Inflation in multi-field random Gaussian landscapes

TL;DR

This paper studies slow-roll inflation in a multi-field Gaussian landscape, showing that inflation typically occurs near inflection or saddle points with properties similar to one-dimensional models, and discusses tunneling dynamics.

Contribution

It introduces a detailed analysis of multi-field inflation in small-field Gaussian landscapes, contrasting it with Dyson Brownian motion models and exploring tunneling behaviors.

Findings

Inflation occurs near inflection or saddle points in small patches.

The inflationary trajectory is usually close to a straight line in field space.

Tunneling endpoints tend to concentrate along flat directions.

Abstract

We investigate slow-roll inflation in a multi-field random Gaussian landscape. The landscape is assumed to be small-field, with a correlation length much smaller than the Planck scale. Inflation then typically occurs in small patches of the landscape, localized near inflection or saddle points. We find that the inflationary track is typically close to a straight line in the field space, and the statistical properties of inflation are similar to those in a one-dimensional landscape. This picture of multi-field inflation is rather different from that suggested by the Dyson Brownian motion model; we discuss the reasons for this difference. We also discuss tunneling from inflating false vacua to the neighborhood of inflection and saddle points and show that the tunneling endpoints tend to concentrate along the flat direction in the landscape.