Inflation as an information bottleneck: a strategy for identifying universality classes and making robust predictions

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. arXiv:1810.05199v2 [hep-th]

Stochastic particle production in a de Sitter background

“…Moreover, the coarse-grained nature of the available cosmological observations is unlikely to shed light on all the microscopic details of the fundamental theory. A theoretical framework that advocates a coarse-grained and approximately model-independent approach, with a focus on universal features, is at the heart of our efforts here and in [1][2][3] (also see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]).…”

“…where the angular parameters can be identified as follows, 18) and n(j) is the occupation number density:…”

Very Hairy Inflation

“…The scales M i typically arise from warping effects or dilution of energy densities with inverse powers of extra dimension volumes (see e.g. section 4.1 in [49] for a summary), which are either power-law or exponentially sensitive to the microscopic parameters in a string compactification. Finally, the axions φ i arise from two mutually sequestered sectors of a given model, only interacting via gravity, and so generically M 1 = M 2 .…”

Harmonic hybrid inflation

“…Let us finally stress that the inflationary predictions are very sensitive to the deformations of the hybrid potential, and moreover, we only considered the simplest modification so far. Therefore, the model lacks a clear prediction and it could be more informative to allude to a statistical approach as in [51].…”