Neutrino Masses, Gravitational Weakness, and the Dark Sector: An Empirical Quantum Gravity Foundation

This article establishes a direct physical connection between the small masses of left-chiral neutrinos and the weakness of gravitational interactions, addressing a fundamental mystery in physics. By extending Gatto-Sartori-Tonin (GST) relations to vacuum expectation values and lepton masses, we derive an empirical link that embeds neutrino masses within the Einstein equation, revealing their critical role in suppressing gravitational strength. We obtain refined predictions for PMNS mixing angles, and for the individual left-chiral neutrino masses, summing to 0.0790 ± 0.0034 eV for normal ordering and 0.0763 ± 0.0022 eV for inverted ordering, consistent with the empirical range of 0.06 to 0.12 eV. We reveal a symmetry that unifies gravitational and weak interactions via simultaneous chiral and vacuum expectation value (vev) swaps, providing a natural seesaw solution to the hierarchy problem that also predicts right-chiral masses. We introduce a renormalizable Lagrangian density for quantum gravity, mediated by gravitinos, neutrino loops, and gravitons, which elucidates how tiny neutrino masses weaken gravitational interactions, illustrated in Figure 1. Extending this framework to cosmology, we demonstrate how a positive cosmological constant drives the emergence of dark energy and dark matter, with gravitons identified as dark energy quanta and neutrino loops as dark matter quanta. We also refine cosmological density parameters and provide empirical estimates for dark sector quanta densities, offering experimentally testable predictions. This establishes an empirical foundation for a complete quantum gravity theory.