty space, what we now call the “vacuum energy.” It is the very simplest form of energy, being completely uniform across space and appearing exactly the same to any observer.71

  For any physical process that does not involve gravity, the vacuum energy makes no difference. It is just there all the time as an unchanging backdrop. The only way to detect it is through its gravity, and the best way to do that is to look at as big a chunk of it as possible. Of course, the biggest piece of space we have is the entire visible universe. By watching the expansion history of this whole region, you can directly measure the vacuum energy’s gravity.

  In 1998, the High-Z Supernova Search Team and the Supernova Cosmology Project — two international ventures led by Australian National University’s Brian Schmidt, Johns Hopkins’s Adam Reiss, and Saul Perlmutter at the University of California, Berkeley — measured the brightness and recession speeds of exploding stars called “supernovae,” which are so bright that they are visible even in very distant galaxies. Their measurements showed conclusively that the expansion of the universe has begun to speed up, pointing to a positive vacuum energy. Perlmutter, Reiss, and Schmidt shared the 2011 Nobel Prize for this discovery. An article on the Nobel Prize website describes the vacuum energy’s repulsive effect: “It was as if you threw a ball in the air and it kept speeding away until it was out of sight.”

  The discovery of a positive vacuum energy was a key step towards settling the makeup of the universe. In today’s universe, the vacuum energy accounts for 73 percent of the total energy. Dark matter accounts for 22 percent, ordinary matter like atoms and molecules 5 percent, and radiation a tiny fraction of a percent. Dark matter, ordinary matter, and radiation emerged from the early universe with gentle ripples, at a level of one part in a hundred thousand on all scales, which seeded the creation of galaxies. This “concordance model” of the universe has, over the past decade, enjoyed one success after another as all kinds of observations fell in line with it. So far, there are no clouds on its horizon.

  So far, we have no idea how to use dark matter or vacuum energy, but it is tempting to speculate that, some day, they might provide a ready source of fuel that we could use to travel across space. In fact, special relativity makes the universe far easier to explore than you might think at first sight. Lorentz contraction means that, for space travellers, the universe can be crossed in a relatively short period of time.

  Think about a spaceship that escapes from Earth’s gravity and continues thereafter at one g — that is, with the same acceleration that a falling object has on Earth. This would be quite comfortable for the space travellers, since they would feel an artificial gravity of just the same strength as gravity on Earth. After a year or so, the spaceship would approach the speed of light, and it would get closer and closer to light speed as time went on. As the universe flashed by, Lorentz contraction would make it appear more and more compressed in the direction of travel. After just twenty-three years of the space travellers’ time, they would have crossed the whole region of space we can currently see. Of course, it would take another twenty-three years to slow down the ship so they could get off and explore. And due to time dilation, billions of years would have elapsed back on Earth.

  For now, these prospects seem very distant. But if history is anything to go on, they may be nearer than we think.

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  THE PICTURE OF COSMOLOGY I have described has been remarkably successful. It has accommodated every new observation, and it now forms the foundation for more detailed studies of the formation of galaxies, stars, and planets in the universe. We have built the science of the universe. Why, then, aren’t we theorists satisfied?

  The problem, as I mentioned earlier, is that working models of inflation are no more beautiful today than they were in 1982. Inflationary models do not explain what happened just before inflation, or how the universe emerged from a cosmic singularity. It is simply imagined that the universe somehow sprang into being filled with inflationary energy.

  And the more we have learned about unification, the more contrived inflationary models appear. In addition to assuming the universe started out inflating, the models’ parameters have to be adjusted to extremely small values in order to fit the data. There is no shortage of inflationary models: there are thousands of them. The problem is that they are all ad hoc, and it would be impossible to distinguish many of them from each other through observations.

  The small patch of space that started out inflating was assumed to be filled with inflationary energy at extremely high density. The inflationary energy will ultimately decay, at the end of inflation, into matter and radiation. However, in any realistic model there must also, at the end, be a tiny residue of vacuum energy to explain what we see today. In any inflationary mod
el, one can ask: what is the ratio of the assumed inflationary energy density at the beginning of inflation to the vacuum energy density we now measure in the universe? That ratio must appear in the description of the model: it is a vast number, typically a googol (a one with a hundred zeros after it) or so. In every known model so far, this number is just assumed, or picked from a vastly greater number of models according to a principle we do not yet understand.

  Every inflationary model suffers from this fine-­tuning difficulty in addition to all of the other problems. Remember, inflationary theory was invented in order to explain the peculiar fine-tuned, smooth, and flat initial conditions required in the ball of light at the start of the hot big bang. But now we find that inflation is itself based on a strange and artificial initial condition in which the inflationary energy takes a vast value for no apparent reason.

  You can think of inflationary energy as a highly compressed spring, like the one you compress when you start a game of pinball. To get the ball going as quickly as possible, you must condense the spring as much as you can. This is similar to what you need for inflation: you need an enormous density of inflationary energy, compressed into a tiny region of space. But how likely would it be for you to come across a pinball machine that spontaneously shot the ball up into the machine? It is possible that the random vibrations of the spring and the collisions of all the surrounding air molecules conspire to kick the ball up, but it is extremely unlikely. The conditions required to initiate inflation are, it turns out, vastly more improbable.

  It is true that the total amount of energy required to get inflation going isn’t so great, and Guth relies on this in his “free lunch” argument. But energy is not a good measure of how extreme such an inflating region is, because energy is not conserved when space is expanding, and certainly not during inflation. There is a known measure of the rarity of inflationary initial conditions, known as the “gravitational entropy.” Roughly speaking, it allows you to ask how unusual it would be to find a patch of the universe with inflating initial conditions. The answer is that inflating initial conditions would be expected around one time in 10 raised to the power of 10 raised to the power of 120. That is an extremely small probability, and points to a serious problem with the inflationary hypothesis.

  The most serious attempt so far to describe the initial conditions required for inflation was made by James Hartle and Stephen Hawking, building on earlier ideas of the Russian cosmologist Alexander Vilenkin. They noticed that because inflationary energy is repulsive, it is possible for universes to avoid a singularity. They considered a curved universe where space takes the form of a small three-dimensional sphere, and showed that such a universe, if you filled it with inflationary energy, could be started out set at some time in a static condition. If you followed time forward, the universe would grow exponentially in size. Likewise, if you followed time backward it would also grow exponentially. So if you followed time forward from some point long before the universe was static, you would see the universe first shrink and then “bounce” from contraction to expansion.

  The effect is like a bouncing ball. Imagine someone shows you a time-lapse movie whose first frame shows the ball at the moment of the bounce, squished up against the floor. As time proceeds, the ball pushes itself off from the floor and becomes spherical again. Now they play the movie again, but this time running backward in time from the moment of the bounce. There is no difference! The laws of physics are unchanged if time is reversed: going backward in time, the ball will do just as it did going forward. Of course, if they show the whole movie, starting at some time well before the bounce, you will see the ball start out spherical as it hits the floor, squish up against the ground, and then unsquish itself as it bounces off.

  Hartle and Hawking, following Vilenkin, employ the powerful mathematical trick of imaginary time, which I explained at the end of the previous chapter. Hawking had applied this trick successfully to black holes, showing that they possess a tiny temperature and emit radiation called “Hawking radiation.” Now he and Hartle tried to apply it to the beginning of the universe. If you follow time back to the bounce, you can use the imaginary number i to change time into another direction of space. And now, it turns out, with four space dimensions the geometry of the universe can be “rounded off” smoothly, with no singularity. Hartle and Hawking called this idea the “no boundary” proposal because in their picture, the universe near its beginning would be a four-­dimensional closed surface, like the surface of a sphere, with no boundary. In spirit, their idea is highly reminiscent of Lemaître’s “Primeval Atom” proposal.

  When I moved to Cambridge, in 1996, I worked with Hawking and a number of our Ph.D. students to develop the predictions of the Hartle–Hawking proposal for general theories of inflation. We showed that in such theories, the universe in the imaginary time region could generally be described as a deformed four-­dimensional sphere, a configuration that became known as the “Hawking–Turok instanton.” It turns out you can work out all the observational quantities within this region, and then follow them forward to the moment of the “bounce” and then into the normal, expanding region of spacetime, where they determine what observers would actually see.

  A beautiful feature of the Hartle–Hawking proposal is that it does not impose an arbitrary initial condition on the laws of physics. Instead, the laws themselves define their own quantum starting point. According to the Hartle–Hawking proposal, the universe can start out with any value for the inflationary energy. Their proposal predicts the probability for each one of these possible starting values. It turns out that this calculation agrees with the estimate of gravitational entropy I mentioned earlier: the probability of getting realistic inflationary initial conditions is around one in 10 to the power of 10 to the power of 120. The most probable starting point, by far, is the one with the smallest possible value of the inflationary energy, that is, today’s vacuum energy. There would be no period of inflation, no matter or radiation. Hartle and Hawking’s proposal is a wonderful theory, but at least in the most straightforward interpretation, it predicts an empty universe.

  Hartle and Hawking and their collaborator Thomas Hertog, of the University of Leuven, propose to avoid this prediction by invoking the “anthropic principle” — the idea that one should select universes according to their ability to form galaxies and life.

  It is not a new notion that the properties of the universe around us were somehow “selected” by the fact that we are here. The idea has grown increasingly popular as theory has found it more and more difficult to explain the specific observed properties of the universe. The problem is that the anthropic arguments are vague: in order to make them meaningful, one needs a theory of the set of possible universes and also the precise condition for us to be located in one of them. Neither of these requirements are yet close to being met. Nevertheless, Hartle, Hawking, and Hertog argue that even if a priori an empty universe is the most likely, the predictions of the Hartle–Hawking proposal, supplemented by anthropic selection, are consistent with what we observe. In principle, I have no objection to this kind of argument, as long as it can really be carried through.

  However, a realistic universe like ours has a minuscule a priori probability in this setup, of one in 10 raised to the power of 10 raised to the power of 120 (the same tiny number mentioned earlier). Anthropic selection has to eliminate all of the other possible universes, and this seems an extremely tall order. A universe in which ours was the only galaxy, surrounded by empty space, would seem to be quite capable of supporting us. And, according to the Hartle–Hawking proposal, it would be vastly more likely than the universe we observe, which is teeming with galaxies (Hartle, Hawking, and Hertog exclude such a universe by fiat in their discussion). When the a priori probabilities are so heavily stacked against a universe like ours, as they are with the Hartle–Hawking proposal, it seems to me very unlikely that anthropic arguments will save the day.

 
A THEORY THAT PREDICTS a universe like ours a priori, without any need for anthropic selection, would seem vastly preferred. Even if anthropic selection could rescue Hartle and Hawking’s theory (which seems to me unlikely), the non-anthropic theory would be statistically favoured over the anthropic one by a huge factor, of 10 raised to the power of 10 raised to the power of 120.

  For the past decade, with Paul Steinhardt of Princeton University and other collaborators, I have been trying to develop such theories as an alternative to inflation. Our starting point is to tackle the big bang singularity. What if it was not the beginning of time, but instead was a gateway to a pre–big bang universe? If there was a universe like ours before the singularity, could it have directly produced the initial ball of light, and if it did, would there be any need for a period of inflation?

  Most of the universe today is very smooth and uniform on scales of a millimetre, and we have no problem understanding why. Matter and radiation tend to spread themselves out through space, and the vacuum energy is completely uniform anyway. Let us imagine following our universe forward into the future. The galaxies and all the radiation will be diluted away by the expansion: the universe will become a cold, empty place, dominated by the vacuum energy. Now imagine that for some reason the vacuum energy is not absolutely stable. It could start to slowly decay, tens of billions of years into our future. We can easily build mathematical models where it declines in this way, becoming smaller and smaller and then going negative. Its repulsive gravity would become attractive, and the universe would start to collapse.