Spectral Dimension Running as the Origin of Dark Energy Activation: A Connection Between Quantum Gravity and 4D Bulk Inflation

This paper refines the 4D Bulk Inflation model by resolving the tension between predicted dark energy density and early-universe constraints (BBN/CMB). We propose that dark energy suppression in the early universe is a geometric consequence of spectral dimension running (ds), a robust result from multiple quantum gravity frameworks including CDT and Loop Quantum Gravity. In the Planckian era, where ds≈2, 4D bulk pressure is geometrically suppressed as it lacks a consolidated 3D volume to act upon. Dark energy "activates" not via a scalar potential, but as spacetime achieves its full 3D character. Key Contributions Geometric Suppression: Explains why dark energy was negligible at early times without fine-tuning. Hubble Tension Resolution: Maintains an equation of state w≈−0.827, consistent with DESI 2024. Testable Predictions: 1. CMB Low-l Anomaly: Predicts power suppression at large angular scales (l<10). 2. Variation of G: Predicts G˙/G≈1.1×10−12 yr−1, testable by next-gen Lunar Laser Ranging. 3. Dark Matter: Identifies dark matter as ultra-light Kaluza-Klein modes of the inflating 4D bulk AI Disclosure: Concept and physical reasoning by the author; mathematical formalism and LaTeX assisted by AI