Dark Geometry: The Unified Origin of Dark Matter and Dark Energy via Exotic Smoothness and Roughness Renormalization
Lee, Sunggil · Zenodo (CERN European Organization for Nuclear Research) · 2025
The Dark Sector (Dark Matter and Dark Energy) constitutes 95% of the universe, yet remains the greatest enigma in physics. We propose a unified geometric solution based on Rough Operator Algebra (ROA). We prove that the "Dark Sector" is not composed of new particles, but is a manifestation of the non-trivial geometry of 4D spacetime. (1) Dark Matter arises from Exotic Smoothness. As the universe evolves (α → 1), spacetime undergoes a 4D Bifurcation, creating "Exotic Layers" where matter is gravitationally active but electromagnetically decoupled. (2) Dark Energy arises from Roughness Pressure. We derive the Cosmological Constant Λ as the entropic cost of the smoothing process. The accelerated expansion is the result of the universe minimizing its geometric roughness. This work completes the application of Sunggil's Grand Unified Mathematics to cosmology.