by Adam Frank
After getting stuck in a briar patch of technical problems, string theory rebounded in the early and mid-1980s. In what is sometimes called the first revolution of string theory, physicists were able to show how many of the known particles and forces in their standard model could be accounted for as vibrations of the elemental strings. Things got really exciting as scientists recognized that the string picture led naturally to a consistent description of the quantum force carrier of gravity—the graviton. By substituting vibrating strings for point particles, a theory that began in the realm of GUTs had expanded to include gravity and, seemingly, hinted at a theory of everything. For theoretical physicists, the early explorations into string theory were a heady time. As physicists Neil Turok and Paul Steinhardt put it, “The string picture is beautiful in that one basic entity—string—can potentially account for the myriad elementary particles observed in nature. . . . Almost overnight, it seemed, the focus of research shifted from particles to strings.”10 While the bits of string are much too small to be seen directly, if string theory is correct, their properties will describe all known and knowable particles, including those that correspond to the four forces.
There was, however, a price to be paid for this triumph. String theory is highly mathematical in a way that would make Pythagoras smile. Its levels of abstraction reach far higher than those of general relativity or ordinary quantum physics and require a serious leap of theoretical faith. String theory can recover known particles and forces only if the universe has more space then we perceive, implying a cosmos with so-called extra dimensions. In addition to the three dimensions we are familiar with, height, breadth and width, string theory requires the universe to possess seven additional dimensions of space.11 The equations fail with anything less.
Why can’t we move into these seven additional directions? String theory answers that question by curling the extra dimensions up on themselves (physicists say the extra dimensions are “compactified”). To picture this, take a sheet of paper and roll it up into a superthin straw. Viewed from far enough away, the 2-D sheet of paper appears to have become a 1-D line. This is how seven extra dimensions of string theory are “hidden”. Each extra dimension loops around on itself on such tiny scales that we can’t experience them (though physicists hope measurable effects of this dimensional looping may exist).
For some physicists this multiplication of dimensions was too strange. The invisible, extra dimensions became reason enough to reject string theory. For others, it was a small price to pay for such a large step towards a quantum theory of gravity.
FIGURE 9.2. String theory and extra dimensions. String theory demands that the universe have seven extra, “hidden” dimensions of space. We would not experience these extra dimensions, even though they exist at every point in our 3-D space, because they are curled up on themselves.
Things got muddied again after the first string revolution. Theorists had realized that there was not one but five distinct ways to construct a string theory. Then in the mid-1990s a second revolution occurred as physicist Ed Witten showed that all five versions of the theory were just images of a deeper, unified construct he called M-theory. (He never said what M stood for, though others took it to mean “mystery” or “mother of all theories”.) A critical feature of this second revolution was the appearance of a new set of actors on the string theory stage—the multidimensional branes (or membranes).
In the exploration of string theory’s remarkable mathematical terrain, physicists found that in addition to vibrating one-dimensional strings, multidimensional vibrating membranes were also possible. A 2-D example of a membrane would be the tightly stretched skin of a drumhead. Physicists call this a 2-brane. Higher-dimensional branes (called p-branes, where p is the number of dimensions) could exist as well. These branes became fundamental players in string theory’s eleven-dimensional universe (ten space dimensions + time dimension). Physicists explored a cornucopia of hyperdimensional geometric possibilities with wiggling strings and branes colliding to produce sprays of oscillations that would, if the theory is correct, appear to us as particles both known and unknown.
In 1999 Brian Greene published his wildly popular book The Elegant Universe and string theory became a household word popping up in everything from TV programmes to pop songs. Articles, books and websites on the theory multiplied, all dedicated to articulating, elucidating and/or obfuscating its meaning for the general public. But by this time, the string tide had already swept across the world of physics. Though many detractors remained, string theory came to dominate the landscape of theoretical fundamental physics. Cosmology could not help entering the string theory revolution too. For two veteran theoretical physicists, string theory’s core ideas would serve as inspiration for making a complete break with the past, severing all ties with both Big Bang cosmology and inflation.
WHEN WORLDS COLLIDE: A STEP TOWARDS A NEW CYCLIC UNIVERSE
For Paul Steinhardt and Neil Turok, the Big Bang ended on a summer day in 1999. The two scientists were sitting together in Cambridge, at a conference they had organized on string theory and cosmology. String theory was well into its next revolution and hopes were riding high that a true theory of quantum gravity was at hand. Given the field’s progress, Steinhardt, Turok and others felt the time was right to explore string theory’s overlap with cosmology.12
Were strings a way to power inflation in the natal universe? Could string theory explain how the twenty constants in the standard model were fixed and the universe fine-tuned for life? Most important, could strings and branes offer a way to get inside the singularity and explain the origin of the universe? These and other questions formed the raw material of the conference.
Steinhardt and Turok were both seasoned veterans of the particle physics/cosmology overlap. Steinhardt, a professor at Princeton, was responsible for important early work on inflation.13 Turok, at Cambridge, had built a career exploring particle physics and its consequences for cosmic evolution. Both came to the conference with doubts about cosmology’s dominant theory for the early universe. By 1999, Steinhardt was beginning to harbour serious questions about inflation even though he had helped establish the theory. It had grown unwieldy, and he was bothered by its continuing inability to explain the beginning. Turok had never fully embraced inflation. There were too many unanswered questions about the fundamental mechanism powering hyperexpansion to make him comfortable. It was with this mind-set that Steinhardt and Turok came to be sitting at opposite ends of a lecture hall when the same alternative to time’s origin appeared to them both, separately and suddenly.
Steinhardt and Turok were listening to a lecture on brane-worlds by Burt Ovrut, a physicist from the University of Pennsylvania. Ovrut’s goal was to explain why gravity appeared so weak compared to the other three fundamental forces. His work began with string theory’s concept of extra dimensions but went a step further. For Ovrut, one of these extra dimensions might not be curled up at all. If the extra dimensions were uncurled and extended, they would allow more space and more possibilities for his physics.
Ovrut was exploring a model in which our entire three-dimensional world—including all the protons, electrons, galaxies, planets and people—constitutes one brane (a 3-brane) in a space with more than three dimensions. Other 3-branes can exist in this hyperdimensional universe and they might have their own versions of protons, electrons, galaxies, planets and (perhaps) people. Thus our 3-D universe is just one 3-brane in a higher-dimensional space (called “the Bulk”). Ovrut concentrated on a model with two of these brane-world separated from each other in the “extra” dimension, like two sheets of newspaper hanging parallel to each other. The point of this theoretical exercise was to show that three of the four known fundamental forces could be made to “live” only on the 3-brane. Only gravity, the fourth force, would extend throughout the entire Bulk. Forcing electromagnetism and the strong and weak nuclear forces to operate only within the three-dimensional membrane was like forcing ants to move onl
y along a 2-D sheet of paper, without being allowed to jump off the sheet. Ovrut’s theory of the universe conspires to force our experience on (actually, in) the 3-brane even though there is more space in the extra dimensions. Gravity, in Ovrut’s theory, was the only force that filled all of this hyperdimensional space, including the space between the world branes. By diluting gravity throughout the Bulk, the concept could offer an explanation for its weakness as a force.
Listening to Ovrut’s lecture from opposite ends of the lecture hall, Steinhardt and Turok were both hit with the same thought: what if the branes could move? Rushing to the podium after the lecture, Steinhardt and Turok peppered Ovrut with questions and quickly recognized that each had the same idea. Could a collision between the brane-worlds mimic a Big Bang? It was one of those flashes of insight scientists live for. This simple idea would launch a collaboration that would produce one of the more thoroughly explored alternatives to the Big Bang: a hyperdimensional cyclic model.
FIGURE 9.3. Branes and cosmology. Our 3-D universe as a sheet or “membrane” in a higher-dimensional space (called “the Bulk”). Other 3-D universes might exist as well and be separated from us by a short distance in one of the extra dimensions of the Bulk.
The heart of Steinhardt and Turok’s insight lay in the fact that each universe—that is, each 3-brane—exerts forces on its neighbour. As they listened to Ovrut’s talk, both physicists imagined what would happen if the branes could move towards each other along the direction defined by the extra dimension. As the two branes drew closer, the “interbrane” forces would become stronger, releasing apocalyptic reserves of energy. Could the eventual collision between the separate 3-D universes—defined by branes—act just like a Big Bang? Could it produce all the cosmic evolution we now associate with that Big Bang? In essence, Steinhardt and Turok hoped to substitute the collision between the branes for the mysterious singularity of classic Big Bang cosmology.
The picture we had in mind was of two widely separated, parallel branes stretching to infinity in three directions. A tiny force existed between the two branes, causing them to attract and move very slowly toward each other along the fourth dimension over a long, perhaps infinite period of time. The force grew ever stronger as they approached, speeding their motion toward the collision. At the bang, the kinetic energy of the branes would be converted into hot radiation.14
If the idea worked, there would be no need for the singularity. More important, there would be no need for a beginning. They would have a cosmological theory of “before”.
The devil would lie in the details. Luckily, the mathematical machinery for working with the brane collisions was exact enough to allow for fairly explicit calculations. The deeper Steinhardt and Turok plunged into the nuts and bolts of their model, the greater the number of happy surprises that awaited them. One of the most important results to fall out of their calculations was the production of a cosmic microwave background with exactly the right spectrum of bumps and wiggles.
As the world-branes pulled towards each other, the force driving the collision created space-time ripples “like bedsheets waving in the wind”. The origins of the ripples were fundamentally quantum mechanical. As the sheets drew closer, quantum mechanics and its inherent probabilities demanded that some parts of the sheet should feel a slightly stronger force while others would feel a slightly weaker force. The consequences were startling—some parts of the branes (the peaks of the ripples) would collide before other parts. As energy was released in the collision, the rippling branes naturally created regions of hotter, lower densities and cooler, higher densities. Thus, the seed for hot and cool regions seen in the CMB was laid down in Steinhardt and Turok’s model not by inflation after the Big Bang but by forces occurring before their brane-world collisions.
Steinhardt and Turok then showed how the story of cosmic evolution on our 3-D slice of the universe played out exactly like the classic Big Bang story. The 3-branes rebound from the collision, each one moving apart from the others along the extra dimension. But the collision releases so much energy that the space within each brane is set into intrinsic expansion, just as in classic Big Bang theory. The ripples imprinted by the brane collision are carried along with the expansion, becoming perturbations in density and temperature. Thus, the physics within our 3-D universe go on just as they would in the standard Big Bang theory. Nucleosynthesis builds up the light elements. The CMB photons decouple from matter. And just like in the standard Big Bang model, the gravity working within our 3-D space eventually grabs hold of the ripples and turns them into galaxies and clusters of galaxies.
With a nod to the Stoics, the two scientists named this first version of their model the ekpyrotic universe—meaning “born in fire”. There were no cycles yet. They just imagined that the branes slowly approached each other, perhaps over an infinite past. Everything focused on the one collision. The remarkable conclusion of their calculations was that this brane-world collision could account for all the features of the post–Big Bang universe just as well as the Big Bang.
BANGS WITHOUT BEGINNING: DARK ENERGY AND THE CYCLIC MODEL
When the ekpyrotic model was launched into the world of physics, it met with a mixed reaction. Many scientists were heavily entrenched in inflationary cosmology and saw no need to look elsewhere. Others thought it was too exotic an alternative to be of much use. In 2001, one particular criticism stung Steinhardt and Turok hard. The ekpyrotic model began with perfectly flat, perfectly smooth brane-worlds. This was necessary if forces between the branes were to imprint space-time ripples of the right form to recover the observed CMB perturbations. Preexisting bumps and lumps would ruin the calculation. Critics rightly argued that this was an unnaturally stringent initial condition. In the wake of the critique, Steinhardt and Turok were left looking for a mechanism that would naturally smooth out the brane-worlds as they approached their collision.
There was a critical difference between 1999, when the two scientists first thought of their brane-world collision idea, and 2001, when they confronted the problem of brane smoothness. In those three years, scientists had absorbed the shock of cosmic acceleration and the dark energy it implied. But dark energy did not fall naturally out of inflationary cosmological models—it remained a new fact that everyone had to deal with. As they mulled over their brane-world smoothing dilemma, Steinhardt and Turok realized that dark energy might not be an unwanted intruder into cosmology. It might be a gift.
In the wake of dark energy’s discovery, inflation suddenly needed two forms of invisible unknown energy: the first to drive inflation and the second to drive the cosmic acceleration we see now. That was a problem for inflation. Steinhardt and Turok, however, soon recognized that dark energy could do double duty in their own theory if they made a simple addition to the story: allowing ekpyrosis to happen more than once.
The two physicists already knew that the space within each 3-D universe would be set into expansion after the brane-world collision. Once they added dark energy, that expansion was accelerated, stretching space so dramatically that it became, over eons, very empty and very smooth. Thus, dark energy gave Steinhardt and Turok the kind of space they needed to make ekpyrosis work, but only if they could force the branes back together. Here, dark energy enters the picture in a second way. Inside the 3-D universes, dark energy makes space accelerate. In the space between the 3-branes, however, Steinhardt and Turok saw how to make dark energy an attractive force that could draw the 3-D “sheets” back together. Using dark energy in this way forced the second brane collision, which then would be followed by another rebound, as in the original ekpyrotic model. Like a spring strung between two plates, dark energy keeps the brane-worlds colliding over and over again, even as it keeps the space inside the branes expanding forever. For Steinhardt and Turok, dark energy not only became the key to solving their smoothness problem but also pulled the entire vision of the model together, creating an entirely new version of the cyclic universe.
Steinhardt
and Turok’s new ekpyrotic cyclic model avoided all the pitfalls of the previous incarnations of the idea. The Mixmaster disaster never occurs because dark energy produces high pressures, keeping the space inside the branes and between them from undergoing any wild gyrations. The entropy dilemma, which killed relativistic cyclic models, is also avoided due to the extra dimensions of the new model. Closer examination of Tolman’s calculations show that it is not entropy itself but the amount of entropy in every cubic centimetre of space (that is, the density of entropy) that dooms eternally recurring cycles. If 3-D space were to contract, then all the entropy would indeed be squeezed into a tiny space, and its density would drive the next bounce to ever larger sizes and ever longer durations. But in the new cyclic model, the 3-D space inside the branes where matter, radiation and entropy live never contracts. It is the space between the branes, the extra dimension only known to the Bulk, that contracts. Since the 3-D space inside the branes is continually and eternally expanding, the entropy generated in each bounce is continually diluted.
FIGURE 9.4. A cyclic brane world cosmology. Steinhardt and Turok’s cyclic model in which two branes (one of which is our universe) collide, draw apart and collide again. Each cycle takes trillions of years.
