A Cosmological Origin of the Infrared Gravitational Scale

A characteristic acceleration scale of low-acceleration gravitational phenomenology — the transition scale of the Radial Acceleration Relation and the zero point of the Baryonic Tully– Fisher Relation, with empirical calibrations spanning approximately (1.1–1.3) × 10−10 m s−2 — has long been noted to lie close to cH0/2π. The dimensional proximity to cH0 is guaranteed to any acceleration constructed from the present expansion rate and c; the normalization is not, and it is the normalization this paper addresses. We propose an origin for it in the thermodynamic structure of the cosmological horizon, developed as two explicitly labeled hypotheses. The Infrared Inheritance hypothesis proposes that a gravitational infrared sector inherits, as its characteristic timescale, the KMS correlation period of the de Sitter horizon, βdS = 2π/HΛ; the associated acceleration aΛ = cHΛ/2π ≈ 0.86 × 10−10 m s−2 is fixed by the cosmological constant alone, lies 20–30% below the empirical calibrations, and carries a factor of 2π inherited structurally from the Euclidean periodicity of the horizon geometry rather than fitted. The Apparent-Horizon Continuation conjectures, separately, that in the evolving universe the scale follows the instantaneous apparent horizon, aIR(t) = cH(t)/2π, whose present-epoch value 1.04 × 10−10 m s−2 lies within the systematic uncertainty of the central empirical calibration and which predicts a specific redshift evolution, aIR(z)/aIR(0) = E(z) — an eighty-percent shift by z = 1 — testable against independently measured expansion histories.