Have your multiverse and eat it

The recent results from the Planck mission have caused a flurry of activity among theoretical physicists, documented on the arXiv in an increasing amount of papers with updates on constraints on various cosmological models. Of particular interest is the question which models of inflation are favored by the data. Interestingly, the simplest potentials for the scalar field that causes inflation are ruled out or disfavored already. For a summary, see Jester’s post Planck about inflation.

Paul Steinhardt and collaborators have taken this as a reason to argue that the data actually hints at cyclic models.

Inflationary paradigm in trouble after Planck2013
Anna Ijjas, Paul J. Steinhardt, Abraham Loeb
1304.2785

Planck 2013 results support the simplest cyclic models
Jean-Luc Lehners, Paul J. Steinhardt
1304.3122

The argument in these papers goes as follows.

The potentials for the inflaton field that are necessary to fit the Planck data are not simple in that they require finetuning, ie delicately adjusted parameters. The finetuning has to produce a suitably flat plateau in the potential, and a power law with coefficients of order one isn’t going to do this. If you’d random pick the potential, it would be very unlikely you’d get a suitably finetuned one.

This, Steinhardt et al argue, is a serious problem because the “inflationary paradigm” draws its justification from our universe being a “likely” outcome of quantum fluctuations that are blown up to produce the structures we see. If the potential, or the initial value of the scalar field, is unlikely, this erodes the basis of believing in the inflationary paradigm to begin with. In the paper this unlikeliness is quantified, and it is noted that the unlikeliness of the initial value of the scalar field can be recast as an unlikeliness of the potential. Then they go on to argue that cyclic models are preferable because in these cases natural parameter ranges for coefficients in the potential are still compatible with the data (they do not comment on how natural these models are in other respects). They then identify observables that could further solidify the case.

There are two gaps in this argument. The first gap is between “inflation” and “inflationary paradigm.”

Inflation is a model that describes very well the observations in our universe by using a familiar framework that makes use of quantum field theory and general relativity. The inflationary paradigm that they refer to (not an expression that is common in the scientific literature) adds requirements beyond the explanation of observation, that being the likeliness of the model.

To begin with, speaking about probabilities makes only sense if one has an ensemble. So to even refer to unlikeliness you have to believe in a distribution over set of possibilities, a multiverse. And for that you must have faith in your model, faith that extends beyond and before and beneath our universe, faith that the model holds outside everything we have ever observed, and that you can actually use it to make a statement about likeliness.

Besides this, the inflaton potential is normally not expected to be fundamental, but some effective limit a few orders of magnitude below the Planck scale. If you want to say anything about the probability of finding a particular potential, you would first have to know the fundamental degrees of freedom and the UV-completion of the theory. Just taking potentials and attempting to assign them a probability doesn’t make a lot of sense.

So talking about probabilities is already a bad starting position. From this starting position then Steinhardt et al argue that the inflationary paradigm says that we should find our universe to be likely. But by going from inflation to the inflationary paradigm, one is no longer talking about testing a model that explains observations. In their own words

“The usual test for a theory is whether experiment agrees with model predictions. Obviously, inflationary plateau-like models pass this test.”

That should be the last sentence of a scientific paper. Alas, there’s a next sentence, and it starts with “However…”

“However, this cannot be described as a success for the inflationary paradigm, since, according to inflationary reasoning, this particular class of models is highly unlikely to describe reality.”

Note the leap from “theory” to “paradigm”. (Let me not ask what “reality” means, I know it’s an unfair question.)

The second gap in the argument is that you could use it to rule out pretty much any model anybody has ever proposed.

In this earlier post I explained that all presently existing theories inevitably lead to a multiverse, a large space of possibilities. It’s just that this multiverse is more apparent in some approaches than in others.

The reason a multiverse is inevitable is that we always need something to specify a theory to begin with. Call it basic axioms or postulates. We need something to start with. And in the context of the theory you’re working with, that postulated basis is an uncaused cause: It was written down with the explicit purpose to explain observations. If you take away that purpose because you’ve misunderstood what science is all about, you are left with only mathematical consistency. And then, layer by layer, you are forced to include everything into your theory that is mathematically consistent. That’s what Tegmark called the “Mathematical Universe.”

Steinhardt et al’s elaboration about the possible shape of potentials is an example of this mathematical multiverse beneath the basis. They take away one postulate and replace it by a larger space of mathematical possibilities. Instead of postulating a specific (purpose bound) real-valued, differentiable, scalar function, they replace them with the space of all continuous functions (though they’re not too explicit on the requirements). But why stop there? Why not take the space of all functions and random pick one of these? Almost all functions on the real axis are discontinuous in infinitely many places, which is a fancy way of saying that the probability to get a continuous one upon random picking is zero. Look, I just ruled out both the “inflationary paradigm” and Steinhardt’s cyclic models without referring to any data at all.

To be fair however, Steinhardt et al are just fighting inflation with its own weapons. It is arguably true that the literature is full of arguments about naturalness and how inflation solves this or that philosophical conundrum. If you believe in the multiverse, or eternal inflation specifically, I think you should take the argument put forward in these papers seriously. For the rest of us, those who see inflation as a model with the purpose to describe observations in our universe, there’s no reason to make these leaps of faith. And that’s what they are - at least for now. One never knows what the data will bring.