The theory of chaotic inflation proposes that the universe we know and love began as a quantum event. The primordial vacuum that spawned it was a roiling sea of quantum fluctuations, and each of them had (or has, the process may be eternal and ongoing) randomly different physical properties. Most of these fluctuations were still-born or never evolved into anything more than an iota of space-time. Some of the fluctuations may have inflated to become vast and old expanses of space-time. String theory, which was derived without any reference to cosmology, provides a landscape for the number of possible states of multi-dimensional space-time, and gives an estimate of the number of physically distinct states that are “familiar” in terms of having four space-time dimensions: 10500.
The conjunct of these two largely untested theories has led to an idea called the multi verse. The multi verse hypothesizes a vast number of parallel universes, unobservable by us, each with randomly different properties and laws of physics. As outlandish as it sounds, the concept has the support of a number of eminent cosmologists, including Martin Rees, England’s Astronomer Royal and member of the House of Lords. He has written: "Our universe may be just one element — one atom, as it were — in an infinite ensemble: a cosmic archipelago. Each universe starts with its own big bang, acquires a distinctive imprint (and its own physical laws), and traces out its own cosmic cycle. The big bang that triggered our universe is, in this grander perspective, an infinitesimal part of an elaborate structure that extends far beyond the range of any telescopes."
With the multi verse we have entered into wild speculation. The last sense available to us is touch. In the everyday world the sense of touch is derived from forces that operate of the scale of an atom. If the universe was once the size of an atom, then a sentient entity in an encompassing space-time might be able to touch our universe, the way we within it would touch a grain of sand. And in the multi verse they might "tweeze" our universe from among many others, because it glitters with potential. All we know for sure is that we can touch our universe with our minds, and that’s the thrill of cosmology.
It used to be simple: the universe was everything that there is. Now there seem to be different layers of observation and reality. The first or top level is the observable universe. This is the volume accessible to telescopes, which stretches 46 billion light years in every direction and contains about 100 billion galaxies. All observations in cosmology take place in this arena; this is very firm ground.
The next level consists of regions of space that we can’t observe that are still part of the same big bang "event" as the observable universe. These regions will become visible if we’re patient; as time passes, the light from hitherto unseen galaxies will reach us. Such a rosy scenario is torpedoed by dark energy, which is snatching unseen galaxies from our light grasp, and which will steadily remove from view the galaxies we’ve already seen. How large is the universe at this level? It could be infinite. Space is flat and nothing in our observable patch gives a sign that it doesn’t go on without end. Although we should recall Einstein, who said: "Two things are infinite: the universe and human stupidity, and I’m not sure about the universe."
The third level is chaotic or eternal inflation. The parallel or "bubble" universes generated 10-35 seconds after the big bang are unobservable because they’re expanding so fast that their light could never reach us. This multi verse is very diverse because the bubbles vary in their initial conditions and in physical laws that we consider immutable. Inflation is a theory that makes concrete predictions, so this regime is still within the realm of conventional science, but only barely.
The last level is highly abstract and might not be testable. Several variations have been presented, any or all of which might be valid. The "many worlds" interpretation of quantum mechanics argues that nature isn’t inherently probabilistic. It says that each time there are many viable possibilities, the world splits into many worlds, one world for each possibility. In each world, everything is identical except for one different outcome. From then on, they each develop independently and no communication is possible between them, so people living in those worlds are unaware that it’s going on. In this way, the world branches endlessly. What is now to us lies in the pasts of an infinite number of possible futures. Everything that can happen, does, somewhere.
It’s easy to map this into multi verses, where each world is a distinct universe with different properties. The idea appeared first in science fiction not in physics, from Olaf Stapledon’s 1937 novel Star Maker: "Whenever a creature was faced with several possible courses of action, it took them all, creating many distinct histories of the cosmos. Since there were many creatures and each was constantly faced with many possible courses of action, and the combination of their courses was innumerable, an infinity of distinct universes exfoliated from every moment of every temporal sequence." This seems like a crazy violation of Occam’s razor, the dictum that physical theories should be simple if possible. But the parallel realities under the many worlds umbrella are part of a single wave function, so the underlying idea is actually very simple.