The multiverse is a current area of research in theoretical physics. It has generated a wide range of public interest due to its nature of describing our universe as being one of possibily an infinity of other universes, each with physics that maybe similar to ours or maybe widely different than ours. Its unclear to me where the idea of the multiverse started in modern theoretical physics. Anyways a problem with it as far as I can tell from reading about it in a variety of places, is that it lacks predictions that can be tested by data. Here I mean I would like to see a graph of some sort of experimental data along with a curve from a theory model that is related to the data. String/m-theory also has this problem with having a graph of data and theory predictions. In reading Peter Woit's Not Even Wrong blog http://www.math.columbia.edu/~woit/wordpress/
there was a mention of an article about predictions of the multiverse, that article is by Yasunori Nomura a theoretical physicist at UC Berkeley http://quantumfrontiers.com/2014/02/13/making-predictions-in-the-multiverse/. I asked a question to the author about his predictions and comparison to data in the comments section of the article. The author was kind enough to provide an understandable answer to my question about data and the theory of the multiverse. My problem is that I don't really understand the details of some of the physics underlying the answer. Basically he gives the following as results, predictions or consequences of the model(s) to experiment:
1). "the most significant observational “evidence” for the multiverse is the value of vacuum energy."
2). The curvature of the universe. He mentions that a positive curvature would rule out the multiverse. "Interestingly, a discovery of a wrong sign, i.e. positive, curvature would falsify the multiverse as we think now, and exploration of curvature might also give us information about possible measures in the multiverse (see e.g. http://arxiv.org/abs/arXiv:1203.6876)."
These are interesting, but not definitive proof of the existence of the multiverse. The problem with the multiverse is that there are almost, if not, an infinity of them. So whatever data we get, other than the positive curvature measurement (I think so far the best measurements say the universe is flat), one can find a universe in the multiverse to match ours. This is the same problem with string/m-theory. Not matter what is measured , with the large number of universes in the string landscape they are sure to find a universe there to match the data. Now this is the situation as far as I can tell. I think some people even try to match the multiverse idea from inflation cosmology with the multiverse idea from string theory. You have a bunch of very bright folks working on these types of models but they have this problem of showing uniqueness. As I saw Steven Weinberg basically say on I believe one of the Fabric of the Cosmos DVD's, is that these types of theories are all we have now and that's why people work on them. As I have posted before, this is a problem, where the question is are people doing physics or metaphysics? This is not a good situation for physicists to get into since it hurts what science stands for and means. This is a question that theoretical physicists really need to think about when developing theories that are not unique. For physics this is using theories, with equations to describe experimental data. One can argue what physical theories really mean. This then becomes an issue for the philosophy of science not physics. This isn't like the issue of the interpretation of quantum mechanics and don't worry what it means just calculate. What quantum mechanics really means is a serious question and has people working on trying to understand its foundations, such as the measurement problem. But in the meantime scientists use quantum mechanics to conduct their research.
These problems as a whole are discussed on a variety of excellent, thoughtful physics blogs listed here
Sean Carroll's the preposterous universe:preposterousuniverse.com/blog/
Peter Woit's Not Even Wrong:http://www.math.columbia.edu/~woit/wordpress/
Sabine Hossenfelder's :http://backreaction.blogspot.com/
All very enjoyable and informative reads along with their comment sections.