The predictive content of Spectral Causal Theory

Abstract

We catalog the predictions of Spectral Causal Theory (SCT), a one-loop gravitational effective field theory derived from the spectral action \(S = \operatorname{Tr}(f(D^2/\Lambda^2))\) of a noncommutative spectral triple encoding the Standard Model. Predictions are classified as cutoff-independent (depending only on the Seeley-DeWitt \(a_4\) coefficient) or cutoff-dependent (sensitive to the shape of the cutoff function \(f\)). The cutoff-independent sector contains the Weyl-squared coefficient \(\alpha_C = 13/120\), the ratio \(c_1/c_2 = -1/3\) (frozen under matter-only one-loop RG flow at conformal coupling \(\xi = 1/6\)), the gravitational wave speed \(c_T = c\), and the absence of a scalar gravitational mode at \(\xi = 1/6\). The logarithmic black hole entropy correction \(c_{\log} = 37/24\) is conditional on stated assumptions. Starobinsky inflation is excluded in the standard spectral action because \(\alpha_R(\xi = 1/6) = 0\). For black hole quasinormal modes, modal stability is proven analytically (\(V > 3f/r^2 > 0\) for \(\ell \geq 2\)) and frequency shifts are bounded by \(\delta\omega/\omega \sim c_2(\omega/\Lambda)^2 \sim 10^{-20}\) for stellar BHs, fifteen orders below LIGO sensitivity; tidal Love numbers \(k_2 \neq 0\) (qualitative difference from GR, but unmeasurably small). Comparison with five quantum gravity programs (LQG, AS, CDT, string theory, IDG) across nine quantitative axes identifies three discriminating observables and five falsification criteria.