A Precise Numerical Coincidence: Mapping Weaire-Phelan Foam Geometry onto the \texorpdfstring{$\Lambda$}{Λ}CDM Cosmic Composition
Year: 2026
Type: dissertation
Abstract: The cosmic composition ratios — ordinary matter $\sim 4.9\%$, dark matter $\sim 26.8\%$, and dark energy $\sim 68.3\%$ — are input parameters of the $\Lambda$CDM model rather than derived outputs. This paper reports a precise geometric mapping: the A15 lattice of the Weaire-Phelan foam, through a set of recursive annihilation rules, produces volume partitions that exactly reproduce these three numbers. The core mechanism is as follows: angular deviations of dodecahedral vertices in the A15 lattice (Type B vertices: $40\%$, deficit $-0.16^\circ$; Type C vertices: $60\%$, surplus $+0.50^\circ$; Type A vertices: minority, surplus $+2.72^\circ$) — all defined relative to the ideal vertex angle sum mandated by Plateau's law, $\Theta = 6 \times \arccos(-1/3) = 656.83^\circ$ — generate stress anisotropy. The two elongated hexagonal faces of the tetrakaidecahedron are orthogonally oriented and twisted by $90^\circ$ relative to each other, causing the structure to develop shear stress concentration under compression. The alternating arrangement of Type B and Type C vertices further intensifies shear stress at the equatorial belt, driving tetrakaidecahedra to annihilate in pairs as positive/negative chiral pairs. The cascading annihilation initiates from Type B regions and is suppressed in Type C regions, converging to an $80\%$ annihilation rate. In each round, approximately $30.72\%$ of the surviving volume transforms into decahedra (ordinary matter), and the remainder splits in a $1:3$ ratio into dodecahedron increments (dark matter) and new tetrakaidecahedra (entering the next round). Dark matter increments are not added until the beginning of the next round. After approximately $1.5$ recursive rounds, the composition converges to ordinary matter $4.9\%$, dark matter $26.8\%$, and dark energy $68.3\%$, consistent with Planck 2018 observations to within precision limits. This work is positioned as a geometric mapping rather than a physical theory. The model contains no free parameters — all inputs are derived from CAD measurements of A15 crystallographic coordinates. The physical plausibility of recursive annihilation is supported by a cascade decay analogy. The model provides independently falsifiable quantitative predictions.
Author: Zeng, Hu
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160602016