Inflation and the Multiverse

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.

8 Responses to “Inflation and the Multiverse”

  1. You might want to check out Max Tegmark’s new book, which discusses various types of multiverse. Even if you don’t agree with all of his points, it is a clear exposition of the topic by one of the top pundits in the field.

    Even from your perspective in the dark you might be aware of the recent trend of blokes uploading to the internet videos of themselves with their wives. I was thus intrigued when I learned that Max Tegmark had done so as well (with his second wife). Alas, this is one of the few times that Max has disappointed me. 🙂

    His book is essentially one long argument for his mathematical universe hypothesis”. However, most of the book is independent of this. He is careful to distinguish between mainstream, speculative and highly speculative topics, with a corresponding table of chapters in the introduction, and also indicates which bits one can skip depending on one’s background knowledge. Each chapter concludes with a list of the main points, so you could read those first and then flip back as required.

    Tegmark’s web pages have links to many (most? all?) of his papers, both technical papers and more popular accounts. I’m sure you’ll find all you need there on the topic of multiverses.

    Although I would use a different nomenclature, Max describes his well and sticks to it. Your first assignment is to understand the four levels of multiverses and the relationships between them. 🙂

    “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.”

    That’s not the case here. Also, Tegmark points out that his multiverse ideas are not a theory or even just a hypothesis, but rather a consequence of other theories which can in principle, and perhaps also in practice, be tested. I agree with you though that a crucial point is between the now well established role of inflation in the early universe (which has convinced even me) on the one hand and the confirmation of a specific model of inflation on the other, which does have a bearing on the existence of some levels of the multiverse.

    • telescoper Says:

      Describing the Universe as “Mathematical” is rather like saying that England is “English”; England can certainly be described in terms of English expressions, but such expressions are not what it is in essence.

      • Max correctly characterizes his MUH as “highly speculative”. Getting back to the multiverse, I think his book is a good exposition of the topic which is not biased by his belief in the MUH. I’m sure there are many who believe (not really a good word; it’s a testable prediction, not an article of faith) in multiverses but don’t believe in the MUH.

        At the end of the day, economy of explanation, i.e. Occam’s razor, should be the deciding factor. Even if an idea seems pretty wild, if it can explain a lot and unify other strands of thought, then it is at least pursuing. For example, something briefly touched on in the book is the cosmological interpretation of quantum mechanics*, which is discussed in more detail in this technical paper, which contains a good pun. Max also wrote the abstract for this interesting paper (about the CMB, but which has found use in oceanography, probably as a result of my mentioning the paper to Björn Grieger (who started out in astronomy, actually in Sjur Refsdal’s gravitational-lensing group in Hamburg, but he had left before I arrived), who has worked both in oceanography and in astronomy) in heroic couplets.

      • *Penrose remarked that there are probably more interpretations of quantum mechanics than there are people who work in the field, but this is possible since some are in mixed states and believe in more than one interpretation at the same time.

      • Note that Max’s ideas might be a bit off the wall, but they are in principle testable and I’m sure he would change his mind if presented with evidence which disproves them.

        On the other hand, there are people who are clearly crazy beyond any hope of recovery. Yes, watch it all the way through and note how convinced of himself the interviewed ex-minister is, including his “knowledge” of astronomy, and how professional and straight-faced the interviewer is.

  2. I had a go at explaining how inflation can lead to a multiverse
    in a blogpost here
    . I’m not sure if it is what you’re looking for. I am also unaware of any actual paper that describes a specific model of inflation which will produce a multiverse of the kind described in the paper you’re writing about (although I’m aware of many which will produce eternal inflation). However, it doesn’t seem outrageously hard to at least construct a toy-model where it would work, so I’m going to assume such papers do exist.

  3. Rob Heusdens Says:

    It’s real simple. Inflation in fact occurs in evert part of the inflating space only for some very small amount of time. However, there are fluctuations that can make some part have the potential go up again, and in that tiny part, inflation still continues. But since inflation itself makes those tiny patches exponentially fast larger, the total effect is then that inflation always takes over and can in fact never stop, once started.

    • telescoper Says:

      Now prove that this is an ergodic process, in that all possible vacuum states are guaranteed to be realised.

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