Chronoscalar Field Theory XVIII: Electroweak Geometry and the Higgs as the Radial Mode of the Primordial Scalar Condensate

Abstract

Chronoscalar Field Theory (CFT) asserts that the Universe is built not from a metric spacetime 3 supplemented by independent gauge fields, scalar fields and Yukawa matrices, but from a single 4 fundamental scalar condensate T(xμ) whose permanent cosmological gradient ∇T was created in 5 a unique, irreversible Machian displacement. All subsequent structure—gravity, inertia, gauge 6 interactions, electroweak symmetry breaking, the Higgs phenomenon, and fermion masses—emerges 7 from the geometry of this condensate. 8 In this eighteenth paper we show that the Standard Model Higgs field is not an independent 9 degree of freedom. Instead it is the radial mode of the chronoscalar condensate, the fluctuation δT∥ 10 along the local gradient direction, while the Goldstone bosons eaten by the W± and Z are simply the three transverse modes δT(i) ⊥ 11 spanning the hypersurface orthogonal to ∇T. The full electroweak 12 symmetry group SU(2) × U(1) is revealed as the transverse isometry group of the chronoscalar 13 vacuum geometry. 14 The Higgs vacuum expectation value vEW, the Weinberg angle θW, the vector boson masses 15 mW and mZ, and the pattern of fermion masses all emerge from geometric projections of ∇T and 16 its Hessian. This eliminates the hierarchy problem, the metastability problem, the fine-tuning of 17 the Higgs self-coupling, and the arbitrary Yukawa matrices of the Standard Model. The result is a 18 geometric unification of electroweak physics and gravity within a single-field framework.

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