Abstract
In this work we propose a statistical approach to handling sources of theoretical uncertainty in string theory models of inflation. By viewing a model of inflation as a probabilistic graph, we show that there is an inevitable information bottleneck between the ultraviolet input of the theory and observables, as a simple consequence of the data processing theorem. This information bottleneck can result in strong hierarchies in the sensitivity of observables to the parameters of the underlying model and hence universal predictions with respect to at least some microphysical considerations. We also find other intriguing behaviour, such as sharp transitions in the predictions when certain hyperparameters cross a critical value. We develop a robust numerical approach to studying these behaviours by adapting methods often seen in the context of machine learning. We first test our approach by applying it to well known examples of universality, sharp transitions, and concentration phenomena in random matrix theory. We then apply the method to inflation with axion monodromy. We find universality with respect to a number of model parameters and that consistency with observational constraints implies that with very high probability certain perturbative corrections are non-negligible.
Highlights
As a consequence of this information loss we do not expect observables to be sensitive to all UV parameters, and in particular we expect them to display universality with respect to variations in some aspects of the UV input. This behaviour is extreme in high-dimensional probability, where models consisting of a large number of random variables very often demonstrate emergent simplicity as the model approaches some form of ‘large n’ limit
Despite our axion monodromy model not being high-dimensional in any sense, we found this approach to be fruitful, since at a qualitative level we identified similar behaviour
Exhausting the range allowed by 4D symmetries underlying the 4D Kaloper-Sorbo effective description of axion monodromy, should capture a large class of effects arising from the typical spectrum of corrections we expect in a string theory model of axion monodromy inflation
Summary
Cosmological inflation [1,2,3] is currently our most promising candidate description of the very early Universe. The couplings of a candidate inflaton to these scalar fields will generically generate at least a finite number of dangerous dimension-6 operators which have a drastic impact on the scalar potential, and of which we have little explicit theoretical control.1 Given this situation, clear statements about the predictions of inflation models in string theory seem to be elusive. As a consequence of this information loss we do not expect observables to be sensitive to all UV parameters, and in particular we expect them to display universality with respect to variations in some aspects of the UV input This behaviour is extreme in high-dimensional probability (a well known subfield being random matrix theory), where models consisting of a large number of random variables very often demonstrate emergent simplicity as the model approaches some form of ‘large n’ limit. The goal of our work is to identify the information bottleneck compressing the UV sensitivity of axion monodromy inflation into the IR observables and find universality classes — identify the conditions under which we can make robust predictions
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