Sunday, March 10, 2019

Inflation: Status Update

 [[My enmpahsis D.G.]]
Model of Inflation.
img src:
The universe hasn’t always been this way. That the cosmos as a whole evolves, rather than being eternally unchanging, is without doubt one of the most remarkable scientific insights of the past century. It follows from Einstein’s theory of general relativity: Einstein’s theory tells us that the universe must expand. As a consequence, in the early universe matter must have been compressed to high density.

But if you follow the equations back in time, general relativity eventually stops working. Therefore, no one presently knows how the universe began. Indeed, we may never know.

Since the days of Einstein, physicists have made much progress detailing the history of the universe. But the deeper they try to peer into our past, the more difficult their task becomes.

This difficulty arises partly because new data are harder and harder to come by. The dense matter in the early universe blocked light, so we cannot use light to look back to any time earlier than the formation of the cosmic microwave background. For even earlier times, we can make indirect inferences, or hope for new messengers, like gravitational waves or neutrinos. This is technologically and mathematically challenging, but these are challenges that can be overcome, at least in principle. (Says the theorist.)

The more serious difficulty is conceptual. When studying the universe as whole, physicists face the limits of the scientific method: The further back in time they look, the simpler their explanations become. At some point, then, there will be nothing left to simplify, and so there will be no way to improve their explanations. The question isn’t whether this will happen, the question is when it will happen.

The miserable status of today’s theories for the early universe makes me wonder whether it has already happened. Cosmologists have hundreds of theories, and many of those theories come in several variants. It’s not quite as bad as in particle physics, [[!!!]] but the situation is similar in that cosmologists, too, produce loads of ill-motivated models for no reason other than that they can get them published. (And they insist this is good scientific practice. Don’t get me started.)

The currently most popular theory for the early universe is called “inflation”. According to inflation, the universe once underwent a phase in which volumes of space increased exponentially in time. This rapid expansion then stopped in an event called “reheating,” at which the particles of the standard model were produced. After this, particle physics continues the familiar way.

Inflation was originally invented to solve several finetuning problems. (I wrote about this previously, and don’t want to repeat it all over again, so if you are not familiar with the story, please check out this earlier post.) Yall know that I think finetuning arguments are a waste of time, so naturally I think these motivations for inflations are no good. However, just because the original reason for the idea of inflation doesn’t make sense doesn’t mean the theory is wrong.

Ever since the results of the Planck in 2013 it hasn’t looked good for inflation. After the results appeared, Anna Ijjas, Paul Steinhardt, and Avi Loeb argued in a series of papers that the models of inflation which are compatible with the data themselves require finetuning, and therefore bring back the problem they were meant to solve. They popularized their argument in a 2017 article in Scientific American, provocatively titled “Pop Goes the Universe.”

The current models of inflation work not simply by assuming that the universe did undergo a phase of exponential inflation, but they moreover introduce a new field – the “inflaton” – that supposedly caused this rapid expansion. For this to work, it is not sufficient to just postulate the existence of this field, the field also must have a suitable potential. This potential is basically a function (of the field) and typically requires several parameters to be specified.

Most of the papers published on inflation are then exercises in relating this inflaton potential to today’s cosmological observables, such as the properties of the cosmic microwave background.

Now, in the past week two long papers about all those inflationary models appeared on the arXiv:
Cosmic Inflation: Trick or Treat?
By Jerome Martin
arXiv:1902.05286 [astro-ph.CO]
Inflation after Planck: Judgement Day
By Debika Chowdhury, Jerome Martin, Christophe Ringeval, Vincent Vennin
arXiv:1902.03951 [astro-ph.CO]

The first paper, by Jerome Martin alone, is a general overview of the idea of inflation. It is well-written and a good introduction, but if you are familiar with the topic, nothing new to see here.

The second paper is more technical. It is a thorough re-analysis of the issue of finetuning in inflationary models and a response to the earlier papers by Ijjas, Steinhardt, and Loeb. The main claim of the new paper is that the argument by Ijjas et al, that inflation is “in trouble,” is wrong because it confuses two different types of models, the “plateau models” and the “hilltop models” (referring to different types of the inflaton potential).

According to the new analysis, the models most favored by the data are the plateau models, which do not suffer from finetuning problems, whereas the hilltop models do (in general) suffer from finetuning but are not favored by the data anyway. Hence, they conclude, inflation is doing just fine.

The rest of the paper analyses different aspects of finetuning in inflation (such as quantum contributions to the potential), and discusses further problems with inflation, such as the trans-planckian problem and the measurement problem (as pertaining to cosmological perturbations). It is a very balanced assessment of the situation.

The paper uses standard methods of analysis (Bayesian statistics), but I find this type of model-evaluation generally inconclusive. The problem with such analyses is that they do not take into account the prior probability for the models themselves but only for the initial values and the parameters of the model. Therefore, the results tend to favor models which shove unlikeliness from the initial condition into the model (eg the type of function for the potential).

This is most obvious when it comes to the so-called “curvature problem,” or the question why the universe today is spatially almost flat. You can get this outcome without inflation, but it requires you to start with an exponentially small value of the curvature already (curvature density, to be precise). If you only look at the initial conditions, then that strongly favors inflation.

But of course inflation works by postulating an exponential suppression that comes from the dynamical law. And not only this, it furthermore introduces a field which is strictly speaking unnecessary to get the exponential expansion. I therefore do not buy into the conclusion that inflation is the better explanation. On the very contrary, it adds unnecessary structure.

This is not to say that I think inflation is a bad idea. It’s just that I think cosmologists are focusing on the wrong aspects of the model. Finetuning arguments will forever remain ambiguous because they eventually depend on unjustifiable assumptions. What’s the probability for getting any particular inflaton potential to begin with? Well, if you use the most common measure on the space of all possible function, then all so-far considered potentials have probability zero. This type of reasoning just does not lead anywhere. So why waste time talking about finetuning?

Instead, let us talk about those predictions whose explanatory value does not depend on finetuning arguments, of which I suspect (but do not know) that ET-correlations in the CMB power spectrum are an example. Since finetuning debates will remain unsolvable, it would be more fruitful to focus on those benefits of inflation that can be quantified unambiguously.

In any case, I am sure the new paper will make many cosmologists happy, and encourage them to invent many more models for inflation. Sigh.