Charting an Inflationary Landscape with Random Matrix Theory

TL;DR

This paper introduces a novel random matrix theory-based method to model multifield inflation with large numbers of scalar fields, enabling efficient analysis of inflationary dynamics and revealing how eigenvalue interactions influence inflation duration.

Contribution

It develops a computationally efficient framework using Dyson Brownian motion for large N scalar fields, advancing the modeling of complex inflationary landscapes.

Findings

Eigenvalue repulsion reduces inflation duration near critical points

Small cross-couplings cause curvature growth around critical points

Method allows analysis of systems with up to 100 scalar fields

Abstract

We construct a class of random potentials for N >> 1 scalar fields using non-equilibrium random matrix theory, and then characterize multifield inflation in this setting. By stipulating that the Hessian matrices in adjacent coordinate patches are related by Dyson Brownian motion, we define the potential in the vicinity of a trajectory. This method remains computationally efficient at large N, permitting us to study much larger systems than has been possible with other constructions. We illustrate the utility of our approach with a numerical study of inflation in systems with up to 100 coupled scalar fields. A significant finding is that eigenvalue repulsion sharply reduces the duration of inflation near a critical point of the potential: even if the curvature of the potential is fine-tuned to be small at the critical point, small cross-couplings in the Hessian cause the curvature to grow in the neighborhood of the critical point.