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arXiv · 1409.5135

Local random potentials of high differentiability to model the Landscape

Thorsten Battefeld·Chirag Modi
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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.

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Thorsten Battefeld, Chirag Modi. 2014-09-17. Local random potentials of high differentiability to model the Landscape. https://doi.org/10.1088/1475-7516%2F2015%2F03%2F010

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