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Title: Geometrically consistent approach to stochastic DBI inflation

Abstract

Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch-sized domains. The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term. We solve the Langevin equation for an inflaton field with a Dirac-Born-Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's probability density function (PDF). In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain. DBI kinetic terms typically arise in string-inspired inflationary scenarios in which the scalar field is associated with some distance within the (compact) extra dimensions. The inflaton's accessible range of field values therefore is limited because of the extra dimensions' finite size. We argue that in a consistent stochastic approach the inflaton's PDF must vanish for geometrically forbidden field values. We propose to implement these extra-dimensional spatial restrictions into the PDF by installing absorbing (or reflecting) walls at the respective boundaries in field space. As a toy model, we consider a DBI inflaton between two absorbing walls and use the methodmore » of images to determine its most general PDF. The resulting PDF is studied in detail for the example of a quartic warp factor and a chaotic inflaton potential. The presence of the walls is shown to affect the inflaton trajectory for a given set of parameters.« less

Authors:
; ;  [1];  [2];  [3];  [4]
  1. Theoretical and Mathematical Physics Group, Centre for Particle Physics and Phenomenology, Louvain University, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve (Belgium)
  2. (France)
  3. (Japan)
  4. (IPMU), University of Tokyo, Kashiwa, Chiba, 277-8568 (Japan)
Publication Date:
OSTI Identifier:
21415218
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 82; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.82.023515; (c) 2010 The American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BORN-INFELD THEORY; CHAOS THEORY; FLUCTUATIONS; LANGEVIN EQUATION; NOISE; PERTURBATION THEORY; PROBABILITY DENSITY FUNCTIONS; SCALAR FIELDS; SPACE; STOCHASTIC PROCESSES; EQUATIONS; FUNCTIONS; MATHEMATICS; VARIATIONS

Citation Formats

Lorenz, Larissa, Martin, Jerome, Yokoyama, Jun'ichi, Institut d'Astrophysique de Paris, UMR 7095-CNRS, Universite Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Tokyo 113-0033, and Institute for the Physics and Mathematics of the Universe. Geometrically consistent approach to stochastic DBI inflation. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.023515.
Lorenz, Larissa, Martin, Jerome, Yokoyama, Jun'ichi, Institut d'Astrophysique de Paris, UMR 7095-CNRS, Universite Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Tokyo 113-0033, & Institute for the Physics and Mathematics of the Universe. Geometrically consistent approach to stochastic DBI inflation. United States. doi:10.1103/PHYSREVD.82.023515.
Lorenz, Larissa, Martin, Jerome, Yokoyama, Jun'ichi, Institut d'Astrophysique de Paris, UMR 7095-CNRS, Universite Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Tokyo 113-0033, and Institute for the Physics and Mathematics of the Universe. 2010. "Geometrically consistent approach to stochastic DBI inflation". United States. doi:10.1103/PHYSREVD.82.023515.
@article{osti_21415218,
title = {Geometrically consistent approach to stochastic DBI inflation},
author = {Lorenz, Larissa and Martin, Jerome and Yokoyama, Jun'ichi and Institut d'Astrophysique de Paris, UMR 7095-CNRS, Universite Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris and Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Tokyo 113-0033 and Institute for the Physics and Mathematics of the Universe},
abstractNote = {Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch-sized domains. The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term. We solve the Langevin equation for an inflaton field with a Dirac-Born-Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's probability density function (PDF). In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain. DBI kinetic terms typically arise in string-inspired inflationary scenarios in which the scalar field is associated with some distance within the (compact) extra dimensions. The inflaton's accessible range of field values therefore is limited because of the extra dimensions' finite size. We argue that in a consistent stochastic approach the inflaton's PDF must vanish for geometrically forbidden field values. We propose to implement these extra-dimensional spatial restrictions into the PDF by installing absorbing (or reflecting) walls at the respective boundaries in field space. As a toy model, we consider a DBI inflaton between two absorbing walls and use the method of images to determine its most general PDF. The resulting PDF is studied in detail for the example of a quartic warp factor and a chaotic inflaton potential. The presence of the walls is shown to affect the inflaton trajectory for a given set of parameters.},
doi = {10.1103/PHYSREVD.82.023515},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 82,
place = {United States},
year = 2010,
month = 7
}
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