Inflationary cosmology is not completely proven, but it remains the best model we have for the formation of our universe. What it doesn’t provide us with is an origin. Our continent of origin is only one of many continents, our planet of origin one of many planets, our solar system one of many solar systems, our galaxy one of many galaxies; it seems reasonable to hypothesize, and even to assume outright, that our observable universe is—in accordance with this pattern—only the nearest of a vast, and perhaps infinite, number of other bubble universes.
But this kind of theory relies so heavily on speculation, and so little on observable evidence, that it trends more towards philosophy and theology than astrophysics. We have no proof. We have no disproof. We float, as we so often do and so often have, in agnosia.
But perhaps not for long.
Astrophysicists as the Perimeter Institute for Theoretical Physics believe that it may be possible to record collisions between our universe and other universes by looking for “bruises” in the cosmic microwave background (CMB). If these “bruises” can be aligned with reasonable mathematical multiverse simulations, and especially if their nature and location can be predicted, that could functionally prove that our universe is not the only universe that exists. That would be a huge discovery.
But there are some practical problems with this approach. The first is that we have no reason to assume that collisions between universes would necessarily produce measurable bruises in the CMB. There also seems to be a surprising amount of certainty coming from this camp; as you’ll note from the video above, one of the Perimeter Institute’s lead researchers—York University’s Matthew Johnson—seems to conflate the general idea of bubble universes, which can be examined in the way he suggests, with infinite expansion and the many-worlds hypothesis, which can’t. (Lee Smolin’s theory of cosmological natural selection, which poses some of the same problems re: unfalsifiability, is at least simpler and more elegant.) This seems to me to suggest that there’s a highly complex, sophisticated, and specific multiverse theory to which the Perimeter Institute has already committed, and that may limit the effectiveness of their research in much the same way alchemy and sacred geometry limited the effectiveness of early research into physics and chemistry.
The other problem I see is that what we need most isn't a model of the universe that can accommodate multiple universes and predict data consistent with same (though obviously it would be helpful to have one); what we need more are ways to theoretically prove alternatives to the existence of multiple universes so that the idea can be rigorously tested, and as the absence of ripples in the CMB would tell us nothing, pro or con, about the possibility of a multiverse, the Perimeter Institute's work wouldn't do this for us. While I tend to assume the existence of bubble universes and infinite inflation in some form, I also recognize that these are not yet hard scientific ideas—and until I can conceive of some way that they might one day be proven wrong, I don’t see how they could ever become scientific ideas.
But even taking all of that into account, scientifically validating multiverse cosmology is an ambitious goal—and if it can be done, it will change our model of the universe in a way that nothing else can. I admire the Perimeter Institute for trying, and I will continue to admire the fact that they tried whether their efforts are successful or not. The cosmological questions posed by the multiple universes hypothesis are audacious. If we are to answer them in any definitive way, our answers must be equally audacious.