The paper and responses are welcomely understandable, at least to gather the gist of the controversy. I don't intend a summary here. But I did want to bring up one issue in particular.
The authors of the paper call into question inflationary theories of the origin of the universe, whereby the universe underwent super-rapid expansion in the fractions of a second after the big bang. This, of course, doesn't sit well with proponents of inflationary theories, which are apparently the dominant collection of theorists in the field.
One major objection the authors put forth is that inflationary theories, as they presently stand, lead to a multiverse -- an infinite collection of universes each with its own properties. As is so commonly the case with multiverse theories, our own universe is then explained as one very random fluctuation. The authors refer to this state of affairs as both a "multimess" and unscientific, being something that isn't scientifically verifiable.
I hope the term multimess catches on. As I make a case for in my book, infinity gives rise to all sorts of truly remarkable paradoxes that remind us we need to be extremely careful when working with it. Multiverse theories have never sat well with me because they dive headlong into the depths of infinity to derive their thus-far scientifically unverifiable conclusions.