[This carries on from a post yesterday where I attempted to explain what inflation has to do with a multiverse]
Is that it?
You might be thinking: "OK, that's a toy-toy model about how a multiverse might come from an inflationary model. Cool. But are there any non-toy models?"
As far as I'm aware, no. And this is where I definitely agree with Peter that, although it is certainly possible to generate a multiverse, it definitely isn't inevitable. In fact, if anyone reading this does know of any full models where a multiverse is generated, with a set of vacua with different energies, please let me know (even if it's just a complete toy model).
In which case, you might now be wondering why is there so much excitement amongst some cosmologists about multiverses? Why do some physicists want it so much? There are two reasons I can think of. The first is that the multiverse, coupled with an anthropic principle, can explain why the cosmological constant has the value it does. If the true model of inflation generated Big Bangs in many vacua (i.e. more than 10^130 vacua), then, even though most of them will have large vacuum energies, the Big Bangs that occur in them also can't support life. Therefore we would expect to find ourselves in a Big Bang bubble where the cosmological constant was small, but just big enough to be detected. And this is actually exactly what we see. [Edit: As Sesh points out in a comment, an additional assumption is required to conclude that the cosmological constant should be both small and measurable. This assumption is that the distribution of vacuum energies in the multiverse favours large energies. See the comment and replies for discussion. Thanks Sesh.]
The second reason multiverses are popular is that there is a candidate for where this absurdly large number of possible minima could come from and this is string theory. In fact, string theory predicts many more than 10^130 possible vacua.
So, that's it. A multiverse needs two things: a way that multiple possible types of universe are possible; and a way to make sure that these universes all actually come into existence. String theory suggests that there may indeed be multiple possible types of "universe" (i.e. sets of laws of physics), but it is eternal inflation that would cause many Big Bangs to occur and thus, potentially, to populate these "universes".
Some parting words...
There are some (perhaps even many) scientists who hate the idea of a multiverse and demand that multiverses are stricken from science for being "unfalsifiable" or "unpredictive" (because we can't ever access the other Big Bangs).
I don't understand this mentality.
Forgetting about whether a multiverse is "scientific" or not, what if it is true? What if we do live in a universe that, it just so happens, is part of a multiverse? Would we not want whatever method we use to try to learn about our existence to be able to deal with it? If we want "science" to be something that examines reality, then (if we are in a multiverse) should it not be able to deal with a multiverse? We might not be able to directly measure other Big Bangs, but we can infer their probable existence by measuring other things. [Edit(06/02): I just want to clarify that I'm not meaning to suggest here that science needs changed to be able to talk about untestable things, but instead that scientists are justified when trying hard to find ways to test this idea. And that there are ways to test it.]
Suppose we all lived 500 years ago and wanted to know why the Earth is exactly the right distance from the sun to allow life to occur. What explanations could we come up with for why this is true?
What is the real reason?