The MOND Acceleration Scale as a de Sitter Curvature Scale: Gauged SO(4,1) Gravity Reduces a0 = c^2 sqrt(Lambda/32pi) to a Single Free Number
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Abstract
Galaxy dynamics organize around an acceleration scale a0 ~ 1e-10 m/s^2 that numerically coincides with c*sqrt(Lambda) and cH0. This paper develops the hypothesis that the coincidence is structural -- that a0 is a de Sitter curvature scale, a0 = c^2*sqrt(Lambda/32pi) = (c/2)*sqrt(G*rho_DE) = c*H_Lambda/Z, Z = sqrt(32pi/3) = 5.789, evaluated on the dark-energy density alone, giving a0 = 9.36e-11 m/s^2 -- and separates, with machine verification, what the proposal DERIVES from what it POSITS. (i) Gauging the de Sitter group SO(4,1) (MacDowell-Mansouri) gives Einstein-Hilbert + Lambda; an exhaustive symbolic enumeration certifies this is the unique two-derivative parity-even invariant in its class (exactly two quadratic-in-curvature SO(4,1) four-forms exist; exactly one is two-derivative). (ii) The deep-MOND form a0 ~ c^2*sqrt(Lambda) is over-determined: a false-discovery-controlled audit certifies FOUR structurally independent mechanisms force it (correcting an earlier inflated count of seven), with the de Sitter-Unruh modified-inertia interpolation reproducing flat rotation curves and v^4 = G*M*a0. (iii) The gravitational route fixes the kernel sqrt(8pi/3) including the half-integer power of pi that no curvature-free thermal route produces, leaving the entire residual unforced content as ONE O(1) number, kappa = 1/2: a0 is exactly half the gravitational free-fall acceleration at the dark-energy density. The limits are stated plainly: the value of Lambda is an input; the inertia mechanism's covariant completion is unbuilt and exists only as a sibling effective field theory degenerate with AeST on the static locus but not joined to it; and the Standard Model is not produced -- the generation number N = 3 is shown to be a topological parity obstruction for the natural index over the de Sitter nucleation saddle, so it stays fitted (the universal status of the flavor puzzle, not a special failure). The proposal is therefore an effective theory at a frontier with a certified gravity spine and a fitted Standard Model -- NOT a theory of everything yet, as frustrating as it may be. Two tests decide its distinctive content: Cassini (in hand) discriminates modified inertia, which it passes by a factor ~30, from an ungated modified-gravity completion, which it fails; and the declining prediction a0(z=3) = 0.74*a0(0), cleanly separable (~6x) from both LCDM and a rival rising branch, is falsifiable with ELT-class spectroscopy this decade, hostage to whether DESI confirms evolving dark energy. Earlier claims that a discrete-holography (DSSYK) kernel forces the galaxy-scale sign and that the coefficient is fixed by a unique entropy calculation are withdrawn.
Related
- The de Sitter-Unruh Modified-Inertia Theory: A One-Parameter Account of the MOND Acceleration Scale
- Gauss--Bonnet running and the de Sitter saddle of quadratic gravity inflation
- A Hybrid Acceleration for Self-gravity Calculation in Infinitesimally Thin Disks with Adaptive Mesh Refinement
- Exploring Cosmic Rays from Gravity-Limited Acceleration at Supermassive Black Holes
- Gravitational wave echoes as probes of the maximum mass of strange stars in quadratic curvature-matter coupled gravity
BibTeX
@misc{zimmerman2026mond,
title = {{The MOND Acceleration Scale as a de Sitter Curvature Scale: Gauged SO(4,1) Gravity Reduces a0 = c^2 sqrt(Lambda/32pi) to a Single Free Number}},
author = {Carl P. Zimmerman},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jun,
doi = {10.5281/zenodo.20721539},
url = {https://doi.org/10.5281/zenodo.20721539},
note = {CC BY},
}
RIS
TY - UNPB
TI - The MOND Acceleration Scale as a de Sitter Curvature Scale: Gauged SO(4,1) Gravity Reduces a0 = c^2 sqrt(Lambda/32pi) to a Single Free Number
AU - Carl P. Zimmerman
PY - 2026
DA - 2026/06/16
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.20721539
UR - https://doi.org/10.5281/zenodo.20721539
AB - Galaxy dynamics organize around an acceleration scale a0 ~ 1e-10 m/s^2 that numerically coincides with c*sqrt(Lambda) and cH0. This paper develops the hypothesis that the coincidence is structural -- that a0 is a de Sitter curvature scale, a0 = c^2*sqrt(Lambda/32pi) = (c/2)*sqrt(G*rho_DE) = c*H_Lambda/Z, Z = sqrt(32pi/3) = 5.789, evaluated on the dark-energy density alone, giving a0 = 9.36e-11 m/s^2 -- and separates, with machine verification, what the proposal DERIVES from what it POSITS. (i) Gauging the de Sitter group SO(4,1) (MacDowell-Mansouri) gives Einstein-Hilbert + Lambda; an exhaustive symbolic enumeration certifies this is the unique two-derivative parity-even invariant in its class (exactly two quadratic-in-curvature SO(4,1) four-forms exist; exactly one is two-derivative). (ii) The deep-MOND form a0 ~ c^2*sqrt(Lambda) is over-determined: a false-discovery-controlled audit certifies FOUR structurally independent mechanisms force it (correcting an earlier inflated count of seven), with the de Sitter-Unruh modified-inertia interpolation reproducing flat rotation curves and v^4 = G*M*a0. (iii) The gravitational route fixes the kernel sqrt(8pi/3) including the half-integer power of pi that no curvature-free thermal route produces, leaving the entire residual unforced content as ONE O(1) number, kappa = 1/2: a0 is exactly half the gravitational free-fall acceleration at the dark-energy density. The limits are stated plainly: the value of Lambda is an input; the inertia mechanism's covariant completion is unbuilt and exists only as a sibling effective field theory degenerate with AeST on the static locus but not joined to it; and the Standard Model is not produced -- the generation number N = 3 is shown to be a topological parity obstruction for the natural index over the de Sitter nucleation saddle, so it stays fitted (the universal status of the flavor puzzle, not a special failure). The proposal is therefore an effective theory at a frontier with a certified gravity spine and a fitted Standard Model -- NOT a theory of everything yet, as frustrating as it may be. Two tests decide its distinctive content: Cassini (in hand) discriminates modified inertia, which it passes by a factor ~30, from an ungated modified-gravity completion, which it fails; and the declining prediction a0(z=3) = 0.74*a0(0), cleanly separable (~6x) from both LCDM and a rival rising branch, is falsifiable with ELT-class spectroscopy this decade, hostage to whether DESI confirms evolving dark energy. Earlier claims that a discrete-holography (DSSYK) kernel forces the galaxy-scale sign and that the coefficient is fixed by a unique entropy calculation are withdrawn.
ER -