The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [191]
5. In the approach to inflation I have just described, there is no fundamental explanation for why the inflaton field’s value would begin high up on the potential energy curve, nor why the potential energy curve would have the particular shape it has. These are assumptions the theory makes. Subsequent versions of inflation, most notably one developed by Andrei Linde called chaotic inflation, find that a more “ordinary” potential energy curve (a parabolic shape with no flat section that emerges from the simplest mathematical equations for the potential energy) can also yield inflationary expansion. To initiate the inflationary expansion, the inflaton field’s value needs to be high up on this potential energy curve too, but the enormously hot conditions expected in the early universe would naturally cause this to happen.
6. For the diligent reader, let me note one additional detail. The rapid expansion of space in inflationary cosmology entails significant cooling (much as a rapid compression of space, or of most anything, causes a surge in temperature). But as inflation comes to a close, the inflaton field oscillates around the minimum of its potential energy curve, transferring its energy to a bath of particles. The process is called “re-heating” because the particles so produced will have kinetic energy and thus can be characterized by a temperature. As space then continues to undergo more ordinary (non-inflationary) big bang expansion, the temperature of the particle bath steadily decreases. The important point, though, is that the uniformity set down by inflation provides uniform conditions for these processes, and so results in uniform outcomes.
7. Alan Guth was aware of the eternal nature of inflation; Paul Steinhardt wrote about its mathematical realization in certain contexts; Alexander Vilenkin brought it to light in the most general terms.
8. The value of the inflaton field determines the amount of energy and negative pressure it suffuses through space. The larger the energy, the greater the expansion rate of space. The rapid expansion of space, in turn, has a back reaction on the inflaton field itself: the faster the expansion of space, the more violently the inflaton field’s value jitters.
9. Let me address a question that may have occurred to you, one we will return to in Chapter 10. As space undergoes inflationary expansion, its overall energy increases: the greater the volume of space filled with an inflaton field, the greater the total energy (if space is infinitely large, energy is infinite too—in this case we should speak of the energy contained in a finite region of space as the region grows larger). Which naturally leads one to ask: What is the source of this energy? For the analogous situation with the champagne bottle, the source of additional energy in the bottle came from the force exerted by your muscles. What plays the role of your muscles in the expanding cosmos? The answer is gravity. Whereas your muscles were the agent that allowed the available space inside the bottle to expand (by pulling out the cork), gravity is the agent that allows the available space in the cosmos to expand. What’s vital to realize is that the gravitational field’s energy can be arbitrarily negative. Consider two particles falling toward each other under their mutual gravitational attraction. Gravity coaxes the particles to approach each other faster and faster, and as they do, their kinetic energy gets ever more positive. The gravitational field can supply the particles with such positive energy because gravity can draw down its own energy reserve, which becomes arbitrarily negative in the process: the closer the particles approach each other, the more negative the gravitational energy becomes (equivalently, the more positive the energy you’d need to inject to overcome the force of gravity and separate the particles once again). Gravity is thus like a bank that has a bottomless credit line and so can