Inflation in multi-field random Gaussian landscapes

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.

25 pages, 5 figures; (v2) minor changes, Fig. 5 updated

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• Anthropic Bound on Dark Radiation and its Implications for Reheating
• Inflation in Random Landscapes with two energy scales
• The Distribution of Vacua in Random Landscape Potentials
• Slepian models for Gaussian Random Landscapes
• Local, algebraic simplifications of Gaussian random fields
• Superposition of Random Plane Waves in High Spatial Dimensions: Random Matrix Approach to Landscape Complexity