Sector-Saturation and the Logarithmic Suppression of Gravitational Evolution

We address the hierarchy problem of gravitational coupling—specifically, why gravity is many orders of magnitude weaker than all other forces, and why fundamental constants appear fine-tuned to their observed values. We propose that the scalar-imprint field Φ couples to the full set of N = 17 independent field sectors of the Standard Model, distributing its cosmological influence uniformly across the particle spectrum. This sector-saturation mechanism suppresses the observable drift of Newton’s constant G by a factor of 1/N, yielding λ= κ/17 where κ is determined by the slow-roll dynamics of the scalar potential. We show that N = 17 follows from a precise accounting of the Standard Model’s independent gauge and matter sectors: three fermion families, four gauge sectors (U(1), SU(2), SU(3), and the Higgs sector). The resulting suppression naturally places |λ|≲3.2 ×10−5, consistent with Lunar Laser Ranging bounds, without fine-tuning of the fundamental coupling constants βG and mΦ. We further demonstrate that the same mechanism explains the logarithmic—rather than power-law—relaxation of couplings toward their present values, providing a structural account of the observed stability of the constants of nature.