Gravity and Dark Energy in Terms of Electroweak Physics: Eliminating Newton's Constant from the Cosmological Constant

Two recently reported numerical relations — Λ · ℓ_Pl² = (α⁴/4π)(m_e/m_Pl)⁵ for the cosmological constant (Zhang 2026a) and α_G = α⁸ y_e⁵ for the gravitational coupling (Zhang 2026b, building on Kalinski 2021) — can be combined to express both Newton's constant G and the cosmological constant Λ entirely in terms of electromagnetic and electroweak quantities:

Λ = α¹⁶ y_e^(15/2) / (4π λ̄_e²)

where α is the fine structure constant, y_e = √2 m_e/v the electron Yukawa coupling, and λ̄_e = ℏ/(m_e c) the electron Compton wavelength. No gravitational quantities (G, m_Pl, ℓ_Pl) appear on the right-hand side. If these relations are physical, gravity would not be an independent interaction — its coupling strength and its vacuum energy contribution are both determined by QED and the electron's coupling to the Higgs field.

The hierarchy problem (why is G so small?) and the cosmological constant problem (why is Λ so small?) reduce to a single question: why does the electron have the mass it has? Five testable predictions follow, including a specific value of G (6.6727 × 10⁻¹¹, in 11σ tension with CODATA 2018), w = −1 exactly (testable by DESI and Euclid within 2–3 years), and a unique correlation δG/G = 8 δα/α. The input formulas were identified using the DAEDALUS dimensional-analysis engine (Zhang 2026g, DOI: 10.5281/zenodo.19743895). No first-principles derivation is available.