The empirical acceleration scale that normalises the radial acceleration relation (RAR) is conventionally written as a₀ ≈ 1. 20 × 10⁻¹⁰ m/s². It marks the scale at which the Newtonian acceleration inferred from the baryonic mass distribution no longer closes the observed galactic acceleration budget. It has long been noted that a₀ lies close to c·H₀/ (2π), although the uncorrected Hubble-temperature scale undershoots the empirical value by about 13%. Working within a two-scale de Sitter cosmological background, we define a cosmic mean acceleration scale ā_∂Λ: = c · Θ₇䃐 · (V_Λ / VH) ^ (1/4) = c · H₀ / 2π · Ω_Λ^ (3/8), where VH is the present Hubble volume, V_Λ the asymptotic de Sitter comparison volume, and Θ₇䃐 = H₀/ (2π) = kB · T₇䃐 / ℏ the Gibbons–Hawking-type Hubble-temperature frequency scale of the present Hubble horizon. Evaluated at Planck 2018 central values, ā_∂Λ = 1. 2006 × 10⁻¹⁰ m/s², in 10⁻³-level agreement with the conventional RAR/Milgrom central normalisation, with no galaxy-level fit parameter. We present this relation as an empirical cosmological identity and test its forward and inverse consistency, including a direct SPARC RAR validation with the cosmological value held fixed (Δχ² ≈ +0. 08 against the free-a₀ optimum; the bare c·H₀/ (2π) scale is disfavoured by Δχ² ≈ +5440 under the same diagnostic). Several equivalent forms expose complementary readings, including a baryon-Hubble form ā_∂Λ ≈ 0. 83 · c · Hb and a Friedmann-sum rewriting in which the baryonic, dark-matter, and dark-energy rates together with ā_∂Λ enter a single dimensionless relation. Within the present ansatz, a finite positive Ω_Λ is required to define the de Sitter comparison horizon: the identity is therefore not a MOND-style replacement of dark energy, and galactic regime closure is tied to the late-time cosmological background within this construction. The identity is offered as a phenomenological cosmological ansatz; the microscopic boundary derivation is reserved for a companion paper.
Yunbeom Yi (2026) studied this question.