Local random potentials of high differentiability to model the Landscape

Abstract

We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble (other ensembles might be chosen if desired). Potentials in such higher differentiability classes are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., smooth first and second derivatives for the power-spectrum) or to search for minima (e.g., suitable de Sitter vacua for our universe). Since potentials are created locally, numerical studies become feasible even if the dimension of field space is large (D ~ 100). In addition to the theoretical prescription, we provide some numerical examples to highlight properties of such potentials; concrete cosmological applications will be discussed in companion publications.

V2: added discussion section to match published version (conclusions unchanged); 25 pages, 5 figures

References in corpus (11)

• The Anthropic Landscape of String Theory
• Mass hierarchies and non-decoupling in multi-scalar field dynamics
• Heavy fields, reduced speeds of sound and decoupling during inflation
• New Universal Local Feature in the Inflationary Perturbation Spectrum
• Cosmology From Random Multifield Potentials
• Accidental Inflation in String Theory
• Standard Clock in Primordial Density Perturbations and Cosmic Microwave Background
• Is a step in the primordial spectral index favored by CMB data ?
• Exploring a string-like landscape
• On the Unlikeliness of Multi-Field Inflation: Bounded Random Potentials and our Vacuum
• A Universal Bound on Excitations of Heavy Fields during Inflation

Cited by in corpus (3)

• Random Functions via Dyson Brownian Motion: Progress and Problems
• Inflation on a Slippery Slope
• Non-Uniqueness of Classical Inflationary Trajectories on a High-Dimensional Landscape