String Theory: Chaotic Inflation and Eternal Inflation
The theories of eternal inflation and chaotic inflation in string theory can be quite confusing. Most people, even physicists, use them fairly interchangeably. This is an excellent example of how concepts on the cutting edge of science can get blurred, even between different experts in the field.
In eternal inflation, the quantum fluctuations in the vacuum energy result in bubble universes. The possible energies that such a universe could have (called the false vacuum) are represented by a graph that looks kind of like a mountain range, which is often referred to as an energy hill. The true vacuum of our universe is represented as one of the valleys in such a graph.
In 1983, Paul Steinhardt and Alex Vilenkin both presented the key ideas of eternal inflation: quantum fluctuations can cause the triggering of new inflationary cycles. The assumption at the time was that each new cycle of inflation would start at the top of the energy hill and, during the inflationary cycle, would progress down toward the true vacuum. The energy state of the universe is decaying into a ground state.
In 1986, Andrei Linde wrote a paper called Chaotic Inflation, in which he pointed out that these universes can be created anywhere on the energy hill, not necessarily at the peak. In fact, the hill itself may not even have a peak; it might continue on forever! He furthermore showed that chaotic inflation is also eternal, because it spawns continued creation of new bubble universes.
Several sources make chaotic inflation sound like a specific type of eternal inflation theory. Max Tegmark’s 2003 article uses chaotic inflation in a way that sounds more like eternal inflation. Wikipedia has an article on chaotic inflation, identifying it as a sub-class of eternal inflation, but has no article on eternal inflation itself.
But Vilenkin, in his 2006 book, Many Worlds in One: The Search for Other Universes, is adamant that chaotic inflation is an entirely different theory, seeming a bit frustrated that they’re so often interchanged, a frustration that certainly seems justified, unless Vilenkin is the one who’s applying the term imprecisely.
Time will tell what consensus cosmologists reach over this distinction between chaotic inflation and eternal inflation. For now, though, it’s useful to know that most chaotic models will yield eternal inflation (but not all of them), and many eternal inflation models are not chaotic.