Derivation of the Gravitational Constant and Variable Effective Gravity from Local Variation of the Lattice Step in Discrete Geometric Physics
Year: 2026
Type: article
Abstract: This work presents a rigorous derivation of the gravitational constant GG and the mechanism of variable effective gravity from the local variation of the lattice step in Discrete Geometric Physics (DGP). The explicit expression G=ℓPl2c3/ℏG=ℓPl2c3/ℏ is obtained from the exchange of spiral contours, using only the fundamental lattice invariants: Σw=14Σw=14, ϕ=(1+5)/2ϕ=(1+5)/2, ℓPlℓPl, and wV/Σw=1/56wV/Σw=1/56. Numerical substitution gives G=6.67430⋅10−11 m3kg−1s−2G=6.67430⋅10−11m3kg−1s−2, matching CODATA 2025 to 10−510−5. The scale‑dependent effective gravitational constant Geff(N)=G⋅22(116−N)Geff(N)=G⋅22(116−N) naturally resolves the Hubble tension: for the early Universe (N≈142N≈142) it yields H0≈73H0≈73 km/s/Mpc, while for the late Universe (N≈204N≈204) it gives H0≈67.4H0≈67.4 km/s/Mpc, in agreement with Planck and SH0ES data. Local variations of GG at the level of 10−910−9–10−610−6 are predicted and are testable in precision experiments such as MICROSCOPE or STEP. This version includes the complete derivation in English, with all key formulas and references to the full two‑volume DGP work.
Author: Ivan Davidenko
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166346517