This analysis derives the tensor-to-scalar ratio in cosmology, resolving a previous error and suggesting further predictions.
Derives the tensor-to-scalar ratio r = 16/[9 ln(16)] × (1−n_s) = 0.0225 from the foam cascade geometry of the Unified Foam Field Theory. Identifies and corrects an error in earlier UFFT documents: the correct logarithm in the cascade formula is ln(r₁r₂) = ln(16) (geometric mean cascade amplitude), not ln(r₂/r₁) (chirality anisotropy). The key identity r₁r₂ = 16 is the constant term of the master equation λ²−9λ+16=0, connecting the inflationary tensor-to-scalar prediction directly to the electroweak sector via r₁r₂ = 16 = λ²_Eg = (C_A+1)². With observed n_s = 0.9649, r = 0.0225; with UFFT's own n_s = 0.9621, r = 0.0243. Both are inside the BK18+Planck 95% bound r < 0.032, resolving the previous ~2σ tension. Additional prediction: tensor spectral index n_t ≈ −0.008. Testable by LiteBIRD ~2032 at approximately 23σ significance. Zero free parameters.
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Luke Martin (2026) studied this question.
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