Our infant universe most likely underwent a sudden growth spurt. Imagine a grain of sand swelling to the size of the Milky Way in a time as brief, relative to a second, as a nanosecond is compared to the entire age of our universe.

It was both larger and more rapid than that.

And no, it was not due to hormones… Scientific concensus instead points towards an enigmatic phenomenon dubbed “cosmic inflation” — a key to understanding structure formation, physics beyond the Standard Model, and many more unanswered questions in fundamental physics. Although inflation itself belongs to the obscured earliest moments of the universe, its fingerprints remain imprinted in the Cosmic Microwave Background (CMB). As cosmologists, it is our job to decipher them.

Think whatever you want about inflation. It is without a doubt a striking theory. To understand and to test it, we do what we physicists do best; write down a model and put it against the data. There is just one subtlety: inflation does not posess just one unique description.

There are many models of inflation.

And by that, I mean many.

“One inflation coming up!”

There are so many models of inflation that not even cosmologists can keep track of them all. Enter the “Encyclopædia Inflationaris”: a compilation and analysis of a staggering 118 distinct inflation scenarios. Sitting at over 700 pages and 1000+ citations, this mammoth paper showcases the legitimate factory that the inflation model building community has become. If you are looking to spit out rapid papers, just join the production line!

Perhaps it’s worth clarifying what I mean by ‘models of inflation’. Broadly speaking, they all build upon the same theoretical scaffolding; introduce a new field called the “inflaton” whose dynamics causes the universe to exponentially expand. They therefore all make roughly the same predictions such as to be compatible with our cosmology. But in the fine details — the number of parameters, fields, their dynamics, and even their motivated origin — they differ, yielding subtly distinct fingerprints in the sky. (I am aware that this may be somewhat underselling the science being done. Let me therefore emphasise that my gripe has little to do with the actual quality of the model building, but rather the sheer quantity.)

Surely — one might think — this is a huge success for the theory itself, since it in multitudinous ways manages to resolve a central problem in cosmology. As a testament, just take a look at the total number of papers with titles related to “inflation”:

The number of ‘inflation’ papers is itself inflating! I find this terribly comedic…

When talking about ‘how many times bigger’ the universe expanded during inflation, we typically talk about the number of “e-folds”. One e-fold is times bigger, is two e-folds, is e-folds. You get the gist. Many cosmology textbooks will often quote that inflation went on for 60 e-folds. That is a huge number!

Here are some ‘inflation paper’ facts: over 45 years we have inflated 6.4 e-folds in “inflation papers per year”. The total number of publications has inflated a staggering 9.1 e-folds. If we keep up the pace, I predict that we will reach those 60 e-folds around year 2276.

The Landscape Dilemma

Jokes aside, as a fundamental physicist, I myself have grown slightly troubled by this unstoppable model building factory. My unrest essentially boils down to a question of extreme malleability. For if a theory such as inflation, with an ever-growing menagerie of scalar potentials, modified mechanisms, and theoretical extensions, is particularly accommodating in its framework, to what extent is it even falsifiable? Before I go on a rant, let me make it clear that I am by far the first person to feel as such, and that this debate has been ongoing in the literature for several years. See e.g. Ijjas, Steinhardt & Loeb (2013) and (2014) (Steinhardt has rather famously turned his back on inflation after being one of its pioneers), Martin (2019), and Vagnozzi & Loeb (2022).

Yes, every inflation model is falsifiable in its own right. Calling the extensive model building “unscientific” would be wildly misguided. But what about the theory itself?

How can we challenge the set of all possible consistent solutions — the Landscape, if you will — if it is too vast to even comprehend?

Before you make up your mind, consider the following suggestions:

• Give up on the theory? The rebellious decision would be to heavily modify or completely discard theories which are unable to crowd control their Landscapes. However, in inflation’s case, no clear alternative theory exists without its own empirical conflicts. So far cosmic inflation seems to be our best bet, and until a better theory appears, abandoning ship appears premature.
  
  
• Wait for experimental input? We can wait for more observational data, hopefully ruling out a large number of models. This slow, expensive process is absolutely obligatory for the science itself, i.e. in order to test our theoretical predictions. However, to hone in on a model without resorting to fine-tuning and/or anthropics requires still a more grounded theoretical justification.
  
  
• Constrain the theory? It is most likely that the original framework we wrote down is not the full story. Further theoretical developments could just automatically solve the overabundance issue and allow for palpable predictions. But unless constraints are strong enough to select a unique solution, fine-tuning issues will persist.

Let’s at least appreciate how each method has had an everlasting impact in physics history:

• Copernicus abandoned the geocentric model in favour of simplicity.
• CERN discovered and honed in on the mass of the Higgs boson (which mismatched theoretical expectations).
• The Coleman-Mandula theorem placed incredible constraints on how we may combine symmetries beyond the Standard Model.

I am by no means implying that the above mindsets are meant to be exhaustive. Rather, my point is to exemplify how the Landscape dilemma can push physicists to think in various, and in some cases diverging, directions. What they nevertheless share — all discord aside — is the commitment to an immeasurable leap of faith. Dig around the hep-th or gr-qc arXiv and you will find precisely that: physicists and sub-communities that force their favourite theories and narratives in complete disregard of what neighbouring fields and research programmes have to offer. Theoretical physicists are a curious species in that they will devote entire careers to pursue fundamental questions and answers in directions that “feel or smell right”. Anything unappealing is often simply ignored. (Part of this is deeply sociological, though that’s for a future post.) But where is the logic in putting all eggs in one basket? As scientists, we ought to admit that we do not know what the final answer will involve. That’s also what makes the job exciting! Perhaps the more grounded stance is to embrace our ignorance and practice a symbyosis of all the strategies mentioned… (At least one can dream.) Less drama, but it’s for science, you know.

A trailblazer needs a compass

Vast theoretical Landscapes inevitably present a dilemma: how can we as physicists most effectively develop our theories amid overwhelming possibilities? Although this question is valuable to ponder upon, we must also crucially acknowledge that it is merely a symptom of a much more unsettling underlying issue: our severe lack of guidance. For while we have outstanding evidence for physics beyond our current frameworks, there remains a long-standing struggle to tame them from a theoretical standpoint. Here I am referring to famous puzzles such as the cosmological constant, strong CP, and hierarchy problems. Of course, we also appreciate and accept the fact that our best frameworks are incomplete. But the phenomenology and observational signatures which point us towards where the issues lie are scarce, obscured by conceptual, technical, or technological barriers.

The bottom line is exactly why we should be alarmed by the Encyclopædia Inflationaris: theorists are overwhelmed and by and large drowning themselves in models, waiting for a mythical beacon to appear in the horizon. To whose benefit is that? Blindly searching for our universe in the Landscape is no different from the purifiers of Borges’s “The Library of Babel”; scouring for omnipotent books in endless religious zeal. Sure, exploring the Landscape can gain us great intuition for what the theory has to offer. But brewing up even more solutions is perhaps not a sustainable strategy. What we need are tools to allow intent navigation.

It has become worryingly trendy to apply this kind of criticism towards String Theory, quoting that it has or number of solutions, to argue that it “makes no predictions” and “can never be falsified”. (Actually the problem is much much worse, as these numbers only concern Calabi-Yau flux compactifications in 10d superstring theory. There is nothing saying you have to compactify on Calabi-Yau manifolds. It is just an incredibly helpful choice, which historically was decided on to make calculations palpable. This nuance is rarely acknowledged.) However, that “problem” has nothing to do with String Theory per se, and is more rooted in the fact that the String Landscape is vast. Although inflation faces the exact same challenge, the broader physics community is much more willing to give it a pass. Just imagine the amount of criticism string theorists would receive if they wrote a “Catalogus Compactificationis”!

At some point we have to ask: how productive is it to keep fuelling the endless onslaught of compactifications, brane engineering, moduli stabilizations, modified gravities, scalar potentials, and whatever new DIY project that happens to catch the community’s fancy? Churning out possibilities is easy; finding direction is the real challenge. What we desperately need is not another patch of parameter space, but actual tools to navigate the Landscape itself. Thankfully, a few programmes have started shifting focus in that direction. Ideas like the Swampland Programme, Positivity Bounds, and related consistency criteria don’t solve the problem for us — though they at least offer a compass of sorts. Not a map, no, but perhaps the first hints of one. And that, is starting to look like progress.

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