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

by Brian Greene

At high enough temperatures, therefore, temperatures that would vaporize today’s Higgs-filled vacuum, there is no distinction between the weak nuclear force and the electromagnetic force. At high enough temperatures, that is, the Higgs ocean evaporates; as it does, the distinction between the weak and electromagnetic forces evaporates, too.

That’s why the electromagnetic and weak nuclear forces appear so different in the world around us. The underlying symmetry between them is “broken,” or obscured, by the Higgs ocean.

Grand Unification

Grand unification addresses a question that naturally follows the success of the electroweak unification: If two forces of nature were part of a unified whole in the early universe, might it be the case that, at even higher temperatures, at even earlier times in the history of the universe, the distinctions among three or possibly all four forces might similarly evaporate, yielding even greater symmetry?

In 1974, Georgi and Glashow put forward the first theory to go partway toward this goal of total unity. Their grand unified theory, together with later insights of Georgi, Helen Quinn, and Weinberg, suggested that three of the four forces—the strong, weak, and electromagnetic forces— were all part of one unified force when the temperature was above 10 billion billion billion (1028) degrees—some thousand billion billion times the temperature at the center of the sun—extreme conditions that existed prior to 10−35 seconds after the bang. Above that temperature, these physicists suggested, photons, gluons of the strong force, as well as W and Z particles, could all be freely interchanged with one another—a more robust gauge symmetry than that of the electroweak theory—without any observable consequence.

Similar to its electroweak cousin, the grand unified Higgs fluctuated wildly above 1028 degrees, but calculations suggested that it condensed into a nonzero value when the universe dropped below this temperature. And, as with the electroweak Higgs, when this grand unified Higgs ocean formed, the universe went through a phase transition with an accompanying reduction in symmetry.

A fraction of a second and a drop of billions and billions of degrees later, the electroweak Higgs condensed, causing the weak and electromagnetic forces to split apart as well.

The consensus among physicists is that grand unification is one of the great, as yet unrealized, ideas in particle physics.

The Return of the Aether

Entropy and Time

Entropy can increase only if it is given room to increase. Entropy can increase only if it starts out low. If the pages of War and Peace begin thoroughly jumbled, further tosses will merely leave them jumbled; if the universe started out in a thoroughly disordered, high-entropy state, further cosmic evolution would merely maintain the disorder.

Deconstructing the Bang

WHAT BANGED?

A common misconception is that the big bang provides a theory of cosmic origins. It doesn’t. The big bang is a theory, partly described in the last two chapters, that delineates cosmic evolution from a split second after whatever happened to bring the univer...

Then, in the 1980s, an old observation of Einstein’s was resurrected in a sparkling new form, giving rise to what has become known as inflationary cosmology. And with this discovery, credit for the bang could finally be bestowed on the deserving force: gravity. It’s surprising, but physicists realized that in just the right environment gravity can be repulsive, and, according to the theory, the necessary conditions prevailed during the earliest moments of cosmic history.

Einstein and Repulsive Gravity

Well, the modern reading of Einstein’s work—one that goes back to Lemaître—interprets the cosmological constant as an exotic form of energy that uniformly and homogeneously fills all of space.

According to Newton’s laws, identical quantities of gold translate into identical masses.

General relativity shows that the strength of the gravitational attraction between two objects does not just depend on their masses5 (and their separation), but also on any and all additional contributions to each object’s total energy.

In his paper presenting general relativity, Einstein showed mathematically that the gravitational force depends not only on mass, and not only on energy (such as heat), but also on any pressures that may be exerted.

whereas positive pressure contributes to ordinary attractive gravity, negative pressure contributes to “negative” gravity, that is, to repulsive gravity!6

Gravity and pressure are two related but separate characters in this story.

According to general relativity, pressure can indirectly exert another force—it can exert a gravitational force—because pressure contributes to the gravitational field. Pressure, like mass and energy, is a source of gravity. And remarkably, if the pressure in a region is negative, it contributes a gravitational push to the gravitational field permeating the region, not a gravitational pull.

The cosmological term Einstein added to the equations of general relativity would mean that space is uniformly suffused with energy but, crucially, the equations show that this energy has a uniform, negative pressure. What’s more, the gravitational repulsion of the cosmological constant’s negative pressure overwhelms the gravitational attraction coming from its positive energy, and so repulsive gravity wins the competition: a cosmological constant exerts an overall repulsive gravitational force.

The new cosmological term, which he envisioned as also being spread uniformly throughout the universe, exerts a repulsive gravitational force, causing every region of space to push on every other. By carefully choosing the size of the new term, Einstein found that he could precisely balance the usual attractive gravitational force with the newly discovered repulsive gravitational force, and produce a static universe.

Moreover, because the new repulsive gravitational force arises from the energy and pressure in space itself, Einstein found that its strength is cumulative; the force becomes stronger over larger spatial separations, since more intervening space means more outward pushing.

Of Jumping Frogs and Supercooling

Einstein’s equations tell us nothing about how the expansion of the universe got started.

Guth made a discovery that finally filled the cosmological silence by providing the big bang with a bang, and one that was bigger than anyone expected.

what if a fluctuating Higgs field’s value should land on the energy bowl’s central plateau and remain there as the universe continues to cool? If this happens, physicists say that the Higgs field has supercooled, indicating that even though the temperature of the universe has dropped to the point where you’d expect the Higgs value to approach the low-energy valley, it remains trapped in a higher-energy configuration.

They suspected that the energy associated with a supercooled Higgs field— remember, the height of the field represents its energy, so the field has zero energy only if its value lies in the bowl’s valley—might have an effect on the expansion of the universe.

A Higgs field that has gotten caught on a plateau not only suffuses space with energy, but, of crucial importance, Guth realized that it also contributes a uniform negative pressure. In fact, he found that as far as energy and pressure are concerned, a Higgs field that’s caught on a plateau has the same properties as a cosmological constant: it suffuses space with energy and negative pressure, and in exactly the same proportions as a cosmological constant.

So Guth discovered that a supercooled Higgs field does have an important effect on the expansion of space: like a cosmological constant, it exerts a repulsive gravitational force that drives space to expand.9

First, whereas a cosmological constant is constant—it does not vary with time, so it provides a constant, unchanging outward push—a supercooled Higgs field need not be constant.

A Higgs field can behave similarly. Its value throughout all of space may get stuck on its energy bowl’s central bump while the temperature drops too low to drive significant thermal agitation. But quantum processes will inject random jumps into the Higgs field’s value, and a large enough jump will propel it off the plateau, allowing its energy and pressure to relax to zero.

Andrei Linde, then working at the Lebedev Physical Institute in Moscow, and Paul Steinhardt, then working with his student Andreas Albrecht at the University of Pennsylvania, discovered a way for the Higgs field’s relaxation to zero energy and pressure throughout all of space to happen even more efficiently and significantly more uniformly (thereby curing certain technical problems inherent to Guth’s original proposal11). They showed that if the potential energy bowl had been smoother and more gradually sloping, as in Figure 10.2, no quantum jumps would have been necessary: the Higgs field’s value would quickly roll down to the valley, much like a ball rolling down a hill.

Now, if we combine these two observations—that the Higgs field will stay on the plateau, in the high-energy, negative-pressure state, only for the briefest of instants, and that while it is on the plateau, the repulsive outward push it generates is enormous—what do we have? Well, as Guth realized, we have a phenomenal, short-lived, outward burst. In other words, we have exactly what the big bang theory was missing: a bang, and a big one at that.

Guth’s language, the inflaton drove the universe to inflate. The repulsion lasted only about 10−35 seconds, but it was so powerful that even in that brief moment the universe swelled by a huge factor. Depending on details such as the precise shape of the inflaton field’s potential energy, the universe could easily have expanded by a factor of 1030, 1050, or 10100 or more.

Guth provided the big bang with a bang.

the bang happened only when conditions were right— when there was an inflaton field whose value provided the energy and negative pressure that fueled the outward burst of repulsive gravity—and that need not have coincided with the “creation” of the universe. For this reason, the inflationary bang is best thought of as an event that the preexisting universe experienced, but not necessarily as the event that created the universe.

A second and related observation is that inflationary cosmology is not a single, unique theory. Rather, it is a cosmological framework built around the realization that gravity can be repulsive and can thus drive a swelling of space.

Inflation and the Horizon Problem

With this kind of cosmic evolution, even though regions were closer together in the past, it becomes more puzzling—not less—that they somehow managed to equalize their temperatures. Relative to how far light can travel, the regions become increasingly cut off as we examine them ever farther back in time.

And, as above, this means that even though the regions of space were closer together at earlier times, it was more difficult—not less—for them to influence each other and hence more puzzling—not less—that they somehow reached the same temperature.

Physicists define a region’s cosmic horizon (or horizon for short) as the most distant surrounding regions of space that are close enough to the given region for the two to have exchanged light signals in the time since the bang.

In inflationary cosmology, there was a brief instant during which gravity was repulsive and this drove space to expand faster and faster. During this part of the cosmic film, you would have to wind the film less than halfway back in order to halve the distance between two regions.

As we go farther back in time, therefore, it becomes easier for any two regions of space to influence each other, because, proportionally speaking, there is more time for them to communicate. Calculations show that if the inflationary-expansion phase drove space to expand by at least a factor of 1030, an amount that is readily achieved in specific realizations of inflationary expansion, all the regions in space that we currently see—all the regions in space whose temperatures we have measured—were able to communicate as easily as the adjacent kitchen and living room and hence efficiently come to a common temperature in the earliest moments of the universe.16

Inflation and the Flatness Problem

But despite the significant challenges that remain, inflation is far and away the front-running cosmological theory.

Quanta in the Sky with Diamonds