{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-origin-of-mond-acceleration-and-deep-mond","title":"On a critical acceleration scale of dark matter in Lambda-CDM and dynamical dark energy","arxiv_id":"2203.05606","date":"2022-03-10","proceeding":null,"authors":["Zhijie","Xu"],"abstract":"Universal acceleration $a_0$ emerges in various empirical laws, yet its fundamental nature remains unclear. Using Illustris and Virgo N-body simulations, we propose $a_0$ is the scale of acceleration fluctuations in collisionless dark matter involving long-range gravity. In contrast, in the kinetic theory of gases, molecules undergo random elastic collisions involving short-range interactions, where only velocity fluctuations are relevant. We identify the redshift evolution $a_0\\propto (1+z)^{3/4}$ that is in good agreement with Magneticum and EAGLE simulations and in reasonable agreement with limited observations. This suggests a larger $a_0$ at a higher redshift such that galaxies of fixed baryonic mass rotate faster at a higher redshift. The velocity fluctuations involve a critical velocity $u_c\\propto (1+z)^{-3/4}$. The acceleration fluctuations involve a critical acceleration $a_c\\propto (1+z)^{3/4}$. Two critical quantities are related by the rate of energy cascade $\\varepsilon_{u}\\approx -{a_c u_c/[2(3\\pi)^2]}$, where factor $3\\pi$ is from the angle of incidence and $\\varepsilon_u\\approx -10^{-7}$m$^2$/s$^3$. With critical velocity $u_c$ on the order of 300 km/s at $z=0$, the critical acceleration is determined to be $a_{c0}\\equiv a_c(z=0) \\approx 10^{-10}$m/s$^2$, suggesting $a_c$ might explain the universal acceleration $a_0\\approx 10^{-10}$m/s$^2$ in the empirical Tully-Fisher relation or modified Newtonian dynamics (MOND). Note that dark energy (DE) density $\\rho_{DE0}\\approx {a_{c0}^{2}/G}=10^{-10}$J/m$^3$, we postulate an entropic origin of the dark energy from acceleration fluctuations of dark matter, in analogy to the gas pressure from velocity fluctuations. This leads to a dynamical dark energy coupled to the structure evolution involving a relatively constant DE density followed by a slow weakening phase, suggesting possible deviations from the standard $\\Lambda$CDM.","url_abs":"https://arxiv.org/abs/2203.05606v5","url_pdf":"https://arxiv.org/pdf/2203.05606v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-origin-of-mond-acceleration-and-deep-mond","repo_url":"https://github.com/ZhijieXu2022/dark_matter_flow_dataset","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}