2015/08/31 by Pierre Fleury, Julien Larena, Jean-Philippe Uzan +1 · 24 citations
Physics and Astronomy · #Angular diameter #Astrophysics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Formalism (music) #Galaxies: Formation, Evolution, Phenomena #Langevin equation #Physics #Stars #Statistical physics #astro-ph.CO #gr-qc
paper · pdf · doi:10.1088/1475-7516/2015/11/022
published in Journal of Cosmology and Astroparticle Physics 2015(11), 022 (Institute of Physics) · 37+13 pages, 8 figures. A few typos corrected. Matches published version
openalex publication_date 2015/11/11 · arxiv created 2015/11/13 · arxiv updated 2015/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integration of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.