Substrate inflation: predictions for n_s and r from non-minimal substrate-curvature coupling

We compute the inflationary observables produced by a substrate scalar field with non-minimal curvature coupling ξ_P |I₀|² R and Mexican-hat self-interaction. The conformal transformation to Einstein frame produces a flat plateau at large field values, making the substrate field a natural inflaton in the same equivalence class as Bezrukov-Shaposhnikov Higgs inflation and Starobinsky R² inflation. For N_★ = 60 e-folds before the end of inflation, the predicted scalar spectral index is

                              n_s = 1 − 2/N_★ ≈ 0.967,

in exact agreement with the Planck 2018 measurement n_s = 0.9649 ± 0.0042. The predicted tensor-to-scalar ratio is r ≈ 12/N_★² ≈ 0.0033, below current upper bounds and detectable by CMB-S4 and the LiteBIRD satellite. The running of the spectral index, the local non-Gaussianity parameter f_NL, and the tensor spectral index n_t are all predicted in agreement with observation. The framework differs from standard Higgs inflation in the identification of the inflaton (substrate field rather than Standard Model Higgs) and in the natural origin of the non-minimal coupling, and it connects to post-inflationary cosmology through the substrate-Higgs portal discussed in companion work.