Inflation in a closed universe or a stage 1 multiverse? With the discovery of gravitational waves, Max Tegmark has been using this to promote his level 1 multiverse in that the universe is open (non-compact) and everything duplicates.
My question is, are there any inflation models for a closed (compact) universe or do they all lead to what Tegmark is saying? An open self-repeating stage 1 multiverse? Does the universe have to be infinite in size for inflation to work?
 A: The BICEP2 data suggests that inflation happened, and in particular the data is compatible with chaotic inflation. Lubos Motl has a blog post on this here, and a quick Google found many related articles like this one.
Chaotic inflation (almost?) invariably results in multiple causally disconnected regions. One of these would constitute our universe, and the others would be the other universes in Tegmark's multiverse.
I'm not sure what point you're making when you ask about a closed universe. We tend to assume that if the universe isn't infinite it has a closed topology but on an extremely large scale i.e. far larger than the observable universe. If so the distinction between infinite and finite but very large isn't very marked.
A: For what i know the "infinite size level 1 multiverse" naturally emerge from the eternal inflation picture . The fact that the universe can appear infinite in size from an inside observer while appearing finite in size from an outside observer has to do with the concept of time. More in detail ;the concept of time when measured in different locations with different inflation field values. When observed from the outside (so measuring time considering an higher inflation field,because of the space expanding faster compared to the inside) the bubble universe appear finite in size but from the inside, the outside observer time's infinity can be "translated" in space's infinity at any moment for the inside observer. The concept it's really hard to swallow and i think that you need to dive deep into the math of the issue for understanding why it's belived to work like that. But like you im not liking a lot the level 1 multiverse picture  so im really tryng to understand if this a key point for inflation to work or if there'are other alternative models that allows finite/closed universe to be part of a level 2 multiverse. And also im not sure if this concept works only because our inability to reach distant Patches of our region of spacetime faster than the speed of light or if this vision of an infinite spacetime (observed from the inside ) will change considering an (hypotetically) ability to reach anyone of this distant Patches avoiding (Always in some hypotetical ways) the universal speed limit.
