Simple emergent power spectra from complex inflationary physics

TL;DR

This paper demonstrates that complex inflationary models with many interacting scalar fields can produce simple, predictable power spectra due to emergent universality, despite initial complexity.

Contribution

It introduces a novel approach using random matrix theory to model scalar potentials and shows how large-field interactions lead to simplified, universal power spectra in inflation.

Findings

For few fields, power spectra are highly non-linear and inconsistent with observations.

For many fields, the power spectra become simple and well approximated by a linear spectrum.

Large N_f universality explains the emergence of simple spectra from complex inflationary physics.

Abstract

We construct ensembles of random scalar potentials for $N_f$ interacting scalar fields using non-equilibrium random matrix theory, and use these to study the generation of observables during small-field inflation. For $N_f={\cal O}({\rm few})$, these heavily featured scalar potentials give rise to power spectra that are highly non-linear, at odds with observations. For $N_f\gg 1$, the superhorizon evolution of the perturbations is generically substantial, yet the power spectra simplify considerably and become more predictive, with most realisations being well approximated by a linear power spectrum. This provides proof of principle that complex inflationary physics can give rise to simple emergent power spectra. We explain how these results can be understood in terms of large $N_f$ universality of random matrix theory.