2018/04/16 by Mordehai Milgrom, Milgrom, Mordehai · 1 citation
Computer Science · Physics and Astronomy · #Astrophysics of Galaxies (astro-ph.GA) #Black Holes and Theoretical Physics #Computational Physics and Python Applications #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph)
paper · pdf · doi:10.48550/arxiv.1804.05840
openalex publication_date 2018/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I describe a heuristic model where MOND dynamics emerge in a universe viewed as a nearly spherical brane embedded in a higher-dimensional flat space. The brane, described by ξ(Ω), is of density σ (ξ and Ω are the radial and angular coordinates in the embedding space). The brane and matter -- confined to the brane and of density ρ(Ω)≪σ -- are coupled to a potential ε(ξ). I restrict myself to shallow perturbations, ξ(Ω)=ℓ0+ζ(Ω), |ζ|≪ℓ0. A balanced brane implies a0≡ε'(ℓ0)∼ T/σℓ0, T is the brane tension, yielding for the velocity of small brane perturbations c2∼ T/σ∼ ℓ0 a0. But, a0 plays the role of the MOND acceleration constant in local gravitational dynamics; so a0∼ c2/ℓ0. What we, in the brane, perceive as the gravitational potential is ϕ≡ε[ξ(Ω)]≈ ϕ0+ a0ζ. Aspects of MOND that may emerge naturally as geometrical properties are: a. The special role of acceleration in MOND, and why it is an acceleration, a0, that marks the transition from the standard dynamics much above a0 to scale-invariant dynamics much below a0. b. The intriguing connection of a0 with cosmology. c. The Newtonian limit corresponds to local departure |ζ|≪ℓ0; i.e., ϕ-ϕ0∼ a0ζ≪ a0ℓ0∼ c2 - whereas relativity enters when |ζ|\not≪ℓ0. The model also opens new vistas for extension, e.g., it points to possible dependence of a0 on ϕ, and to a0 losing its status and meaning altogether in the relativistic regime. The required global balance of the brane might solve the `old' cosmological-constant problem. I discuss possible connections with the nearly-de-Sitter nature of our Universe. (Abridged.)