II. BEFORE AND AFTER INFLATION

Research in recent years has included investigations of what might have preceded inflation, and how an inflationary epoch might have ended.

Soon after the first inflationary models were introduced, several physicists [19, 20, 21] realized that once inflation began, it would in all likelihood never stop. Regions of space would stop inflating, forming what can be called "pocket universes," one of which would contain the observed universe. Nonetheless, at any given moment some portion of the universe would still be undergoing exponential expansion, in a process called "eternal inflation." In the model depicted in Fig. 1, for example, quantum-mechanical effects compete with the classical motion to produce eternal inflation. Consider a region of size H^-1, in which the average value of is near (b) or (d) in the diagram. Call the average energy density ₀. Whereas the classical tendency of is to roll slowly downward (red arrow) toward the minimum of its potential, the field will also be subject to quantum fluctuations (green arrows) similar to those described above. The quantum fluctuations will give the field a certain likelihood of hopping up the wall of potential energy rather than down it. Over a time period H^-1, this region will grow e³ 20 times its original size. If the probability that the field will roll up the potential hill during this period is greater than 1/20, then on average the volume of space in which > ₀ increases with time [4, 21, 22]. The probability of upward fluctuations tends to become large when the initial value of is near the peak at (a) or high on the hill near (d), so for most potential energy functions the condition for eternal inflation is attainable. In that case the volume of the inflating region grows exponentially, and forever: Inflation would produce an infinity of pocket universes.

An interesting question is whether or not eternal inflation makes the big bang unnecessary: Might eternal inflation have been truly "eternal," existing more or less the same way for all time, or is it only "eternal" to the future once it gets started? Borde and Vilenkin have analyzed this question (most recently, with Guth), and have concluded that eternal inflation could not have been past-eternal: Using kinematic arguments, they showed [23] that the inflating region must have had a past boundary, before which some alternative description must have applied. One possibility would be the creation of the universe by some kind of quantum process.

Another major area of research centers on the mechanisms by which inflation might have ended within our observable universe. The means by which inflation ends have major consequences for the subsequent history of our universe. For one thing, the colossal expansion during inflation causes the temperature of the universe to plummet nearly to zero, and dilutes the density of ordinary matter to negligible quantities. Some mechanism must therefore convert the energy of the scalar field, , into a hot soup of garden-variety matter.

In most models, inflation ends when oscillates around the minimum of its potential, as in region (c) of Fig. 1. Quantum-mechanically, these field oscillations correspond to a collection of particles approximately at rest. Early studies of post-inflation "reheating" assumed that individual particles would decay during these oscillations like radioactive nuclei. More recently, it has been discovered [24, 25, 26, 27, 28] that these oscillations would drive resonances in 's interactions with other quantum fields. Instead of individual particles decaying independently, these resonances would set up collective behavior - would release its energy more like a laser than an ordinary light bulb, pouring it extremely rapidly into a sea of newly created particles. Large numbers of particles would be created very quickly within specific energy-bands, corresponding to the frequency of 's oscillations and its higher harmonics.

This dramatic burst of particle creation would affect spacetime itself, as it responded to changes in the arrangement of matter and energy. The rapid transfer of energy would excite gravitational perturbations, of which the most strongly amplified would be those with frequencies within the resonance bands of the decaying field. In some extreme cases, very long-wavelength perturbations can be amplified during reheating, which could in principle even leave an imprint on the CMB [29].