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Title: Local random potentials of high differentiability to model the Landscape

We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class C{sup k}, 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 (k≥2) are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., k=2 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.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Department of Physics, University of Minnesota, 1023 University Dr., Duluth, MN 55812 (United States)
  2. (Germany)
  3. Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai-40076 (India)
  4. (United States)
Publication Date:
OSTI Identifier:
22454516
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 03; Other Information: PUBLISHER-ID: JCAP03(2015)010; OAI: oai:repo.scoap3.org:9480; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)
Sponsoring Org:
SCOAP3, CERN, Geneva (Switzerland)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BROWNIAN MOVEMENT; COSMOLOGICAL INFLATION; COSMOLOGY; DE SITTER SPACE; NUMERICAL ANALYSIS; PERTURBATION THEORY; RANDOMNESS; STRING MODELS; STRING THEORY; UNIVERSE