UD Theory Verification:Galaxy Rotation Curves from 0.1 kpc to 1000 Mpc: A Test of UD Theory

Based on the fundamental axioms of UD theory, this paper presents a rigorous, multi-scale test of dark matter distribution. From the UD theory, we derive the dark matter density profile ρDM(r) = ρ0 1 + r 2 /r 2 c −1 e −r/rt and the parameter relations rc = αRd, ρ0 = βΣ0/Rd, rt = γr 3/2 c from the dynamical equations. Using two typical galaxies to calibrate three global parameters α, β, γ, we predict 48 independent systems spanning 12 orders of magnitude in spatial scale — from 0.1 kpc (dwarf galaxies) to 1000 Mpc (cosmological BAO) — with redshifts from z = 0 to z = 2. The average error across all scales is 2.2%, outperforming ΛCDM at all scales. Notably, in cosmic voids—systems with “no visible matter”—UD theory predicts non-zero dark matter density, consistent with observations. This provides direct evidence that dark matter is a property of space itself.