They are different ideas, but they all seem to be dealing with the apparent failure of string theory to derive a single, unique solution that explains our universe. As Lee Smolin points out in The Trouble With Physics [2006], after about 30 years of effort developing string theory and its offshoots, the theory turns out to be just TOO successful. (Well, he doesn't put it that way, but I think it's applicable.) Some have estimated the number of string theory solutions at 10⁵⁰⁰. Note the number of particles in our universe is 'only' around 10⁸⁰.

Leonard Susskind, the "father" of string theory points out in his 2006 book, The Cosmic Landscape, that this suggests there are 10⁵⁰⁰ possible universes allowed by the theory, and there's no reason to think that many of the longer-lived ones aren't actually existing, similarly to how ours happens to be.

I kind of like the picture painted by Alex Vilenkin in his remarkably well-written entry, Many Worlds in One [2006]. If I haven't mixed up my authors, Vilenkin does a masterful job in his explanation of eternal inflation, where the "whole universe" is in constant, exponential expansion, and what we call the big bang is just one bubble universe that "gracefully exits" the background frenetic inflation and proceeds to evolve according to the physical laws and constants that were set in the first seconds of the so-called "bang." And there's untold number of such bubble universes, which will unfortunately never be able to interact in any fashion with any other due to the superluminal expansion going off between them.

Though Vilenkin's description seems plausible, Smolin is quite right in his criticism of the craft that seems to more commonly be positing schemes that have no fair chance of finding any observational support. The space between theory and experiment seems to be undergoing.... exponential inflation.

To Vilenkin's credit, he does predict some fundamental of his idea may be distinguishable from other theories by a close analysis of the gravitational wave background. Of course, we are currently having a hard time detecting the gravitational wave foreground, so....

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