Escape Clause: Circumventing the Big Bang Singularity

*Naturally we were all there…. Where else could we have been?* *Nobody knew then that there could be space. Or time either:* *what use did we have for time, packed in there like sardines?* *I say “packed like sardines,” using a literary image: in reality* *there wasn’t even space to pack us into. Every point of each of us* *coincided with every point of each of the others in a single point,* *which was where we all were.*

Italo Calvino (*Cosmicomics*), translated by William Weaver

Pity the hapless soul who comes face to face with a singularity, the nemesis of anyone trying to find a finite, well-defined solution to an equation. Einstein notably despised these mathematical beasts. In the 1930s and 1940s, while working with his assistants on various attempts to unify the various aspects of nature, he counseled that singularities were unnatural, even ungodly. Like a meticulous merchant wrapping up a precious package, he felt that an intelligent creator would not allow open ends. This cautionary note was passed down by Einstein’s assistants, such as Nathan Rosen, to their own students. For example, Fred Cooperstock, a student of Rosen’s, was used to such admonitions. Distaste for singularities has not faded

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6
Escape Clause: Circumventing the Big Bang Singularity
Naturally we were all there…. Where else could we have been? Nobody knew then that there could be space. Or time either: what use did we have for time, packed in there like sardines? I say “packed like sardines,” using a literary image: in reality there wasn’t even space to pack us into. Every point of each of us coincided with every point of each of the others in a single point, which was where we all were.
Italo Calvino (Cosmicomics), translated by William Weaver
TIME ZERO
Pity the hapless soul who comes face to face with a singularity, the nemesis of anyone trying to find a finite, well-defined solution to an equation. Einstein notably despised these mathematical beasts. In the 1930s and 1940s, while working with his assistants on various attempts to unify the various aspects of nature, he counseled that singularities were unnatural, even ungodly. Like a meticulous merchant wrapping up a precious package, he felt that an intelligent creator would not allow open ends. This cautionary note was passed down by Einstein’s assistants, such as Nathan Rosen, to their own students. For example, Fred Cooperstock, a student of Rosen’s, was used to such admonitions. Distaste for singularities has not faded

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over time. Today, despite the hard evidence of the background radiation, many researchers still find it hard to accept the idea that the universe was created in a state of infinite density and zero volume. How could it ever get out of such a state?
Almost nobody doubts there was a period in the early universe when it was extremely hot and dense; in fact, WMAP and other measures of the cosmic microwave background provide unmistakable proof. There have been numerous other attempts to account for this radiation, but none of them can explain why its temperature is very nearly the same in all directions. Thus, for want of a better explanation most cosmologists accept that it is the remnant of a primeval fireball.
The debate has to do with the Big Bang singularity itself. Could there be a way of accounting for all observed cosmological results without having the mathematics of the theory go haywire some 13.7 billion years in the past? Could the initial creation of matter be explained by a known physical process, rather than just by fiat?
In the late 1960s, Hawking and Penrose demonstrated that just as black holes must have final singularities, the standard Big Bang must have had an initial singularity. The theorems they proved assumed that the universe contained material of typical density and pressure and that its dynamics could be modeled through ordinary general relativity. Most physicists have accepted these conditions as reasonable and have resigned themselves to a universe of indeterminate origin.
In recent decades, however, researchers have sought ways around this knotty issue. One such proposal was put forth, interestingly enough, by Hawking himself. At a 1981 conference organized by the Vatican, he suggested that space-time has no boundary. By substituting “imaginary time” (mathematically, real time multiplied by the square root of negative one) for real time, Hawking found that he could transform the Big Bang singularity into a smooth surface— akin to Earth’s South Pole. Just as Antarctic explorers don’t fall off

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the face of the Earth when they pass the pole, but rather change their direction from south to north, Hawking argued that if someone could travel back in imaginary time, past the Big Bang, they would simply start to move forward in time again. This is all well and good and shows a mathematical way of eschewing the initial glitch. However, to many physicists this explanation doesn’t seem physical enough, given that nobody can really travel in imaginary time.
Other suggestions for eschewing the initial singularity have been based on quantum randomness. In 1973, Hunter College physicist Edward Tryon published a provocative article in the prestigious journal Nature, entitled “Is the Universe a Vacuum Fluctuation?” In quantum field theory, particles continuously pop in and out of the vacuum froth. Tryon pointed out that under extraordinarily rare circumstances a particle could randomly emerge from the foam with the mass of the universe. Though the chances of it coming forth at any given moment would be almost nil, it could literally take all the time in the world to make its debut. Eternity’s infinite patience would guarantee its emergence. This quantum fluctuation would serve as the creation event for the entire universe we see today.
Through the theories of Starobinsky, Guth, and others, physicists came to realize that it wasn’t necessary for all matter to emerge directly in a single fluctuation. Rather, it could surge forth during an era of negative pressure, spawned indirectly by the fluctuation. Hence, the fluctuation would serve as a catalyst rather than the actual influx of matter itself. For example, a fluctuation that was a scalar field could induce negative pressure—or, the equivalent, a positive cosmological constant—that would inflate a region of space. (Recall how under negative pressure space balloons outward.) Large enough negative pressure would coax matter and energy from sheer nothingness, rapidly filling the universe with material. The fluctuation would therefore seed an inflationary era—or its equivalent.
Guth has pointed out that during the inflationary era mammoth quantities of energy could have emerged from sheer nothingness.

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Like the bursting of a colossal dam, more than 1088 particles could have rushed into the void—providing the building blocks of everything we see today. He refers to this immense creation of material as “the ultimate free lunch.”
This mechanism for the rapid production of matter suggests a two-stage model for the universe: vacant up to a certain time, when a quantum perturbation would trigger an era of negative pressure (inflation), and matter-filled thereafter. The Big Bang would be replaced by a “blip”—a transition between one universal phase and another. Because the early matter-filled cosmos would be extremely hot, there would be sufficient thermal energy to build up the light elements and generate the observed background radiation. Thus, the issues that plagued the steady state cosmology would be avoided.
Another idea, called eternal inflation or the self-reproducing universe, imagines Linde’s chaotic inflationary cosmology as an unlimited process, with each universe generating fluctuations that spawn new universes. All that would be needed is an appropriate scalar field emerging in a particular region of space, and a bubble from that sector would blow up into a cosmic offspring. Thus, each generation would constitute the breeding ground for the next.
There is nothing to stop this process from continuing ad infinitum into the future. Could then the Big Bang singularity be avoided by extrapolating this mechanism indefinitely into the past— that is, imagining our universe as the prodigal son or daughter of an earlier one, and so forth? Apparently not. In 1993, Borde and Vilenkin proved that even eternal inflationary models would have to start with an initial singularity. Push the moment of reckoning as far back in time as you like, but there still would have to have been a singularity at some point in the past.
UNITING THE FORCES
All of the attempts to avoid the Big Bang singularity discussed so far are four-dimensional in character. Some of the most promising

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The scale factor as a function of time for a cosmological model that does not start in a Big Bang but evolves instead from a flat (Minkowski) space-time. The density goes through a sharp spike because matter is produced when the pressure becomes negative, in accordance with Einstein’s equations. Models like these have been studied by Bonnor and Wesson. They are interesting because they can exist forever, suffer a (quantum) perturbation, experience a period of matter creation, and then evolve into something like what we observe today. (Illustration designed by Paul Wesson.)

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modern cosmologies, however, are based on the intriguing notion that the universe has more dimensions than just space and time. The major motivation for these theories is to obtain a unified description of all the natural interactions. Ideally, such a unification would account for the rest masses of all known elementary particles, the interaction strengths of all known forces, and other aspects of the subatomic world. A successful theory would help fulfill Einstein’s quest for a single set of equations that would hold the secret to universal dynamics.
The concept of higher-dimensional unification has a long and turbulent history. Shortly after Minkowski first described special relativity in terms of four-dimensional space-time, a young Finnish physicist, Gunnar Nordström, decided to extend these four to five. In his research, published in 1914, Nordström attempted to add a dimension to Maxwell’s equations of electromagnetism and thus describe gravitation, the only other fundamental force known at the time, as well. Unfortunately, the gravitational component of his theory turned out to be flawed. When Einstein’s successful gravitational theory appeared two years later, Nordström’s work crumbled— slipping into the dustbin of forgotten theories.
In 1919, Theodor Kaluza, working as a mathematician in Königsberg, East Prussia (now Kaliningrad, Russia), had more success extending general relativity itself. When he wrote down the five-dimensional equivalent of Einstein’s equation, he found that it elegantly divided into two groups of relationships. One set reverted to standard general relativity and the other to Maxwell’s formalism. Kaluza’s theory thus showed how gravity and electromagnetism as four-dimensional physical forces could be derived from pure, five-dimensional geometry. The theory seemed to wrap the then-known natural interactions up into a single, unified description. Nobel laureate Abdus Salam described Kaluza’s reaction as follows: “To his amazement he discovered that he had … written down not only Einstein’s theory of gravity, but also Maxwell’s theory of electromagnetism…. It was an incredible and miraculous idea…. What

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Kaluza did is he sent the paper to Einstein and asked him to get it published.”
At the time, Einstein helmed one of the most important journals in Europe, the Proceedings of the Prussian Academy of Sciences. Well known throughout the scientific community, he was at the brink of international fame. Very soon thereafter, Eddington’s eclipse results would confirm general relativity and boost Einstein to celebrity status.
Kaluza, on the other hand, was at the time virtually unknown. He eked out a living selling tickets to his lectures—a common way that junior professors in Germany functioned until they gained enough status for a permanent position. Fortunately, though Einstein had likely never heard of Kaluza, he was willing to read over the mathematician’s results. Although at first glance he found Kaluza’s idea extraordinary, he suggested improvements to the paper before it could be published. For example, Einstein hoped Kaluza would provide a sound physical explanation of why the fifth dimension couldn’t be observed. Instead, he offered only a mathematical rationale that seemed rather unsatisfactory. Given such a promising but unusual idea, Einstein pressed for a more solid justification.
As Kaluza’s son recalled this discourse: “Einstein asked a question or made a suggestion. Then my father did something about it and sent it to Einstein. Einstein asked another question and so on. There are five or six letters of this sort.”
For more than two years they corresponded, until Einstein at last decided that the article ought to be published. One of the reasons for the delay, strangely enough, was that Germany was just emerging from the First World War and had a severe paper shortage. Therefore, Einstein felt justified being somewhat picky about the articles he recommended. In 1921 the article finally appeared in print.
QUANTUM CONNECTIONS
In 1926, around the same time that modern quantum theory emerged, Oskar Klein, working in Copenhagen, published an

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intriguing, independently derived variation of Kaluza’s five-dimensional theory. In quantum physics, Klein is known for his work on what is now called the Klein-Gordon equation (a special-relativistic extension of quantum mechanics), among other contributions. He was Niels Bohr’s assistant during a critical period and thus played a central role in the development of quantum notions. Later he would become a professor at the University of Stockholm, where he continued his theoretical research. He was also a close friend and lifelong correspondent with Gamow, with whom he discussed cosmology and other topics.
Klein translated Kaluza’s theory into quantum terms by writing down a five-dimensional variation of the now well-known Schrödinger wave equation. He showed that this five-dimensional equation had solutions corresponding to both gravitational and electromagnetic waves in four-dimensional space-time.
Klein’s approach had several advantages over Kaluza’s. The first was that the former had a more mathematically rigorous derivation. (Kaluza had taken some shortcuts.) The second was that Klein’s model incorporated quantum physics. Lastly, Klein offered a neat hiding place for the fifth dimension. Instead of slipping it under a mathematical carpet, he rolled the carpet up—so tightly, in fact, that no physical observations could be done. Each point in space would comprise a five-dimensional loop, with a diameter less than 10–31 inches—far, far smaller than any known elementary particle. Hence, no detector could possibly sense it. The method he used has come to be known as “compactification.”
Imagine a garden hose lying on the ground, viewed from a helicopter lifting off nearby. As the chopper ascended, the hose would look less and less like a hollow pipe—with a diameter wide enough to carry water. More and more, it would seem like a straight line, slashing through the field. Ultimately, if the helicopter were high enough, its pilot would have no way of detecting the “extra dimension” of the hose.
Klein’s theory, like Kaluza’s, turned out to have a major shortcoming. Physicists discovered two additional forces of nature—the

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strong and weak nuclear interactions. During the late 1930s, Klein attempted to incorporate these forces as well, but his theory received little notice due to the tumult of the Second World War. After the war, the idea slowly made a comeback, picking up momentum during the 1970s and 1980s with the introduction of supergravity and superstring theories. To recognize the contributions of the two original thinkers, all such higher-dimensional methods for unification are now commonly known as Kaluza-Klein theories.
AND THEN THERE WERE 11
One difference between the older theories and the newer ideas is that physicists have come to realize that more dimensions are needed to incorporate all the forces. In 1981, Edward Witten proved that at least 11 dimensions were required to merge gravity with the other interactions. This 11-dimensional theory, called supergravity, seemed to provide a fully supersymmetric description of nature. (Recall that supersymmetry is a hypothesized connection between the two major categories of elementary particles: fermions and bosons.)
The direct motivation for supergravity was a long-standing struggle to find a mathematical description of gravitation consistent with quantum field theory. Attempts to quantize gravity in a similar manner to electromagnetism failed to materialize because of the presence of infinite terms that couldn’t be canceled out. Supergravity promised a chance to rectify this situation by proposing that gravity, at ultrahigh energies, forms part of a unified field that can be treated through standard quantum mechanisms. This field “lives” in a world of 10 spatial dimensions plus time. As the temperature lowers—for example, in the expansion of the universe—a phase transition occurs called “spontaneous compactification.” Then, seven of the 10 spatial dimensions curl up into compact loops, leaving only three large spatial dimensions—namely, the ones we see today.
When supergravity ran into mathematical difficulties in the early 1980s, theorists flocked to superstring theory as an alternative

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path to unification. By replacing point particles with minute but finite energy vibrations, superstring theory avoids the issue of infinite terms. The prospect of constructing a completely finite field theory provided welcome relief to bleary-eyed gravitational physicists, exhausted from trying to cancel out infinities.
Like supergravity, superstring theory requires higher dimensions to thrive. The minimum number, as John Schwarz and André Neveu demonstrated, is 10—nine spatial dimensions plus time. Six of them become compact with the lowering of energy. Thus, at ordinary energies the extra dimensions are so minuscule they cannot be observed. To probe such depths it would take an accelerator the size of the Milky Way—unlikely to be built any time soon!
Researchers discovered special configurations, called Calabi-Yau shapes (named after mathematicians Eugenio Calabi of the University of Pennsylvania and Shing-Tung Yau of Harvard), into which these added dimensions could twist up to produce various symmetries. The peculiar topology of each pretzellike figure, especially its number of holes, represents the theoretical properties of a certain symmetry group. Astonishingly, there are tens of thousands of such six-dimensional configurations, offering string theory considerable flexibility.
Theorists hoped the exotic rhythms that superstrings performed as they enacted various modes of vibration would reproduce the properties of familiar subatomic particles—from light neutrinos to massive Z bosons. Like a modern ballet performance, each type of dance would offer a unique representation—capturing the mood (spin, mass, and so on) of a particular particle state. Strings can indeed be very expressive—too expressive, in fact. Not only can they replicate known particles, they can enact the features of myriad entities that have never been seen in nature.
By the late 1980s and early 1990s, researchers were buried under a mountain of excess. There seemed to be too much of everything— too many ways for strings to vibrate, too many types of Calabi-Yau

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configurations, even too many kinds of string theory itself. As Witten, David Gross, Jeff Harvey, Emil Martinec, and Ryan Rohm of Princeton (the latter four known as the “string quartet”) demonstrated, there are five varieties of string theory, each a distinct representation. Classified by their mathematical properties, they have been designated Type I, Type IIA, Type IIB, Heterotic-O, and Heterotic-E.
Heterotic theories deftly combine superstrings with bosonic strings into amalgams that are in certain ways superior to each. (A term borrowed from biology, heterotic means “with qualities better than those of the parents.”) In these merged pictures the superstrings travel in one direction and the bosonic strings in the other, like traffic on a two-lane highway, a configuration that offers a natural description of chirality, or handedness, a property possessed by particles such as neutrinos.
The various models include two different categories of strings: open and closed. Open strings are like belts draped across a hanger; their ends dangle loose. Closed strings, in contrast, are like the belt on your waist; they form complete loops. Most known particles can be represented by open strings—with gravitons the notable exception. If all this seems overwhelming, think of the armies of poor young graduate students trying to sort out this mess and make original contributions to the field.
Why five different theories? Could nature be so blatantly redundant? And what of 11-dimensional supergravity? Where did that fit in? By the mid-1990s, unanswered questions called for a new revolution to establish connections between the various models and— researchers hoped—whittle them down to a single, unified theory.
THE SECRETS OF M
About the same time that superstrings were on the roll, assorted theorists, mainly centered at the University of Texas, the University of California at Santa Barbara, and the University of Cambridge,

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were developing a more general approach called membrane theory. Mavericks included American researchers Joseph Polchinski and Andrew Strominger and British physicists Gary Gibbons, Paul Townsend, and Michael Duff (among many others, too numerous to mention). Extending an idea originally proposed by Dirac, membranes represent particles as flapping multidimensional sheets. These entities can be one-dimensional (like strings), two-dimensional (like conventional surfaces), or indeed any number of dimensions. The only stipulation is that the dimensionality of the object must be less than that of the space in which it resides. Thus, a three-dimensional membrane would be perfectly happy living in a six-dimensional manifold but not on a two-dimensional plane. Townsend dubbed p-dimensional objects “p-branes.” Now, many researchers just call them “branes.”
For many years, membrane theory was considered string theory’s obscure cousin. Few outside the field saw the sense in modeling particles with pulsating sheets if vibrating strings were simpler and would do quite nicely. But then researchers began to find commonalities between strings and branes that encouraged useful connections between various approaches. These links, called dualities, paved the way for what is called the “second superstring revolution.”
Many string theorists date this groundbreaking development to a talk by Witten at the University of Southern California in February 1995, where he proclaimed the dawn of M-theory, a smorgasbord of string theory, membrane theory, and supergravity that seemed to include something for everyone. Witten wryly told the audience that the meaning of “M” had not yet been determined. It could represent anything from “magic” to “mystery” to “mother of all theories.” Calling it simply “membrane theory” seemed perhaps too restrictive.
Through the wonder of dualities, M-theory brought the five varieties of string theory under a single umbrella. In M-theory, two types of duality come into play. The first, called T-duality, relates certain types of string theory, looped around small circles, with others

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arranged around large circles. In other words, it ties together two different scales of compactification—the tiny and the potentially observable. The other type, called S-duality, links theories with strong coupling (interaction strength) to those with weak coupling. The latter turns out to be more physically realistic. By applying both kinds of duality, we can mold tightly compactified, less viable models into more acceptable theories with a large extra dimension. Consequently, as Witten and his colleagues discovered, linking the string theories implies an 11-dimensional framework that includes the three dimensions of space, the dimension of time, the six curled-up dimensions of the Calabi-Yau space, and the extra dimension produced through duality mechanisms.
Let’s set aside the six-dimensional Calabi-Yau geometry (twisted up beyond detection) for the moment, and focus on the remaining five: space, time, and the extra dimension. That way, we’ll concentrate on what we can measure. According to M-theory, this fifth dimension does not have to be tiny; it can be indefinitely large in size.
How can this be? Recall the tale of an ant crawling on the surface of a basketball. Because it is constrained to be on the ball’s surface, it does not care about the distance to its center. Similarly, a fifth dimension could exist for which we do not have access. Therefore, it could be as large as the other dimensions but wholly undetectable, except perhaps for its impact on gravitation.
The idea that the fifth dimension could be comparable in scale to the others dates back decades. As we’ll see in Chapter 7, it underlies induced-matter theory, first proposed in the 1980s. However, M-theory helped focus the attention of the physics community on this concept. M-theory pictures this extra dimension as forming a gulf between two three-dimensional spaces—with only gravity able to navigate the gap. The two “shores” are known as Dirichlet p-branes, or D-branes for short, and the sea in between is called the bulk. For mathematical reasons, open strings—representing almost all known particles—must forever stick like barnacles to the

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D-branes, while gravitons, as closed strings, are free to swim through the bulk. Thus, composed of closed strings, we remain perpetually landlocked—with only our gravitational emissions able to plunge beyond our brane.
Because of gravity’s special ability to escape, its immersion in the bulk would effectively dilute it. The larger the bulk, the less contact with our brane it would have and the weaker it would appear. Gravity becomes the puny partner of the other forces.
String theorists soon realized that the relative weakness of gravity was one of M-theory’s strengths. From the time of Dirac, researchers have sought a solution to the question of why the other three sub-atomic forces are so much more powerful than gravitation. With the hope that M-theory would resolve this riddle, several groups set out to construct “brane-world models”: interplays of bulk and brane designed to replicate precisely gravity’s distinctive behavior.
BRANE BENDERS
In 1998 a team of Stanford physicists published one of the first and simplest brane-world scenarios. Known as the “ADD model,” for the initials of its designers Nima Arkani-Hamed, Gia Dvali, and Savas Dimopoulos, it offered a bold attempt to resolve the hierarchy puzzle and other issues. Remarkably—for the abstruse world of string theory—it stuck its neck out with clear, testable predictions.
According to the ADD scenario, everything we see in space— visible galaxies, quasars, and the like—resides on a D-brane. Separated from our brane by roughly a millimeter (1/25 of an inch) is a second shadow realm. In between, like the filling in a sandwich, is a thin layer of bulk, accessible only by gravitons.
The ADD team chose that particular thickness of the bulk to model the actual weakness of gravity compared to the other forces. Too much filling would create an indigestibly large discrepancy; too little would not produce enough of a bite to provide a distinction. Even for the best matching case, the researchers realized that their

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scenario would slightly modify the long-established law of gravity. Such a minute difference could be picked up, however, only at distances comparable to or smaller than the bulk thickness—that is, at one millimeter or less. Since at the time they made the prediction, gravitational measuring instruments had not yet probed such tiny ranges, the researchers felt free to make such an assertion. Within a few years, however, Eric Adelberger of the Eöt-Wash group used ultrasensitive torsion balance experiments to rule out such deviations down to scales much smaller than a millimeter. These investigations placed sharp restrictions on the model, and theorists await the results of further testing.
One variation of the large extra dimension scenario, called the “manyfold universe model,” offers an intriguing possible explanation for dark matter. Developed by the ADD group, along with Stanford researcher Nemanja Kaloper, it posits that the visible universe resides on a single brane, folded up like an accordion. In between each crease, slivers of bulk preclude light from passing through. Photons, after all, are open strings and must cling forever to the brane. Gravitons, on the other hand, can freely jump from one fold to the next. Thus, in this model, gravitation reaches beyond where luminous radiation can penetrate. For example, imagine that a star or galaxy is located on the next fold over from ours. Because its light rays would need to travel a long distance along the brane to reach us, it would appear extremely remote—or, perhaps, not even visible at all. Yet its gravitons could jump across the thin layer of bulk and influence a part of space much closer to us—the Milky Way’s halo, for example. They could slightly warp that region, leading to a gravitational lensing effect. The result would be the phenomena we associate with dark matter. Hence, according to the theorists, what we call dark matter could well be visible material situated on another fold of our brane.
As we’ve found with many theories, in battling one cosmological mystery, it’s tempting to try to vanquish them all. While attempting to exorcise the dark-matter demon, the ADD group tried to slay the

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horizon problem as well—without applying the broad sword of inflation. The idea is that the universe, once twisted up into a tight space, has since opened up (along at least one dimension)—like origami restored to its original sheets—thereby separating regions that were originally in close contact, leading to large-scale uniformity. As the group wrote: “The folded universe picture permits apparently superluminal communication between different segments of the brane through the bulk. This could give a non-inflationary solution to the horizon problem, if the brane was originally crumpled in a small higher-dimensional box and later unfolded.”
Competing with the ADD scenario and its “manyfold” variation are other brane-world types with fundamentally different properties; chief among them are the models (mentioned earlier) of Lisa Randall and Raman Sundrum. While one of these types has the standard two branes delineated by M-theory, another possesses but a single brane with a warped infinite extra dimension. The warping refers to the bulk having a nonflat five-dimensional geometry—namely, anti-de Sitter space, which serves as a trough, focusing the gravitons in a region close to our brane. Hence, gravity is weak but not too weak.
The Randall-Sundrum model can be pictured as an endless desert with a giant rock in the middle—akin to Uluru (Ayers rock) standing tall in the Australian wilderness. Uluru’s location represents our brane; the desert stands for the bulk around it; and the rock itself, all matter and energy besides gravitons. Naturally, the rock remains fixed to the site, like conventional matter on the brane.
Now suppose that a desert spirit suddenly transforms the rock into a giant block of ice, like a glacier. This picture represents gravitons. If the desert is completely flat, the ice would quickly melt, then spread out over an extremely large area. This thin coating of water would rapidly evaporate. By analogy, gravitons exuding into a flat, infinite bulk would have absolutely no strength. But if the desert around Uhuru were slanted toward the center, it would collect the water into a substantial pond. Similarly, a warped brane would

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localize gravitation—producing a weakened but still significant force like that which we actually observe.
COSMIC COLLISIONS
The unusual designs of the ADD, manyfold and Randall-Sundrum models seem to call out for a study of their dynamics. Following the well-trodden path of Einstein, Eddington, Hoyle, de Sitter, Gamow, and others, it would seem natural to explore the cosmological implications of these theories, pushing them forward into the future and backward into the past. Many string theorists have certainly considered this exercise. As Sundrum, for instance, has remarked:
When I find a model of physics or a theory of physics that I find particularly attractive for other reasons, then I think it’s intriguing to go and study its cosmology. For example, the standard model of particle physics is certainly a very well motivated theory, backed by experiments and certainly it’s a good thing to study the cosmology associated with the standard model very seriously.
That said, Sundrum quickly adds:
I have not yet found theories with brane cosmologies so attractive that I want to directly study the cosmology. I don’t find it personally a robust enough activity that points towards the answers that I’m looking for. But I’m very happy that other people do engage in this, because it may turn out something more robust than I had anticipated.
One of the most active groups studying brane cosmologies includes researchers from Princeton and the University of Cambridge. With Gibbons, Townsend, and Neil Turok on staff, Cambridge has become one of the foremost international centers for membrane theory

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research. Appropriately, these researchers concoct their odd-shaped multidimensional creations within a building of similarly unusual geometry, the Centre for Mathematical Sciences. With curious, grass-covered domes and striking triangular towers, it resembles the futuristic set of a science fiction epic or of the children’s television program Teletubbies. If a sign was posted that read “Portals to other branes inside,” we would not be all too surprised. Ironically, the structure lies on the outskirts of one of England’s most traditional university towns.
In a fruitful transatlantic collaboration, Steinhardt, Turok, and several other theorists—including Justin Khoury, then at Princeton, and Burt Ovrut of the University of Pennsylvania—proposed two related cosmological models involving colliding branes. These two cosmologies differed mainly in their time frames. While the first, called the Ekpyrotic (renewed by fire) universe, was a one-time smash-up, the second, called the Cyclic universe, repeated its sequence indefinitely. In either case, enormous quantities of energy would be produced in the crash, enough to represent the output of either the Big Bang (in the original standard model) or the end of an inflationary phase.
In codeveloping these theories, Steinhardt decided to take a break from his quest for a seamless inflationary scenario. Although he still valued inflation, he thought it important to explore alternative descriptions of the universe, including ones involving strings and branes. As he explained: “I’ve been waiting for string theory to get to a point where there was some kind of loosely speaking phenomenological model you could begin to think about more seriously. Then I asked the question, could you do something interesting with it that would be a different kind of cosmology?”
In the Ekpyrotic model, the universe begins as a standard M-theory solution, with several three-dimensional branes immersed in a higher-dimensional bulk. One of them is the “visible brane,” representing our own spatial enclave. Another is the “hidden

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brane” signifying the shadow world suggested by M-theory. At first our visible brane bears scarce resemblance to the matter and energy-filled space with which we are familiar. Rather, it is a cold and empty place—as welcoming as an icefield in Antarctica.
All this would remain frozen, if it weren’t for a third mobile brane—a cosmic daredevil. Like a reckless racer, it moves through the fifth dimension and crashes head on into our brane. The wreckage produces a blazing inferno of energy and matter, distributed throughout our space. Thus, in contrast to the standard Big Bang model (which starts off infinitely hot), the observable universe begins its life at a finite temperature.
The fact that the moving brane hits ours all at once suggests a noninflationary resolution of the horizon problem. A common cause—the collision—explains large-scale uniformity. Additionally, quantum fluctuations scattered throughout the moving brane generate the seeds of structure as that brane touches ours. Thus, according to the Ekpyrotic researchers, neither a Big Bang nor an inflationary era would be needed to explain what we see around us.
CYCLES OF FIRE AND ICE
Many ancient cultures consider cosmic time as renewable and repetitive as the rising and setting of the Sun. It’s natural to wonder— whether philosophically or scientifically—if the Big Bang was not the beginning, then what grand eras preceded our own? Could there have been exotic worlds and advanced civilizations that vanished in the fires of a cosmic transition?
Tolman’s oscillatory model, proposed early on in the history of general relativity, bore some resemblance to traditional cyclic schemes. However, because it accumulated entropy (disorder) from era to era, it was not truly renewable. Thus, it could not produce an eternal succession of viable cosmologies. The Cyclic universe, proposed by Steinhardt and Turok, attempts to address these issues while

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos
explaining the origin of dark energy and resolving other cosmological questions. Like the Ekpyrotic model, it involves colliding branes— in this case bouncing off each other.
Let’s run through the cycle that Steinhardt and Turok proposed. First, the branes collide, essentially wiping out all traces of what existed in the universe before. The resulting burst of power replicates what we construe as the Big Bang but with no singularity. Quantum fluctuations in the impacting brane seed the formation of structure in observable space—the galaxies we see today. As the colliding branes move apart, the vacuum energy of the universe changes. The resulting dark energy produces universal acceleration—driving the galaxies farther and farther apart. That’s the phase we’re in today. Then, as the universe evolves, it will exhaust its usable energy. With stars dying out—turning into white dwarfs, neutron stars, and black holes—entropy will build up more and more. However, as galactic recession speeds up, this measure of disorder will become more and more dilute. In due course, for any given region, it will effectively revert to zero.
Meanwhile, the branes will eventually reverse course and come together again. The visible universe will cease its acceleration and begin to slow down, heralding the calm before the storm. Then, there will be unmistakable harbingers of doom. As Steinhardt describes these signs:
Once the universe turns to the decelerating phase you still have roughly another 10 billion years to go. But finally, in the last few seconds you’d see some significant changes in the fundamental constants and that would be the hint that something is about to happen. You would notice that something really strange is happening in the universe. Some tremendous form of energy is building up all of a sudden. It would reach a crescendo, and then, bam, the universe would fill with matter and radiation. That would be the collision. You and I would be vaporized unless we were otherwise protected.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos
Black holes would survive, but most things would be vaporized. So then that universe is full of matter and radiation again.
All earthly civilization would cease. There would be nowhere to escape. However, as Steinhardt relates, you could try to contact any intelligent souls in future eras, providing them with some inkling that our culture once existed:
You might be able to send messages, although [respondents] would be pretty rare. A black hole survives, so you could make an arrangement of black holes that spell out ‘Hello.’ The problem is that during this period of accelerated expansion, the universe has expanded exponentially. So the only people able to read that message are people right near where you were. That’s a very small fraction of the total population of the universe. We can only see 14 billion light-years today, so the chances of communicating with civilizations spread out [to the extent of] maybe one every hundreds of trillions is negligible. So you can only send messages to your local neighborhood at best.
Unlike the Tolman model, this sequence of events could repeat itself forever, because the accelerating phase dilutes the entropy for a given region, before it fills with new matter and energy. It serves as a conveyer belt to remove the scraps from the table, before new help-ings are served. What an efficient cosmic cafeteria.
Despite their clever attempt to use M-theory to resolve cosmological issues, Steinhardt and Turok’s model has been met with skepticism by string theorists as well as cosmologists. Many string theorists believe that the model isn’t ready to be used in a dynamic description of the evolution of the cosmos. Many cosmologists, on the other hand, ardently believe in the inflationary model, the anthropic principle, or other longstanding resolutions of the horizon and flatness problems.
Many mainstream physicists and astronomers simply aren’t used

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos
to dealing with five or higher dimensions. Yet we should point out that the fourth dimension was controversial for a number of years after Minkowski first identified it as time. Even Einstein needed to be convinced. Eventually, he and others came to accept the four-dimensional nature of space-time.
Just as the fourth dimension provided a natural way of describing time, introducing the fifth dimension can do the same for mass. It provides a natural way of resolving one of the fundamental mysteries: How did all the mass in the universe arise?