by Adam Frank
In this way, by 2005, the WMAP data could be combined with other observations to nail down parameters cosmologists had spent decades arguing over. The exact amount of normal baryonic matter: 5 percent. The exact amount of the now accepted dark matter: 25 percent. Most astonishing was that the newly discovered dark energy was also indirectly locked in by observations at 70 percent. Add it all up and you got an omega of 1. Big Bang cosmology, with inflation included, had now become an exact science.
FIGURE 8.8. The ages of inflationary cosmology. Schematic diagram of cosmic history flowing from the Big Bang (left) to today (right). The width of the figure represents the radius of the universe as time progresses.
That was inflation’s triumph. But hiding offstage was also a story of its failures. Inflation was not really one theory; it was many. While the WMAP data supported inflation’s prediction for the cosmic density perturbation spectrum, many versions of inflation included quantum fluctuations. The WMAP data did nothing to sort through competing versions. In addition, enough unknowns remained in even the generic versions of inflation to keep many scientists sceptical. No one, for instance, knew what constituted the inflation field or from what physical principle it originated. Worse still, the inflation theory required a good deal of its own fine-tuning. Descriptions of inflation’s evolution have to be tweaked in just the right way to keep the universe from breaking apart into empty, disconnected regions or not working at all.
Even more damning for some scientists is the fact that dark energy, the greatest discovery in cosmology since the CMB, came as a surprise. It was never predicted as an inevitable part of inflation. The acceleration the universe is experiencing now seems, on the face of it, like a milder version of the hyperexpansion that occurred during the early universe, and yet inflation theory offers no link between the two. The current era of cosmic acceleration must be grafted onto inflation like a Jonagold apple tree branch onto a Granny Smith tree trunk. For many scientists, a true, complete theory would not have to be grafted on this way. Inflation, in a word, should not have been taken by surprise.
Finally, and most important, inflation was still a theory of after. The orthodox versions of inflation still started their story after the initial and impossible singularity. They still began with a mysterious beginning. The universe and time still started without explanation, and we are all still left wondering why. Inflation, for all its promise, left the most important question unanswered.
By the first decade of the twenty-first century, the entire field of cosmology and particle physics seemed ready, one way or another, to push against the temporal frontier of the beginning. A chorus of scientists began demanding an answer to the question: “What came before the Big Bang?” As the new millennium began, radical new visions of the universe and time would be offered as science and the culture it was embedded within would find itself standing, once again, at the edge.
Chapter 9
WHEELS WITHIN WHEELS: CYCLIC UNIVERSES AND THE CHALLENGE OF QUANTUM GRAVITY
Eternal Time Through Repeating Time
ATHENS • THIRD CENTURY BCE
The handful of students was leaving the Stoa of Zeus, just north of the Athenian agora. Some were more advanced in their studies; others, like the young man from the noble family, were new to philosophy.
He had travelled here against his father’s wishes. “You should concern yourself with our estates and the affairs of state,” his father told him, shaking his head. “I can’t see what these Stoics have to offer you other than wild ideas.”
“Questions,” the young man reflected as he walked. “That is what they offer me.”
The young man had many questions about life, about the world and about their tangled origins. The questions had plagued him since his first childhood encounters with philosophy (during the very studies his family encouraged), and his heart leapt at the possibility of answers.
He had heard Chrysippus speak before. Chrysippus was a Stoic and, like others of that school, he taught that the world was composed primarily of fire. All we see, all we encounter, is nothing more than fire and its transformations. Most important, Stoics such as Chrysippus claimed an understanding of the universe’s origins.1 This was the young man’s most burning question and his reason for coming to the see the philosopher today. The old man had not disappointed him. In Chrysippus’ answer the youth felt like the sky itself had opened up before his mind’s eye.
There was no origin. Time and the universe repeated in endless cycles. Beginning in fire, ekpyrosis, each cycle ended in fire—creation followed by destruction followed by creation, from eternity and to eternity. It was so perfect, and so . . . elegant.
As he crossed the market by the piers the young man took no notice of the merchants with their large clay urns of goods and the clamour of ships being unloaded. Chrysippus’ words still echoed in his ears: After the conflagration of the cosmos everything will again come to be in numerical order, until every specific quality, too, will return to its original state, just as it was before and came to be in that kosmos.
“So simple,” murmured the young man, unaware of anything but the endless blue sky in his mind’s eye. “So simple . . . so beautiful.”
CATASTROPHIC FAILURES AND ETERNAL HOPES: THE CYCLES OF CYCLIC COSMOLOGY
Across more than twenty centuries of human cosmological investigation, the possibility that time simply repeats itself has been powerfully seductive. Forcing the cosmos to just begin ex nihilo holds so many paradoxes that the logical alternative—an eternally existing cosmos—seems too clean a solution to easily give up on. But the great triumph of Big Bang cosmology in the 1960s showed that the universe had evolved. It had changed.
The universe was not at rest, as Einstein and so many others had hoped. Static models were doomed by Hubble’s discovery of cosmic expansion. Steady-state models, in which the universe moves but always looks the same, offered another kind of eternity. But the discovery of the CMB doomed Fred Hoyle’s popular version of that idea too. In seeking a way out from the seemingly absurd notion of time “just beginning,” scientists felt they had to explore repeating cycles within the context of a relativistic space-time framework. The theories were explored in great detail but each attempt ended in catastrophic failure.
Cyclic cosmological solutions to Einstein’s equations were recognized early on. Friedmann’s seminal papers in the 1920s revealed three possibilities for a universe that seemed to be expanding. In two of Friedmann’s solutions, expansion continued forever. In the third, expansion was followed by contraction. If the cosmological constant was assumed to be zero in these models, then it was just the matter density of the universe—the all-important omega parameter—that determined which fate awaited the universe. If the store of mass-energy was above the critical value (Ω > 1), then gravity would eventually halt cosmic expansion and the universe would turn back in on itself like a deflating balloon.
If expansion and contraction happened once, there was no reason to believe it could not happen many times. Thus Friedmann called his third solution a “periodic world.” He imagined that time “could vary from minus infinity to plus infinity, and then we come to a real [endless] periodicity.”2 Einstein, in his own distaste for a universe that “just” begins, explored Friedmann’s periodic-world solutions for a time in his own cosmological studies.3
Friedmann was, however, a mathematical physicist and did not attempt to think about his solutions in a physical context. Richard Tolman, a Caltech theorist with a background in physical chemistry, took up a study of Friedmann’s oscillating universe models. Tolman’s research ended in a devastating critique of cyclic cosmology. His objection to the cyclic models arose from the same science that explained cycles in steam engines: thermodynamics. Filling Friedmann’s oscillating universe with matter and radiation, Tolman showed how the accumulation of cosmic entropy had to sound a death knell for repeating cosmic cycles.
Recall that the second law of thermodynamics states that transformations of e
nergy doing work (like expanding a universe) always create entropy. While entropy can be thought of as waste heat, it is more helpful to picture it as a measure of disorder. The second law demands that energy transformations in an isolated system increase its entropy. Thus the disorder within the system must also increase. Since the universe as a whole is the very definition of an isolated system, Tolman could apply the second law to it and track the long-term evolution of the periodic universe cycle after cycle. He found that every cycle generated more entropy. With nowhere to go, the entropy would be carried through to the next cycle.
If we let a bag of Lego stand in for the universe, we can metaphorically see Tolman’s entropy problem. Imagine beginning with a block of Lego all neatly snapped together. The disorder and hence the entropy of the bag is small. If you break all the blocks apart, their disorder—their entropy—increases. If you throw them back into the bag in this state, they now take up more room. This is, essentially, the situation Tolman found in tracking the entropy of an oscillating universe. After each bounce, increasing entropy inflated the cosmos to a larger size, delaying the eventual turnaround to the next contraction. Each cycle got longer, with a trend pointing towards a final cycle that would last forever. Tracking backwards, Tolman also showed that time between cycles got progressively smaller. Go back far enough and the cycle duration heads to zero. Thus, entropy forces a beginning for even a cyclic universe. An eternal past was not an option.4
Though Tolman’s entropy crisis prevented most scientists from exploring cyclic models further, hope remained that the physics of the bounce itself might somehow eat the entropy and save the oscillating model. But in the 1950s and 1960s, a group of Russian theorists studying the problem killed that hope too.5 Exploring the fate of small space-time ripples, or irregularities, during the cosmic contraction phase, the Russian theorists showed that these perturbations were driven into catastrophic amplification. As the universe closes in on itself, any tiny wiggles in the space-time fabric grow wildly in one direction and then the next. Like a ball of dough kneaded by a strong baker, space-time is stretched and pulled this way and that until it becomes so chaotic that what emerges from the Big Crunch looks nothing like our universe. Reaching to the very real-world experience of electrical appliances for a metaphor, American physicist Charles Misner called this fate the “Mixmaster universe”, and it formed the second blow to oscillatory models.
FIGURE 9.1. Oscillations in relativistic cosmology. Originally cosmologists hoped to use Friedmann’s closed-universe solutions to create repeating cycles of Big Bangs and Big Crunches. By considering entropy from one cycle to the next, Tolman showed that such cycles could not continue forever and still required an original Big Bang.
By the 1990s, the entropy problem, the Mixmaster disaster and the eventual discovery that the density of the universe was too low to imply a future Big Crunch had doomed the relativistic version of the oscillatory universe. For the idea to be revived it would have to come in a radically different form compared with a standard version explored for seven decades by general relativistic cosmologists.
THE HOLY OF HOLIES: A THEORY OF QUANTUM GRAVITY
The singularity. It always came down to the singularity. Ever since Friedmann and Lemaître discovered their expanding universes hidden in Einstein’s equations, the damnable singular behaviour at t = 0 has plagued cosmology. Run the film of cosmic expansion back all the way to the beginning and the radius of the universe shrinks to zero. There is, literally, no room for all the stuff in the universe. Every point in the fabric of space is piled on top of every other point. The universe’s mass-energy is crushed into a single geometric point with zero volume. At t = 0 the cosmic density, temperature and even the curvature of space reach to infinity. That point for physicists is nothing other the abomination of a singularity.
The infinities encountered in a singularity are not like the infinities philosopher-cosmologists had been wrestling with for millennia. They are not the infinities of the five great cosmological questions, as in “Will the universe exist forever?” or “Is space infinite?” Instead, the singularity with its infinite density and infinite temperature speaks of something far more mundane. Rather than philosophical profundity, these infinities imply a failure of physics. The singularity’s impossibly high temperatures and densities near t = 0 simply mean Einstein’s equations are no longer working and are no longer an accurate description of reality. This kind of problem can happen even in terrestrial physics. Infinities sometimes appear in equations describing phenomena as ordinary as fluid flow or the conduction of heat. When they do appear, physicists know the equations have been pushed beyond usefulness. The prescription for moving forward always involves finding a new set of equations with a deeper description of the underlying physics. Thus, the cosmic singularity at the Big Bang’s beginning was a stop sign.
A similar kind of blow-up occurs at the centre of a black hole. Singularities appear in the general relativistic description of a massive star collapsing in on itself. The density at the centre of the collapsing star is driven to infinity along with the curvature of space-time. In the end, the collapse produces a black hole with a singularity in the middle—an apparent tear in the fabric of space-time.6
There had always been hope among general relativists that singularities and their seemingly violent end of space-time might be avoided for both black holes and Big Bang cosmology. In the 1960s and 1970s, however, Stephen Hawking and Roger Penrose probed deeply into the structure of general relativity and discovered that the singularities were unavoidable. Collapsing stars always ended in a singularity and Big Bang cosmologies always began with them. The main message of these singularity theorems was to show that the singular beasts lurk within general relativity as limits, places where the equations can go no further. To make any additional progress meant moving beyond the equations of general relativity.
While general relativity’s problem with singularities has been known for years, its solution has eluded physicists for just as long. General relativity is a classical theory. It treats space-time as a smooth fabric—an infinitely divisible continuum. But quantum physics had shown scientists that on its deepest levels nature never appeared as a continuum. The principal lesson of quantum mechanics had been to teach physicists that everything in nature came in discrete bundles. Nature, at its root, is granular. Energy, momentum, rotation, spin—at the smallest levels, nature was not continuous but was quantized, discrete, bundled the way a beach resolves itself upon close inspection into a multitude of tiny flecks of sand.
Thus, physicists understood that at some point Einstein’s classical continuum-based equations must cease to hold true and space-time itself must become quantum mechanical. They could even calculate the physical scales where this occurs. Below the Planck length, an impossibly small 10–35 of a metre, smooth space-time had to break down.7 The limit can also be expressed as a time scale, which is particularly useful for cosmology. When the universe was younger than the Planck time of 10–44 of a second, space-time must have taken on its true quantum mechanical guise. How are we to imagine a quantum background for all existence? In thinking about these domains, physicists will sometimes speak of a space-time “foam”, with bubbles of space-time separated by, literally, nothing. The bubbles of space-time are reality and between them is nonexistence.
If you don’t know how to picture foamy, or quantized, space-time, don’t worry. No one else does either, at least not in a fully consistent way. In spite of more than five decades of effort the best minds in physics have yet to develop a complete theory of quantum gravity. More important than grand unified theories, quantum gravity has been the one true holy grail of physics for decades.
In the last years of the twentieth century, the search for a grand unified theory that united the strong, weak and electromagnetic forces lost momentum. The pathways first explored in the 1960s and 1970s were not panning out. In the wake of stalled efforts, quantum gravity took on new urgency as a way of vaulting ov
er the problems of GUTs and going straight to superunification. A true account of quantum gravity would, most physicists believed, become a theory of everything (TOE), a grand overarching theory that could explain all particles and all forces. Physicists were convinced that achieving this lofty goal would vault them through the Big Bang’s singularity to see what lay beyond and before.
THE MANY REVOLUTIONS OF STRING THEORY
Though there are many routes to developing a theory of quantum gravity, as of this writing all of them remain tentative. The most obvious approach would be to take Einstein’s equations for space-time and simply quantize them. Physicists have done this before in other domains of physics. You start with the classical continuum equation and cast it in a form that behaves quantum mechanically, with all the associated uncertainties, probabilities and discrete jumps.8 But what works for something like an electron in a silicon wafer could not be made to work with general relativity. The straightforward path to quantizing the equations of general relativity has been explored many times, always leading to a dead end. The straight-line route to quantum gravity appeared closed and physicists were forced to search through stranger theoretical terrain. It was in one of these unexpected corners that string theory appeared. In an astonishing twist of fate, what some scientists see as the best hope for quantum gravity began as a possible route to describe just the strong force.9
String theory began in 1968 when Gabriele Veneziano at CERN, the European Organization for Nuclear Research, proposed a new equation describing the behaviour of the strong nuclear force. A few years later, his equations were reinterpreted and shown to describe particles as vibrating strings. The move from thinking of a quark as a zerodimensional “point particle” to thinking of it as a very small but still extended one-dimensional string gave the new theory attractive characteristics. Point particles pose their own singularities since they must be treated as if their size (radius) is zero. Divide by zero and, of course, you end up with infinity. The problems point particles forced on physicists must therefore be cleaned up, or avoided entirely, through mathematical gymnastics. In the string picture these kinds of difficulties did not appear, making it an appealing new route of research.
