Local random potentials of high differentiability to model the Landscape
- Department of Physics, University of Minnesota, 1023 University Dr., Duluth, MN 55812 (United States)
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai-40076 (India)
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.
- Sponsoring Organization:
- SCOAP3, CERN, Geneva (Switzerland)
- OSTI ID:
- 22454516
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, 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); ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
Similar Records
Charting an Inflationary Landscape with Random Matrix Theory
Field dynamics and tunneling in a flux landscape