The Eternally Existing, Self-Reproducing, Frequently Puzzling Inflationary Universe

My inaugural column for Discover discussed the lighting-rod topic of the inflationary multiverse. But there’s only so much you can cover in 1500 words, and there are a number of foundational issues regarding inflation that are keeping cosmologists up at night these days. We have a guest post or two coming up that will highlight some of these issues, so I thought it would be useful to lay a little groundwork. (Post title paraphrased from Andrei Linde.)

This summer I helped organize a conference at the Perimeter Institute on Challenges for Early Universe Cosmology. The talks are online here — have a look, there are a number of really good ones, by the established giants of the field as well as by hungry young up-and-comers. There was also one by me, which starts out okay but got a little rushed at the end.

What kinds of challenges for early universe cosmology are we talking about? Paul Steinhardt pointed out an interesting sociological fact: twenty years ago, you had a coterie of theoretical early-universe cosmologists who had come from a particle/field-theory background, almost all of whom thought that the inflationary universe scenario was the right answer to our problems. (For an intro to inflation, see this paper by Alan Guth, or lecture 5 here.) Meanwhile, you had a bunch of working observational astrophysicists, who didn’t see any evidence for a flat universe (as inflation predicts) and weren’t sure there were any other observational predictions, and were consequently extremely skeptical. Nowadays, on the other hand, cosmologists who work closely with data (collecting it or analyzing it) tend to take for granted that inflation is right, and talk about constraining its parameters to ever-higher precision. Among the more abstract theorists, however, doubt has begun to creep in. Inflation, for all its virtues, has some skeletons in the closet. Either we have to exterminate the skeletons, or get a new closet.

Inflation is a simple idea: imagine that the universe begins in a tiny patch of space dominated by the potential energy of some scalar field, a kind of super-dense dark energy. This causes that patch to expand at a terrifically accelerated rate, smoothing out the density and diluting away any unwanted relics. Eventually the scalar field decays into ordinary matter and radiation, reheating the universe into a conventional Big Bang state, after which things proceed as normal.

Note that the entire point of inflation is to make the initial conditions of our observable universe seem more “natural.” Inflation is a process, not a law of nature. If you don’t care about naturalness, and are willing to say “things just happened that way,” there is absolutely no reason to ever think about inflation. So the success or failure of inflation as a scenario depends on how natural it really is.

This raises a problem, as Roger Penrose has been arguing for years, with people like me occasionally backing him up. Although inflation does seem to create a universe like ours, it needs to start in a very particular kind of state. If the laws of physics are “unitary” (reversible, preserving information over time), then the number of states that would begin to inflate is actually much smaller than the number of states that just look like the hot Big Bang in the first place. So inflation seems to replace a fine-tuning of initial conditions with an even greater fine-tuning.

One possible response to this is to admit that inflation by itself is not the final answer, and we need a theory of why inflation started. Here, it is crucial to note that in conventional non-inflationary cosmology, our current observable universe was about a centimeter across at the Planck time. That’s a huge size by particle physics standards. In inflation, by contrast, the whole universe could have fit into a Planck volume, 10-33 centimeters across, much tinier indeed. So for some people (like me), the benefit of inflation isn’t that it’s more “natural,” it’s that it presents an easier target for a true theory of initial conditions, even if we don’t have such a theory yet.

But there’s another possible response, which is to appeal to eternal inflation. The point here is that most — “essentially all” — models of inflation lead to the prediction that inflation never completely ends. The vicissitudes of quantum fluctuations imply that even inflation doesn’t smooth out everything perfectly. As a result, inflation will end in some places, but in other places it keeps going. Where it keeps going, space expands at a fantastic rate. In some parts of that region, inflation eventually ends, but in others it keeps going. And that process continues forever, with some part of the universe perpetually undergoing inflation. That’s how the multiverse gets off the ground — we’re left with a chaotic jumble consisting of numerous “pocket universes” separated by regions of inflating spacetime.

It’s therefore possible to respond to the “inflation requires even more finely-tuned initial conditions than the ordinary Big Bang” critique by saying “sure, but once it starts, it creates an infinite number of smooth `universes,’ so as long as it starts at least once we win.” A small number (the probability of inflation starting somewhere) times infinity (the number of universes you make each time it starts) is still infinity.

But if eternal inflation offers solutions, it also presents problems, which might be worse than the original disease. These problems are at the heart of the worries that Steinhardt mentioned. Let me just mention three of them.

The one I fret about the most is the “unitarity” or “Liouville” problem. This is essentially Penrose’s original critique, updated to eternal inflation. Liouville’s Theorem in classical mechanics states that if you take a certain number of states and evolve them forward in time, you will end up with precisely the same number of states you started with; states aren’t created or destroyed. So imagine that there is some number of states which qualify as “initial conditions for inflation.” Then eternal inflation says we can evolve them forward and get a collection of universes that grows with time. The problem is that, as this collection grows, there is an increasing number of states that look identical to them, but which didn’t begin with a single tiny inflating patch at all. (Just like an ice cube in a glass of water will evolve to a glass of cooler water, but most glasses of cool water didn’t start with an ice cube in them.) So while it might be true that you can generate an infinite number of universes, at the same time the fraction of such states that actually began in a single inflating patch goes to zero just as quickly. It is far from clear that this picture actually increases the probability that a universe like ours started from inflation.

There is an obvious way out of this challenge, which is to say that all of these “numbers of states” are simply infinite, and this purported calculation just divides infinity by infinity and gets nonsense. And that’s very plausibly true! But if you reject the argument that universes beginning with inflation are an infinitesimally small fraction of all the universes, you are not allowed to accept the argument that there’s some small probability inflation starts and once it does it makes an infinite number of universes. All you can really do is say “we can’t calculate anything.” Which is fine, but we are left without a firm reason for believing that inflation actually solves the naturalness problems it was intended to solve.

A second problem, much more celebrated in the recent cosmological literature and closely related to the first, is known as the measure problem. (Not to be confused with the “measurement problem” in quantum mechanics, which is completely different.) The measure problem isn’t about the probability that inflation starts; it assumes so, and tries to calculate probabilities within the infinite ensemble of universes that eternal inflation creates. The problem is that we would like to calculate probabilities by simply counting the fraction of things that have a certain property — but here we aren’t sure what the “things” are that we should be counting, and even worse we don’t know how to calculate the fraction. Say there are an infinite number of universes in which George W. Bush became President in 2000, and also an infinite number in which Al Gore became President in 2000. To calculate the fraction N(Bush)/N(Gore), we need to have a measure — a way of taming those infinities. Usually this is done by “regularization.” We start with a small piece of universe where all the numbers are finite, calculate the fraction, and then let our piece get bigger, and calculate the limit that our fraction approaches. The problem is that the answer seems to depend very sensitively on how we do that procedure, and we don’t really have any justification at all for preferring one procedure over another. Therefore, in the context of eternal inflation, it’s very hard to predict anything at all.

This quick summary is somewhat unfair, as a number of smart people have tried very hard to propose well-defined measures and use them to calculate within eternal inflation. It may be that one of these measures is simply correct, and there’s actually no problem. Or it may be that the measure problem is a hint that eternal inflation just isn’t on the right track.

The final problem is what we might call the holography/complementarity problem. As I explained a while ago, thinking about black hole entropy has led physicists to propose something called “horizon complementarity” — the idea that one observer can’t sensibly talk about things that are happening outside their horizon. When applied to cosmology, this means we should think locally: talk about one or another pocket universe, but not all of them at the same time. In a very real sense, the implication of complementarity is that things outside our horizon aren’t actually real — all that exists, from our point of view, are degrees of freedom inside the horizon, and on the horizon itself.

If something like that is remotely true, the conventional story of eternal inflation is dramatically off track. There isn’t really an infinite ensemble of pocket universes — or at least, not from the point of view of any single observer, which is all that matters. This helps with the measure problem, obviously, since we don’t have to take fractions over infinitely big ensembles. But one would be right to worry that it brings us back to where we started, wondering why inflation really helps us solve naturalness problems at all.

Personally I suspect (i.e. would happily bet at even money, if there were some way to actually settle the bet) that inflation will turn out to be “right,” in the sense that it will be an ingredient in the final story. But these concerns should help drive home how far away we are from actually telling that story in a complete and compelling way. That should hardly come as a surprise, given the remoteness from our view of the events we’re trying to describe. But the combination of logical consistency and known physics is extremely powerful, and I think there’s a good chance that we’re making legitimate progress toward understanding the origin of the universe.

  1. I understand quite a bit less about a much larger list of things now – my number of known unknowns has increased. Epistemological win.

  2. In our observable universe, inflation and entropy is increasing. In order to ‘reverse’ entropy in a closed-system, such as a hypothetical box of particles, it takes energy to rearrange the particles from less to more ordered states, but no conventional energy (rather, it is dark energy) or hand is needed so that our observable universe continues inflating and expanding. So what if, as our universe increases in entropy and inflates, it spreads and is ‘feeding’ other areas in space wherein it instead takes energy to rearrange particles from more to less ordered states? Since we do not know what exists ‘outside’ the horizon of our universe, and based on the knowledge that the only difference between believing the world was flat and knowing it was round but flat when standing on its surface, then doesn’t it make sense to presume that what lies beyond our universe may in fact be ‘chains’ of universes like ours ‘feeding’ others, growing, dying, and vice versa?

  3. “A small number (the probability of inflation starting somewhere) times infinity (the number of universes you make each time it starts) is still infinity.”

    Am I missing something, or is that crazy statistics? Let’s say something like “If I flip a coin heads, then infinitely many universes will be created, including at least one looking like ours; If a flip a coin tails, no smooth universes will be created.” The probably of finding a smooth universe is effectively determined by the odds of flipping a coin, as opposed to the number of universes that occur if the coin is flipped heads.

    Maybe eternal inflation could imply that any beginning of inflation (including the type that wouldn’t straightforwardly be finely tuned to create a smooth universe), would inevitably go on long enough to create infinite universes (including infinitely many smooth universes). I’m not sure if that helps make the initial state of inflation less finetuned than the hot big bang, but maybe.

  4. Probably my biggest feeling of unease over the idea of the inflationary universe is that
    it requires a hypothetical “inflaton” scalar field which does not exist in the Standard Model of
    particle physics, and as far as I know does not have a theoretical basis even in SUSY. The idea
    of just making up new fields out of the blue and adding them into a theory strikes me as
    analogous to invoking the tooth fairy.

  5. I like this summary – just one minor comment about the measure problem. From my perspective the issue is that the measure is inherently an arbitrary choice. When you use a measure, say the different ensembles of statistical mechanics, it is a way for you to specify the question you are interested in. There is no sense in which the canonical ensemble is more “correct” than the microcanonical one, or is forced on you by some law of nature. You can ask all kinds of questions about any system, motivated by which experiments are easy to do and which calculations are possible, and all kinds of other psychological and sociological factors. None of these choices is “out there” as part of nature, they are choices we make, all of which equally valid. Similarly, I personally don’t see what sort of argument, even in principle, would make one measure any different from any other one, let alone single out a preferred one.

  6. A couple of overly enthusiastic ad hominem comments have been deleted.

    Moshe, I utterly agree. I tried to get that across with “we don’t really have any justification at all for preferring one procedure over another,” but it deserves to be emphasized.

    Zwirko– a one-centimeter region of the universe can certainly have a center, whether the universe itself does or not. (“Our observable universe” has a center, namely us, but that says nothing about the universe as a whole.)

    Colin– the statistics aren’t crazy, although my presentation of them may have been inadequate. To make the argument work, you need to imagine that the small probability of inflation starting attaches to an infinite number of places it could start — either positions in spacetime, or branches in the wave function of the universe. What you’re really comparing is the probability that a region like the one we live in came from inflation, vs. popping into existence without inflation. It’s the relative probability that matters (and is hard to calculate).

  7. Moshe : I am from your camp regarding “measures”. However, I have since start to be sympathetic to, if not totally a believer of, Raphael Bousso’s point of view, which (I won’t do justice here) seems to imply that the “correct measure may be something fundamental theory can tell us”, or the stronger version, “the correct measure *is* something part of fundamental theory itself”.

    Of course, I don’t think any of the current measures in the market (including my own) has anything to do with deep fundamental theory — it’s more of an ad hoc collection of things that haven’t catastrophically broke under the infinities.

  8. Eugene, I am ready to be convinced by either you or Raphael. Currently I cannot really imagine what the expression “correct measure” might mean, or how one would go about arguing for a specific measure, even in a completely well-defined and well-understood context (say any Hamiltonian system with finitely many degrees of freedom). Maybe when I drop by you can help me out with my lack of imagination, so I can be in on all the fun.

  9. @ Mark N.

    Indeed. The part I find especially disagreeable is when Sean wrote: “If you don’t accept that inflation is part of the answer, you will spend eternity in Hell. I am absolutely certain this is the case and there’s nothing you could possibly say that would ever change my mind.”

  10. So, if horizon complementarity is right, then it doesn’t even make theoretical sense for us to talk about anything beyond our observable universe ?

    That would surely resolve the issue of whether theorizing about the mutiverse is science ! 🙂

  11. Inflation is a cure much worse then the disease.

    Invoking inflation to explain away initial state of the Universe works just as well as invoking god to explain it’s existence, in both cases you are just hiding the real well-defined problem behind an elaborate abstract and ill-defined concept invented for exactly this purpose.

    This seems to be an example of human bias – to prefer some explanation no matter how incomprehensible, arbitrary or superficial to no explanation at all. I guess questions to which we know there are no answers are more unsettling to us then questions to which we think there are satisfactory answers but we are just too dumb/uneducated/lazy to properly understand them.

  12. i agree with al. i like roger penroses idea of multiple, seqential, big bangs with no change in the size of each universe as time goes on. each universe transforms its mass into massless fermibosonic matter. the next universe forms from this matter with the help of gigantic black holes which feed on the fermibosonic matter, separating it into ordinary matter and dark matter in equal amounts. fermibosonic matter is my idea.

  13. Shantanu– I’m not exactly sure what he’s referring to. Eternal inflation is fundamentally a quantum process; it wouldn’t happen in classical general relativity. So it’s not clear that the Bianchi identities are relevant.

  14. Well done.

    While I disagree with your conclusion about final ingredients, this article is very well summarized, explained and organized.

    I especially appreciate your diplomatic manner of explaining how Multiverse concepts (and invoking Inflation itself) may evaporate when held up to physics and physical reality, and your sentiments about the problems illustrated.

    Thank you.
    (I intend to link to your article.)

  15. Pingback: Nice article explaining Inflation’s Problems | Cosmology Science Blog © 2011 David Dilworth

  16. Sean wrote: ‘If you don’t care about naturalness, and are willing to say “things just happened that way,” there is absolutely no reason to ever think about inflation.’

    This is an interesting remark that I’ve not often come across. And as someone who is definitely willing to say the above quoted phrase, I’d like to understand it better. Could someone expand on it? In particular, there are three incontrovertible (AFAIK) pieces of observational data: (a) homogeneity of CMB, (b) spectrum of CMB inhomogeneities, (c) statistics of matter distribution in the large scale structure.

    If “naturalness” is eliminated from consideration, is there still a compelling argument that these three data are best jointly explained by an early phase of accelerated expansion driven by quantum scalar field? Or are there other models that step up to this challenge equally well?

  17. Igor, the state of the universe at early times, as you know, is nearly homogeneous, with fluctuations with certain amplitude and spectrum. This is a series of regularities which are unexplained within the big bang framework, so it is tempting to explain it as consequence of earlier history of the universe. Alternatively, as you can do with any observation of a regular pattern, you can just shrug it off as a coincidence. Nothing ever forces you to find explanations for regularities, clearly some aspects of nature are just historical, without any deep explanation, maybe this is just one of them.

  18. myrtle $20 penroses ccc theory does not require any huge expansion to form a new universe, instead, it only uses matter already present from the previous universe (in massless form, which i have dubbed fermibosonic matter) to form the next universe, etc. matter is immortal in ccc theory

  19. Is the inflaton an unconvincing type of particle? Are both the inflaton and the Higgs boson wrong ideas that have a somewhat arbitrary form? According to Gian Francesco Giudice, “The Higgs sector is that part of the theory that describes the Higgs mechanism and contains the Higgs boson. Unlike the rest of the theory, the Higgs sector is rather arbitrary, and its form is not dictated by any deep fundamental principle. For this reason, its structure looks frightfully ad hoc.” (quoted from page 174 of “A zeptospace odyssey: a journey into the physics of the LHC”)

  20. This is a much more trivial (perhaps naive) question than the ones above. Is it the case that one must have inflation to justify the notion that one looks back in time when one looks out in space. Or is there some other explanation for how we could have “outrun” light so that we can look back on it as it catches up.