The predictive content of Spectral Causal Theory

Assumes 1–2 courses of background. Domain terms may appear without definition.

This paper catalogs the empirical predictions of Spectral Causal Theory (SCT), a one-loop gravitational effective field theory derived from the Chamseddine–Connes spectral action S = Tr f(D²/Λ²) of a noncommutative spectral triple that already encodes the Standard Model gauge group and particle content. The framework is an EFT in the Wilsonian sense: a cutoff scale Λ separates a UV completion (the spectral action itself) from an IR effective theory whose form factors are computed diagrammatically. The central distinction is between cutoff-independent predictions (determined entirely by the universal Seeley–DeWitt a₄ coefficient and the SM matter content) and cutoff-dependent ones (sensitive to the shape of the cutoff function f). The cutoff-independent sector is rigid: - Weyl-squared coefficient α_C = 13/120 - Ratio c₁/c₂ = −1/3 (frozen under matter-only one-loop RG flow at conformal coupling ξ = 1/6) - Gravitational wave speed c_T = c - No scalar gravitational mode at ξ = 1/6 - Starobinsky inflation excluded in the standard spectral action because α_R(ξ = 1/6) = 0 - Logarithmic black hole entropy correction c_log = 37/24 (conditional) For Schwarzschild black holes, modal stability of quasinormal modes is proven analytically (V > 3f/r² > 0 for ℓ ≥ 2) and frequency shifts are bounded by δω/ω ~ c₂(ω/Λ)² ~ 10⁻²⁰ for stellar BHs — fifteen orders below LIGO sensitivity. Tidal Love numbers are k₂ ≠ 0 (qualitatively distinct from GR's k₂ = 0, but unmeasurably small). The paper then benchmarks SCT against five competing quantum gravity programs (LQG, asymptotic safety, CDT, string theory, infinite-derivative gravity) across nine quantitative axes. Three discriminating observables and five falsification criteria are identified, each with a stated verification status (proven / verified / established / conditional).

AI-generated · created 2026-05-21