Hubble Tension as Dimensional Transition: A Parameter-Free Prediction from Spacetime Ladder Theory

The todiscrepancy between cosmic microwave background (CMB) and local distance-ladder measurements of the Hubble constant remains the most significant unresolved anomaly in modern cosmology. We propose a geometric resolution within Spacetime Ladder Theory (STLT), in which a primordial dark-matter field polarizes into contracting matter and expanding dark energy, generating a hierarchical spacetime structure through iterative solutions to a single polarization equation. We identify the fine-structure constant as a universal polarization coupling constant that operates across all scales—from the electron-nucleus coupling in atoms to the dark matter-dark energy coupling in cosmology. The hierarchy——emerges naturally as scaling, with each level corresponding to a fundamental interaction. CMB measurements probe the electromagnetic 54D Void Spacetime, while galaxy-scale distance-ladder measurements, governed by atomic nuclei, probe the strong-force 162D Tao Spacetime. From the standard quantum-field-theoretic result that interaction amplitudes scale as, where  is the fine-structure constant, we derive a parameter-free prediction:

Using Planck 2018 () and SH0ES 2025 () values, the observed fractional tension agrees with prediction at (). We further derive a complete energy-scale hierarchy via topological quantum field theory (TQFT), predicting a sixth layer at PeV scale with , which simultaneously resolves the high-redshift Ly-forest anomaly, JWST “too-early galaxy” crisis, and TeV-PeV gamma-ray transparency anomaly. Sharp predictions are made: gravitational-wave standard sirens will measure; PeV neutrino arrival directions will systematically deviate from optical source distributions; and high-redshift TeV gamma-ray sources will appear anomalously transparent. The Hubble tension is therefore not a systematic error or a failure of CDM, but a natural consequence of different cosmological probes accessing different dynamic phases of dark-energy expansion. Future observations from LISA, the Einstein Telescope, IceCube-Gen2, CTA, DESI, and JWST will provide decisive tests.