Vacuum Energy from Icosahedral Coherence
Abstract
We derive the vacuum energy density of the universe from icosahedral geometry and the Planck length, with no free parameters. In a companion paper (Keeble 2026a), we established that the Casimir effect encodes dimensional mode counting through ζ(−1) = −1/D(D+1), and that its natural scale is electromagnetic rather than gravitational. Here we identify the cosmological Casimir scale: the maximum coherent icosahedral domain in flat 3-space, limited by five-fold frustration to V^(V−1) = 12^11 lattice units, where V = 12 is the icosahedral vertex count. Combined with the lattice spacing e^(V+E) l_P = e^42 l_P matched to the strong force anchor (Keeble 2026c), this gives a coherence length of 20.9 μm and a characteristic energy scale of ℏc/d_max = 9.4 meV. The observed vacuum energy scale (2.25 meV) lies below this by a geometric prefactor of order unity representing the 3D soft-wall mode density — an open calculation that replaces the ad hoc 10^120 fine-tuning of standard approaches. Every quantity in the formula is either a mathematical constant or an icosahedral number.
Fields of Study & Subjects
Quantum Electrodynamics and Casimir Effect
Advanced Mathematical Theories and Applications
Noncommutative and Quantum Gravity Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 15 February 2026
- Document type
- Preprint