Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

  Penzias and Wilson measured the intensity of the radiation at a single frequency (to which their antenna was tuned), while the theory predicted that the radiation should be spread over a range of frequencies, with the intensity following a simple formula derived by Max Planck at the turn of the twentieth century. This prediction was spectacularly confirmed in 1990 by the Cosmic Background Explorer (COBE) satellite experiment, which found agreement with the Planck formula at the level of one part in 10,000.

  The discovery of the cosmic radiation was no doubt an epoch-making event in cosmology. This tangible relic of the primeval fireball gives us faith that we have not dreamed it all up, that there was indeed a hot early universe some 14 billion years ago. Penzias and Wilson received the 1978 Nobel Prize “for their discovery of cosmic microwave background radiation.” No prize for its theoretical prediction has ever been awarded.

  IMPERFECTIONS OF CREATION

  If the universe had started out perfectly homogeneous, then it would remain homogeneous to this day. The thin, uniform gas filling the universe would gradually be getting ever thinner, and the universe would remain permanently dark, with cosmic radiation slowly shifting to radio waves of lower and lower frequency. But one look at the night sky should be enough to convince you that our universe is not nearly so dull. The universe is lit up with shining stars that are scattered throughout space, forming a hierarchy of structures. The basic unit of this hierarchy is the galaxy, with a typical galaxy containing about 100 billion stars. Galaxies are grouped in clusters, which in turn form superclusters that extend up to a few hundred million light-yearsi—only 100 times smaller than the size of the currently observable universe.

  Cosmologists attribute the origin of all these magnificent structures to tiny inhomogeneities that existed in the primeval fireball. Small inhomogeneities can grow into galaxies as a result of gravitational instability. Suppose some region of the universe is slightly denser than its surroundings. It will have stronger gravity and will attract more matter from the surrounding regions. As a result, the density contrast will keep growing, and a nearly homogeneous initial distribution of matter will evolve into a highly inhomogeneous one. Cosmologists believe that this is how galaxies, clusters, and superclusters were formed. According to the theory, the first galaxies were formed about 1 billion years after the big bang. Stars lit up the universe, and thus the cosmic dark age ended. The process of galaxy formation was complete in the not-so-distant past—at the cosmic age of about 10 billion years (“only” 4 billion years ago).

  You might think that this story is destined to remain just that—a story—since nobody was there to confirm it. But as I already emphasized, we see distant objects as they were a long time ago, when the light we now detect was emitted. Thus, by studying more distant galaxies, we go further back in time. The travel time of light from the most distant galaxies that we can observe is about 13 billion years, so we see them when the universe was a billion years old. Compared to the grand spirals we find nearby, these galaxies are small and irregular—a sign of their youth.

  Still earlier epochs in the history of the universe can be observed through cosmic microwaves. These waves traveled without scattering for nearly 14 billion years, since the time when the universe became transparent to radiation. The regions where the waves were last scattered are now 40 billion light-years awayj (not 14 billion light-years as one might think, since the universe was expanding in the meantime). Thus, the microwaves come to us from the surface of a gigantic sphere, 40 billion light-years in radius; it is called the surface of last scattering. Radiation emitted from regions of slightly higher density has to overcome stronger gravity and arrives to us with a slightly diminished intensity. As a result, denser regions look dimmer on the microwave sky. By mapping the radiation intensity from different directions in the sky, we can obtain an image of the universe at the epoch of last scattering, when it was only 300,000 years old.

  The first successful map of the microwave sky was made by the COBE team in 1992. A more detailed map, produced 10 years later by the WMAP satellite,k is shown in Figure 4.2. Darker shades of grey correspond to higher radiation intensity, but the difference in intensity between the lightest and darkest spots is only a few parts in 100,000. This means that at the time of last scattering the universe was almost perfectly homogeneous. All the glorious structures that we now see in the sky were then encoded in tiny amorphous ripples on the smooth cosmic background.

  Figure 4.2. Microwave sky as mapped by the WMAP satellite. (Courtesy of Max Tegmark)

  THE MODERN STORY OF GENESIS

  The picture in Figure 4.3 illustrates the story of genesis as we have discussed it so far. This story is supported by an abundance of observational data, and there is little doubt that it is basically correct. The details are still being worked out, and some outstanding questions remain open. One of the big unknowns is the nature of the dark matter that manifests itself by its gravitational pull in galaxies and clusters. There are strong reasons to believe that most of this dark matter is not made up of nucleons and electrons, but rather consists of some yet undiscovered particles. The details of the galaxy formation process depend on the masses and interactions of these particles, but the general picture outlined in Figure 4.3 does not.

  It is truly remarkable that we can observe the universe as it was 14 billion years ago and accurately describe the events that took place a fraction of a second after the big bang. This brings us tantalizingly close to the moment of creation. But what actually happened at that moment remains as enigmatic as ever. In fact, on closer examination the big bang turns out to be even more peculiar than it seemed before.

  Figure 4.3. Abridged history of the universe.

  5

  The Inflationary Universe

  An invasion of armies can be resisted, but not an idea whose time has come.

  —VICTOR HUGO

  COSMIC PUZZLES

  Suppose one day you receive a radio message from a distant galaxy saying “Elvis lives.” You point your antenna to a different galaxy, and to your surprise you get an identical message! Mystified, you turn the antenna from one galaxy to another, but the same message keeps coming to you from all over the sky. One conclusion that you draw is that the universe is full of Elvis fans; the other is that they are in communication with one another. How else would they come up with identical messages?

  Silly as it is, this example closely resembles the situation we observe in our universe. The intensity of the microwave radiation coming to us from all directions in the sky is the same, with a very high degree of accuracy, which indicates that the density and temperature of the universe were highly uniform at the time when the radiation was emitted. This observation suggests that there was some interaction between the radiation-emitting regions that led to equilibration of densities and temperatures. The problem is, however, that the time elapsed since the big bang is too short for such an interaction to have occurred.

  The crux of the problem is that physical interactions cannot propagate faster than the speed of light. The distance traveled by light since the big bang, about 40 billion light-years, is the horizon distance. It puts a limit on how far we can see in the universe and gives the maximum range over which communications could be established. The cosmic radiation that we now observe was emitted shortly after the big bang and comes to us from distances approximately equal to the horizon. Now, consider the radiation coming from two opposite directions in the sky (Figure 5.1). The regions where this radiation was emitted are now separated by twice the horizon distance, and thus could not possibly interact. In particular, they could not exchange heat to equalize their temperature.

  At earlier times the two regions were closer to one another, and you might think this could have helped them to equilibrate. But actually at early times the difficulty is even more severe. The reason is that as we go back in time, the horizon distance shrinks even faster than the separation between the regions. At the time of last scattering, when the radiatio
n was emitted, the observable part of the universe was fragmented into thousands of small regions that could not “talk” to one another. We are thus driven to the conclusion that no physical process could make the fireball uniform if it was not uniform to begin with.

  Figure 5.1. Cosmic radiation coming from opposite directions in the sky originated in regions that are now separated by twice the horizon distance.

  This mysterious feature of the big bang is often referred to as the horizon problem. The only explanation we can give to the remarkable uniformity of density and temperature in the early universe is that this is how the infant universe emerged from the big bang. Logically, there is nothing wrong with this “explanation.” The physical conditions at the singularity are undetermined, so one can postulate any physical state immediately after the big bang. But one cannot help feeling that this does not explain anything at all.

  Another puzzling feature of the big bang is the precarious balance between the power of the blast that sent all particles rushing away from one another and the force of gravity that slows the expansion down. If the density of matter in the universe were a bit higher, its gravitational pull would be strong enough to halt the expansion and the universe would eventually recollapse. If it were a bit lower, the universe would continue expanding forever. The observed density is within a few percentage points of the critical density, at the borderline between the two regimes. This is very peculiar and calls for an explanation.

  The problem is that in the course of cosmic evolution the universe tends to be quickly driven away from the critical density. If, for example, we start 1 percent above the critical density at 1 second A.B., then in less than a minute we would get to twice the critical density and in a little over 3 minutes the universe would already have collapsed. Similarly, if we start 1 percent below the critical density, then in 1 year the density would be 300,000 times smaller than critical. In such a low-density universe, stars and galaxies would never form; there would be nothing but dilute, featureless gas. In order to have a nearly critical density at the present cosmic age of 14 billion years, the initial density has to be fine-tuned with a surgical accuracy. A calculation shows that at 1 second the density had to be equal to critical within 0.00000000000001 percent.

  A closely related issue is the geometry of the universe. As we know from Friedmann, there is a connection between the density of the universe and its large-scale geometry. The universe is closed if the density is above critical, open if it is below critical, and flat if the density is exactly equal to critical. Thus, instead of asking why the density of the universe is so close to critical, we could just as well ask why its spatial geometry is so close to flat. That is why this fine-tuning puzzle is often called the flatness problem.

  The horizon and flatness problems had been recognized since the 1960s, but had almost never been discussed—simply because no one had any idea as to what could be done about them. These problems could not be attacked without confronting an even greater puzzle that was looming behind them: What actually happened at the big bang? What was the nature of the force that caused the cosmic blast and sent all particles flying away from one another? With no progress in that direction for nearly half a century, physicists grew accustomed to the thought that this was one of those questions that you never ask—either because it does not belong to physics or because physics is not yet ready to tackle it. It therefore came as a total surprise when in 1980 Alan Guth made his dramatic breakthrough, pointing the way to resolve the stubborn cosmological puzzles in one shot.1

  Guth came up with the idea that it was repulsive gravity that blew the universe up. He suggested that the early universe contained some very unusual material, which produced a strong repulsive gravitational force. If you ever try to give a talk with this kind of idea, you had better have a piece of antigravity stuff in your pocket, or at least be prepared to give a very good reason why anybody should believe that it really exists. Luckily for Guth, he did not have to invent any magic material. The leading elementary particle theories had it already in stock: it was called false vacuum.

  FALSE VACUUM

  “Can you make no use of nothing, nuncle?”

  “Why, no, boy; nothing can be made out of nothing.”

  —SHAKESPEARE, King Lear

  Vacuum is empty space. It is often regarded as synonymous with “nothing.” That is why the idea of vacuum energy sounded so weird when Einstein first introduced it. But the physicist’s view of the vacuum has been drastically transformed, as a result of developments in particle physics over the last three decades. The study of the vacuum still continues, and the more we learn about it, the more complex and fascinating it becomes.

  According to modern theories of elementary particles, vacuum is a physical object; it can be charged with energy and can come in a variety of different states. In physics terminology, these states are referred to as different vacua. The types of elementary particles, their masses, and their interactions are determined by the underlying vacuum. The relation between particles and the vacuum is similar to the relation between sound waves and the material in which they propagate. The types of waves and the speed at which they travel vary in different materials.

  We live in the lowest-energy vacuum, the true vacuum.2 Physicists have accumulated a great deal of knowledge about the particles that inhabit this type of vacuum and the forces acting between them. The strong nuclear force, for example, binds protons and neutrons in atomic nuclei; the electromagnetic force holds electrons in their orbits around nuclei in atoms; and the weak force is responsible for the interactions of elusive light particles called neutrinos. As their names suggest, the three types of forces have very different strengths, with the electromagnetic force intermediate between the strong and the weak.

  The properties of elementary particles in other vacua may be completely different. We do not know how many vacua there are, but particle physics suggests that apart from our true vacuum, there are likely to be at least two more, both having more symmetry and less diversity among particles and their interactions. The first is the electroweak vacuum, in which the electromagnetic and weak interactions have the same strength and are manifested as parts of a single, unified force. Electrons in this vacuum have zero mass and are indistinguishable from neutrinos. They dash about at the speed of light and cannot be captured into atoms. No wonder we do not live in this type of vacuum.

  The second is the grand-unified vacuum, where all three types of particle interactions are unified. Neutrinos, electrons, and quarks (of which protons and neutrons are made) are all interchangeable in this highly symmetric state. While the electroweak vacuum almost certainly exists, the grand-unified vacuum is more speculative. Particle theories that predict its existence are attractive from the theoretical point of view, but they are concerned with extremely high energies, and observational evidence for these theories is scant and rather indirect.

  Each cubic centimeter of the electroweak vacuum carries a huge energy and, by Einstein’s mass-energy relation, a huge mass, approximately 10 million trillion tons (roughly the mass of the Moon). When faced with such colossal numbers, physicists resort to a shorthand power-of-ten notation. A trillion is 1 followed by 12 zeros; it is written as 1012. Ten million trillion is 1 with 19 zeros; hence, the mass density of electroweak vacuum is 1019 tons per cubic centimeter. In a grand-unified vacuum, the mass density is still higher, by a whopping factor of 1048. Needless to say, these vacua have never been synthesized in a laboratory: this would require energies far in excess of the present technological capabilities.

  In contrast to these enormous energies, the energy of the normal, true vacuum is minuscule. For a long time it was thought to be exactly zero, but recent observations indicate that our vacuum has a small positive energy, which is equivalent to the mass of three hydrogen atoms per cubic meter. The significance of this finding will become clear in Chapters 9, 12, and 14.

  High-energy vacua are called “false” because, unlike our true vacuum, they ar
e unstable. After a brief period of time, typically a small fraction of a second, a false vacuum decays, turning into the true vacuum, and its excess energy is released in a fireball of elementary particles. We shall delve into the details of the vacuum decay process in the following chapter.

  If vacuum has energy, then we know from Einstein that it should also have tension.3 And, as we discussed in Chapter 2, tension has a repulsive gravitational effect. In the case of a vacuum, the repulsion is three times stronger than the attractive gravity caused by the mass, and the net effect is a strong repulsive force. Einstein used this antigravity of the vacuum to balance the gravitational pull of ordinary matter in his static model of the world. He found that the balance is achieved when the mass density of matter is twice that of the vacuum. Guth had a different plan: instead of balancing the universe, he wanted to blow it up. So he allowed the repulsive gravity of false vacuum to reign unopposed.