• Choose a category
• All
• Classic-Fiction

By Root 2048 0

has a uniform value throughout a region of space, it will fill that region not only with energy but also with negative pressure. And, as is now familiar, such negative pressure yields repulsive gravity, which drives an ever-quickening expansion of space. When Guth slotted into Einstein’s equations the likely numerical values for the inflaton’s energy and pressure consonant with the extreme environment of the early universe, the mathematics revealed that the resulting repulsive gravity would be stupendous. It would easily be many orders of magnitude stronger than the repulsive force Einstein envisioned years earlier when he dallied with the cosmological constant, and would propel a spectacular spatial stretching. That alone was exciting. But Guth realized there was an indispensable bonus.

The same reasoning that explains why a uniform field has negative pressure applies as well to a cosmological constant. (If the bottle contains empty space endowed with a cosmological constant, then when you slowly remove the cork the extra space you make available within the bottle contributes extra energy. The only source for this extra energy is your muscles, which therefore must have strained against an inward, negative pressure supplied by the cosmological constant.) And, as with a uniform field, a cosmological constant’s uniform negative pressure also yields repulsive gravity. But the vital point here is not the similarities, per se, but the manner in which a cosmological constant and a uniform field differ.

A cosmological constant is just that—a constant, a fixed number inserted on the third line of general relativity’s tax form that would generate the same repulsive gravity today as it would have billions of years ago. By contrast, the value of a field can change, and generally will. When you turn on your microwave oven, you change the electromagnetic field filling its interior; when the technician flips the switch on an MRI machine, he or she changes the electromagnetic field threading the cavity. Guth realized that an inflaton field filling space could behave similarly—turning on for a burst and then turning off—which would allow repulsive gravity to operate during only a brief window of time. That’s essential. Observations establish that if the blistering growth of space happened at all, it must have happened billions of years ago and then sharply dropped off to the statelier-paced expansion evidenced by detailed astronomical measurements. So an all-important feature of the inflationary proposal is that the era of powerful repulsive gravity be transient.

The mechanism for turning on and then shutting off the inflationary burst relies on physics that Guth initially developed but that Linde, and Albrecht and Steinhardt, refined substantially. To get a feel for their proposal, think of a ball—better still, think of nearly round Eric Cartman—perched precariously on one of South Park’s snow-covered mountains. A physicist would say that because of his position, Cartman embodies energy. More precisely, he embodies potential energy, meaning that he has pent-up energy that’s ready to be tapped, most easily by his tumbling downward, which would transform the potential energy into the energy of motion (kinetic energy). Experience attests, and the laws of physics make precise, that this is typical. A system harboring potential energy will exploit any opportunity to release that energy. In short, things fall.

The energy carried by a field’s nonzero value is also potential energy: it, too, can be tapped, resulting in an incisive analogy with Cartman. Just as the increase in Cartman’s potential energy as he climbs the mountain is determined by the shape of the slope—in flatter regions his potential energy varies minimally as he walks, because he gets hardly any higher, while in steeper regions his potential energy rises sharply—the potential energy of a field is described by an analogous shape, called its potential energy curve. Such a curve, as in Figure 3.1, determines how a field’s potential energy varies with its value.

Following inflation