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The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation
Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation...
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Lenguaje: | eng |
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2011
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Acceso en línea: | https://dx.doi.org/10.1088/1475-7516/2011/10/003 http://cds.cern.ch/record/1341405 |
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author | Riotto, Antonio Sloth, Martin S. |
author_facet | Riotto, Antonio Sloth, Martin S. |
author_sort | Riotto, Antonio |
collection | CERN |
description | Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects. |
id | cern-1341405 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2011 |
record_format | invenio |
spelling | cern-13414052023-03-14T18:06:10Zdoi:10.1088/1475-7516/2011/10/003http://cds.cern.ch/record/1341405engRiotto, AntonioSloth, Martin S.The Kramers-Moyal Equation of the Cosmological Comoving Curvature PerturbationAstrophysics and AstronomyFluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.arXiv:1103.5876CERN-PH-TH-2011-56CERN-PH-TH-2011-056oai:cds.cern.ch:13414052011-03-31 |
spellingShingle | Astrophysics and Astronomy Riotto, Antonio Sloth, Martin S. The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation |
title | The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation |
title_full | The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation |
title_fullStr | The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation |
title_full_unstemmed | The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation |
title_short | The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation |
title_sort | kramers-moyal equation of the cosmological comoving curvature perturbation |
topic | Astrophysics and Astronomy |
url | https://dx.doi.org/10.1088/1475-7516/2011/10/003 http://cds.cern.ch/record/1341405 |
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