2011/03/30 by Antonio Riotto, Martin S. Sloth, Martin S Sloth
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #astro-ph.CO #hep-ph #hep-th
paper · pdf · doi:10.1088/1475-7516/2011/10/003
27 pages
arxiv created 2011/03/30 · openalex publication_date 2011/10/03 · arxiv updated 2015/05/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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.