UD Theory Verification:UD Theory in CMB:A Geometric Test

This paper derives three core geometric parameters of the cosmic microwave background radiation—the acoustic peak position lA, the sound horizon rs, and the primordial fluctuation spectral index ns—from the fundamental axioms of UD theory. By precise comparison with Planck 2018 satellite data, we obtain lA = 301.5 (Planck 301.76 ± 0.14), rs = 144.2 Mpc (Planck 144.43 ± 0.26 Mpc), and ns = 0.9667 (Planck 0.9649±0.0042), with all three parameters agreeing well within statistical uncertainties. A χ 2 test yields χ 2 = 4.41 with 3 degrees of freedom (p = 0.22), demonstrating excellent consistency between UD theory and Planck observations.