The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

  This success has convinced many physicists of the inflationary theory's validity. What is of equal importance, these and other precision astronomical measurements, which have only recently become possible, have allowed cosmology to mature from a field based on speculation and conjecture to one firmly grounded in observation—a coming of age that has inspired many in the field to call our era the golden age of cosmology.

  Creating a Universe

  With such progress, physicists have been motivated to see how much further inflationary cosmology can go. Can it, for example, resolve the ultimate mystery, encapsulated in Leibniz's question of why there is a universe at all? Well, at least with our current level of understanding, that's asking for too much. Even if a cosmological theory were to make headway on this question, we could ask why that particular theory—its assumptions, ingredients, and equations—was relevant, thus merely pushing the question of origin one step further back. If logic alone somehow required the universe to exist and to be governed by a unique set of laws with unique ingredients, then perhaps we'd have a convincing story. But, to date, that's nothing but a pipe dream.

  A related but somewhat less ambitious question, one that has also been asked in various guises through the ages, is: Where did all the mass/energy making up the universe come from? Here, although inflationary cosmology does not provide a complete answer, it has cast the question in an intriguing new light.

  To understand how, think of a huge but flexible box filled with many thousands of swarming children, incessantly running and jumping. Imagine that the box is completely impermeable, so no heat or energy can escape, but because it's flexible, its walls can move outward. As the children relentlessly slam into each of the box's walls—hundreds at a time, with hundreds more immediately to follow—the box steadily expands. Now, you might expect that because the walls are impermeable, the total energy embodied by the swarming children will stay fully within the expanding box. After all, where else could their energy go? Well, although a reasonable proposition, it's not quite right. There is some place for it to go. The children expend energy every time they slam into a wall, and much of this energy is transferred to the wall's motion. The very expansion of the box absorbs, and hence depletes, the children's energy.

  Even though space doesn't have walls, a similar kind of energy transfer takes place as the universe expands. Just as the fast-moving children work against the inward force exerted by the box's walls as it expands, the fast-moving particles in our universe work against an inward force as space expands: They work against the inward force of gravity. And just as the total energy embodied by the children drops because it's continuously transferred to the energy of the walls as the box expands, the total energy carried by ordinary particles of matter and radiation drops becasue it is continually transferred to gravity as the universe expands. In short, by drawing an analogy between the inward force exerted by the box's walls and the inward force exerted by gravity (an analogy that can be established mathematically), we conclude that gravity depletes the energy in fast-moving particles of matter and radiation as space swells. The loss of energy from fast-moving particles from cosmic expansion has been confirmed by observations of the microwave background radiation. 26

  Let's now modify our analogy a bit to gain insight into how an inflaton field impacts our description of energy exchange as space expands. Imagine that a few pranksters among the children hook up a number of enormous rubber bands between each of the opposite, outward-moving walls of the box. The rubber bands exert an inward, negative pressure on the box walls, which has exactly the opposite effect of the children's outward, positive pressure; rather than transferring energy to the expansion of the box, the rubber bands' negative pressure "saps" energy from the expansion. As the box expands, the rubber bands get increasingly taut, which means they embody increasing amounts of energy.

  This modified scenario is relevant to cosmology because, as we've learned, like the pranksters' rubber bands, a uniform inflaton field exerts a negative pressure within an exanding universe. And so, just as the total energy embodied by the rubber bands increases as the box expands because they extract energy from the box's walls, the total energy embodied by the inflaton field increases as the universe expands because it extracts energy from gravity. 27

  To summarize: as the universe expands, matter and radiation lose energy to gravity while an inflaton field gains energy from gravity.

  The pivotal nature of these observations becomes clear when we try to explain the origin of the matter and radiation that make up galaxies, stars, and everything else inhabiting the cosmos. In the standard big bang theory, the mass/energy carried by matter and radiation has steadily decreased as the universe has expanded, and so the mass/energy in the early universe greatly exceeded what we see today. Thus, instead of offering an explanation for where all the mass/energy currently inhabiting the universe originated, the standard big bang fights an unending uphill battle: the farther back the theory looks, the more mass/energy it must somehow explain.

  In inflationary cosmology, though, much the opposite is true. Recall that the inflationary theory argues that matter and radiation were produced at the end of the inflationary phase as the inflaton field released its pent-up energy by rolling from perch to valley in its potential-energy bowl. The relevant question, therefore, is whether, just as the inflationary phase was drawing to a close, the theory can account for the inflaton field embodying the stupendous quantity of mass/energy necessary to yield the matter and radiation in today's universe.

  The answer to this question is that inflation can, without even breaking a sweat. As just explained, the inflaton field is a gravitational parasite—it feeds on gravity—and so the total energy the inflaton field carried increased as space expanded. More precisely, the mathematical analysis shows that the energy density of the inflaton field remained constant throughout the inflationary phase of rapid expansion, implying that the total energy it embodied grew in direct proportion to the volume of the space it filled. In the previous chapter, we saw that the size of the universe increased by at least a factor of 10 30 during inflation, which means the volume of the universe increased by a factor of at least (10 30 ) 3 = 10 90 . Consequently, the energy embodied in the inflaton field increased by the same huge factor: as the inflationary phase drew to a close, a mere 10 -35 or so seconds after it began, the energy in the inflaton field grew by a factor on the order of 10 90 , if not more. This means that at the onset of inflation, the inflaton field didn't need to have much energy, since the enormous expansionit was about to spawn would enormously amplify the energy it carried. A simple calculation shows that a tiny nugget, on the order of 10 -26 centimeters across, filled with a uniform inflaton field—and weighing a mere twenty pounds— would, through the ensuing inflationary expansion, acquire enough energy to account for all we see in the universe today. 2

  Thus, in stark contrast to the standard big bang theory in which the total mass/energy of the early universe was huge beyond words, inflationary cosmology, by "mining" gravity, can produce all the ordinary matter and radiation in the universe from a tiny, twenty-pound speck of inflatonfilled space. By no means does this answer Leibniz's question of why there is something rather than nothing, since we've yet to explain why there is an inflaton or even the space it occupies. But the something in need of explanation weighs a whole lot less than my dog Rocky, and that's certainly a very different starting point than envisaged in the standard big bang. 28

  Inflation, Smoothness, and the Arrow of Time

  Perhaps my enthusiasm has already betrayed my bias, but of all the progress that science has achieved in our age, advances in cosmology fill me with the greatest awe and humility. I seem never to have lost the rush I initially felt years ago when I first read up on the basics of general relativity and realized that from our tiny little corner of spacetime we can apply Einstein's theory to learn about the evolution of the entire cosmos. Now, a few decades later, technological progress is subjecting these
once abstract proposals for how the universe behaved in its earliest moments to observational tests, and the theories really work.

  Recall, though, that besides cosmology's overall relevance to the story of space and time, Chapters 6 and 7 launched us into a study of the universe's early history with a specific goal: to find the origin of time's arrow. Remember from those chapters that the only convincing framework we found for explaining time's arrow was that the early universe had extremely high order, that is, extremely low entropy, which set the stage for a future in which entropy got ever larger. Just as the pages of War and Peace wouldn't have had the capacity to get increasingly jumbled if they had not been nice and ordered at some point, so too the universe wouldn't have had the capacity to get increasingly disordered—milk spilling, eggs breaking, people aging—unless it had been in a highly ordered configuration early on. The puzzle we encountered is to explain how this high-order, low-entropy starting point came to be.

  Inflationary cosmology offers substantial progress, but let me first remind you more precisely of the puzzle, in case any of the relevant details have slipped your mind.

  There is strong evidence and little doubt that, early in the history of the universe, matter was spread uniformly throughout space. Ordinarily, this would be characterized as a high-entropy configuration—like the carbon dioxide molecules from a bottle of Coke being spread uniformly throughout a room—and hence would be so commonplace that it would hardly require an explanation. But when gravity matters, as it does when considering the entire universe, a uniform distribution of matter is a rare, low-entropy, highly ordered configuration, because gravity drives matter to form clumps. Similarly, a smooth and uniform spatial curvature also has very low entropy; it is highly ordered compared with a wildly bumpy, nonuniform spatial curvature. (Just as there are many ways for the pages of War and Peace to be disordered but only one way for them to be ordered, so there are many ways for space to have a disordered, nonuniform shape, but very few ways in which it can be fully ordered, smooth, and uniform.) So we are left to puzzle: Why did the early universe have a low-entropy (highly ordered) uniform distribution of matter instead of a high-entropy (highly disordered) clumpy distribution of matter such as a diverse population of black holes? And why was the curvature of space smooth, ordered, and uniform to extremely high accuracy rather than being riddled with a variety of huge warps and severe curves, also like those generated by black holes?

  As first discussed in detail by Paul Davies and Don Page, 3 inflationary cosmology gives important insight into these issues. To see how, bear in mind that an essential assumption of the puzzle is that once a clump forms here or there, its greater gravitational pull attracts yet more material, causing it to grow larger; correspondingly, once a wrinkle in space forms here or there, its greater gravitational pull tends to make the wrinkle yet more severe, leading to a bumpy, highly nonuniform spatial curvature. When gravity matters, ordinary, unremarkable, high-entropy configurations are lumpy and bumpy.

  But note the following: this reasoning relies completely on the attractive nature of ordinary gravity. Lumps and bumps grow because they pull strongly on nearby material, coaxing such material to join the lump. During the brief inflationary phase, though, gravity was repulsive and that changed everything. Take the shape of space. The enormous outward push of repulsive gravity drove space to swell so swiftly that initial bumps and warps were stretched smooth, much as fully inflating a shriveled balloon stretches out its creased surface. 29 What's more, since the volume of space increased by a colossal factor during the brief inflationary period, the density of any clumps of matter was completely diluted, much as the density of fish in your aquarium would be diluted if the tank's volume suddenly increased to that of an Olympic swimming pool. Thus, although attractive gravity causes clumps of matter and creases of space to grow, repulsive gravity does the opposite: it causes them to diminish, leading to an ever smoother, ever more uniform outcome.

  Thus, by the end of the inflationary burst, the size of the universe had grown fantastically, any nonuniformity in the curvature of space had been stretched away, and any initial clumps of anything at all had been diluted to the point of irrelevance. Moreover, as the inflaton field slid down to the bottom of its potential-energy bowl, bringing the burst of inflationary expansion to a close, it converted its pent-up energy into a nearly uniform bath of particles of ordinary matter throughout space (uniform up to the tiny but critical inhomogeneities coming from quantum jitters). In total, this all sounds like great progress. The outcome we've reached via inflation —a smooth, uniform spatial expansion populated by a nearly uniform distribution of matter— was exactly what we were trying to explain. It's exactly the low-entropy configuration that we need to explain time's arrow.

  Entropy and Inflation

  Indeed, this is significant progress. But two important issues remain.

  First, we seem to be concluding that the inflationary burst smooths things out and hence lowers total entropy, embodying a physical mechanism—not just a statistical fluke—that appears to violate the second law of thermodynamics. Were that the case, either our understanding of the second law or our current reasoning would have to be in error. In actuality, though, we don't have to face either of these options, because total entropy does not go down as a result of inflation. What really happens during the inflationary burst is that the total entropy goes up, but it goes up much less than it might have. You see, by the end of the inflationary phase, space was stretched smooth and so the gravitational contribution to entropy—the entropy associated with the possible bumpy, nonordered, nonuniform shape of space—was minimal. However, when the inflaton field slid down its bowl and relinquished its pent-up energy, it is estimated to have produced about 10 80 particles of matter and radiation. Such a huge number of particles, like a book with a huge number of pages, embodies a huge amount of entropy. Thus, even though the gravitational entropy went down, the increase in entropy from the production of all these particles more than compensated. The total entropy increased, just as we expect from the second law.

  But, and this is the important point, the inflationary burst, by smoothing out space and ensuring a homogeneous, uniform, low-entropy gravitational field, created a huge gap between what the entropy contribution from gravity was and what it might have been. Overall entropy increased during inflation, but by a paltry amount compared with how much it could have increased. It's in this sense that inflation generated a low-entropy universe: by the end of inflation, entropy had increased, but by nowhere near the factor by which the spatial expanse had increased. If entropy is likened to property taxes, it would be as if New York City acquired the Sahara Desert. The total property taxes collected would go up, but by a tiny amount compared with the total increase in acreage.

  Ever since the end of inflation, gravity has been trying to make up the entropy difference. Every clump—be it a galaxy, or a star in a galaxy, or a planet, or a black hole—that gravity has subsequently coaxed out of the uniformity (seeded by the tiny nonuniformity from quantum jitters) has increased entropy and has brought gravity one step closer to realizing its entropy potential. In this sense, then, inflation is a mechanism that yielded a large universe with relatively low gravitational entropy, and in that way set the stage for the subsequent billions of years of gravitational clumping whose effects we now witness. And so inflationary cosmology gives a direction to time's arrow by generating a past with exceedingly low gravitational entropy; the future is the direction in which this entropy grows. 4

  The second issue becomes apparent when we continue down the path to which time's arrow led us in Chapter 6. From an egg, to the chicken that laid it, to the chicken's feed, to the plant kingdom, to the sun's heat and light, to the big bang's uniformly distributed primordial gas, we followed the universe's evolution into a past that had ever greater order, at each stage pushing the puzzle of low entropy one step further back in time. We have just now realized that an even earlier stage of inflationary ex
pansion can naturally explain the smooth and uniform aftermath of the bang. But what about inflation itself? Can we explain the initial link in this chain we've followed? Can we explain why conditions were right for an inflationary burst to happen at all?

  This is an issue of paramount importance. No matter how many puzzles inflationary cosmology resolves in theory, if an era of inflationary expansion never took place, the approach will be rendered irrelevant. Moreover, since we can't go back to the early universe and determine directly whether inflation occurred, assessing whether we've made real progress in setting a direction to time's arrow requires that we determine the likelihood that the conditions necessary for an inflationary burst were achieved. That is, physicists bristle at the standard big bang's reliance on finely tuned homogeneous initial conditions that, while observationally motivated, are theoretically unexplained. It feels deeply unsatisfying for the low-entropy state of the early universe simply to be assumed; it feels hollow for time's arrow to be imposed on the universe, without explanation. At first blush, inflation offers progress by showing that what's assumed in the standard big bang emerges from inflationary evolution. But if the initiation of inflation requires yet other, highly special, exceedingly low-entropy conditions, we will pretty much find ourselves back at square one. We will merely have traded the big bang's special conditions for those necessary to ignite inflation, and the puzzle of time's arrow will remain just as puzzling.