An Evolving MOND Acceleration Scale from the Planck–Cosmological Density Hierarchy
Year: 2026
Type: article
Abstract: We present a geometric scaling framework that connects the ~122-order-of-magnitude hierarchy between the Planck density and the cosmological critical density to the characteristic acceleration scale of Modified Newtonian Dynamics (MOND). Starting from a Planck-normalized mass–radius scaling relation, we show that the mean density of a critical-scale system is suppressed relative to a geometrically normalized Planck density ρpl-bar = 3ρpl/4π by exactly N2, where N = Rc/lpl is a dimensionless hierarchy parameter. Identifying this density with the Friedmann critical density of a spatially flat universe yields a horizon-closure relation Rc = √2RH, in which the factor √2 emerges from consistency rather than being fitted. Applying the Newtonian acceleration scaling of a homogeneous sphere to the same critical-scale configuration then gives an infrared acceleration scale ac = (3√2/8π)×cH0, with the numerical coefficient 3√2/8π ≈ 0.169 determined entirely by the spherical volume normalization and the horizon-closure factor. For H0 = 73.0 km/s/Mpc this predicts ac = 1.2×10–10 m/s2, coinciding with the empirically inferred MOND scale a0 ≈ 1.2×10–10 m/s2; the CMB-inferred H0 = 67.4 km/s/Mpc gives 1.11×10–10 m/s2, a deviation of 7.5%. The framework further predicts that a0 should scale with the cosmic expansion rate, a0(z) µ H(z), providing a concrete observational test.
Author: Roopkom, Ittipat
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204172154