I was quite excited when I discovered, via Twitter, a paper on the arXiv with the title Quantum Fluctuations in Cosmology and How They Lead to a Multiverse, which was written by one of the architects of the inflationary universe scenario, Alan Guth. Despite numerous attempts to understand the argument how inflation leads to a Multiverse I’ve never really succeeded. To me it always seemed like a version of the Mind Projection Fallacy inspired by a frequentist interpretation of probability: the construction of notional ensembles for the purposes of calculation in quantum mechanics does not imply that such ensembles are realized in nature. In fact I’ve never found much more substance in articles about this issue than the assertion that Quantum Physics = Woo! = Multiverse.
Anyway, since the paper I found is a review article I hoped it would help teach me the error of my ways. Here is the abstract
This article discusses density perturbations in inflationary models, offering a pedagogical description of how these perturbations are generated by quantum fluctuations in the early universe. A key feature of inflation is that that rapid expansion can stretch microscopic fluctuations to cosmological proportions. I discuss also another important conseqence of quantum fluctuations: the fact that almost all inflationary models become eternal, so that once inflation starts, it never stops.
My eye was drawn to the phrase “almost all inflationary models”. I had hoped to see “almost all” used in its strict mathematical sense, ie “apart from a set of measure zero” with the measure being fully specified. Disappointingly, it isn’t. Guth discusses the consequences of the tail the inflationary potential V (for large values of the inflaton field ϕ) on the long-term evolution of inflationary dynamics and then states
Since V3/2/|V ′| grows without bound as ϕ → ∞ for most potentials under consideration, almost all models allow for eternal inflation.
This means, to me, most models people have constructed but doesn’t mean all possible models. I don’t doubt that some inflationary models become eternal, but would have preferred a more rigorous statement. This is particularly strange because Guth spends the last section of his paper discussing the “measure problem”:
While the multiverse picture looks very plausible in the context of inflationary cosmology — at least to me — it raises a thorny and unsolved problem, known as the “measure problem.” Specifically, we do not know how to define probabilities in the multiverse.
The measure problem to my mind also extends to the space of all possible inflationary theories.
And then there’s the title, which, I remind you, is Quantum Fluctuations in Cosmology and How They Lead to a Multiverse. Guth’s argument consists of going through the (standard) calculation of the spectrum of cosmological density fluctuations (which does fit a host of observational data). He then states:
Since the density perturbation calculations have been incredibly successful, it seems to make sense to take seriously the assumptions behind these calculations, and follow them where they lead. I have to admit that there is no clear consensus among cosmologists, but to many of us the assumptions seem to be pointing to eternal inflation, and the multiverse.
I have to admit that I get a bit annoyed when I read a paper in which the actual conclusions are much weaker than implied by the title, but that seems to be par for the course in this field.
For the record, I’ll state that I am an agnostic about the multiverse. It may be a correct idea, it may not. I will say, however, that I still haven’t found any article that puts it on a firm scientific footing. That may well, of course, just be a measure of my ignorance. If you know of one, please let me know through the comments box.
In the Dark 