From John D. Norton:
(2018) Eternal Inflation: When Probabilities Fail. [Preprint]
In eternally inflating cosmology, infinitely many pocket universes are seeded. Attempts to show that universes like our observable universe are probable amongst them have failed, since no unique probability measure is recoverable. This lack of definite probabilities is taken to reveal a complete predictive failure. Inductive inference over the pocket universes, it would seem, is impossible. I argue that this conclusion of impossibility mistakes the nature of the problem. It confuses the case in which no inductive inference is possible, with another in which a weaker inductive logic applies. The alternative, applicable inductive logic is determined by background conditions and is the same, non-probabilistic logic as applies to an infinite lottery. This inductive logic does not preclude all predictions, but does affirm that predictions useful to deciding for or against eternal inflation are precluded. More.
Here’s the pdf (public access).
See also: Cosmic inflation theory loses hangups about the scientific method What if naturalism changes the role of a science program? Perhaps stubbornly contrary evidence merely shows the need for more drive and zeal in generating new naturalist theories, not more reflection and evaluation of that direction.