2001/07/31 by Patrick Valageas, P. Valageas · 3 citations
Engineering · Physics and Astronomy · #Cosmology and Gravitation Theories #Fluid Dynamics and Turbulent Flows #Galaxies: Formation, Evolution, Phenomena #astro-ph
paper · pdf · doi:10.1051/0004-6361:20011309
published as A&A (2001), 379, 8 · 13 pages, final version published in A&A
arxiv created 2001/10/09 · openalex publication_date 2001/11/01 · arxiv updated 2009/12/01 · openalex created_date 2022/08/09 · openalex updated_date 2026/07/31
We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit calculation of the second-order terms which are shown to agree with the results obtained from the hydrodynamical description of the system. Then, we explain that this identity extends to all orders of perturbation theory and that the perturbative series actually diverge for hierarchical scenarios. However, since the collisionless Boltzmann equation provides the exact description of the dynamics (including the non-linear regime) these results may serve as a basis for a study of the non-linear regime. In particular, we derive a non-perturbative quadratic integral equation which explicitly relates the actual non-linear distribution function to the initial conditions (more precisely, to the linear growing mode). This allows us to write an explicit path-integral expression for the probability distribution of the exact non-linear density field.