Nonlinear field equations and FLRW cosmology of the spectral action with Standard Model content

We derive the complete nonlinear variational field equations from the spectral action Tr(f(D²/Λ²)) with full Standard Model content and study their cosmological reduction. The field equations take the form Gμν/κ² + nonlocal curvature-squared corrections = Tμν/2, where the nonlocal form factors F̂₁(□/Λ²) and F̂₂(□/Λ²,ξ) are determined by the spectral triple with SM-derived coefficients α_C = 13/120 and α_R(ξ) = 2(ξ − 1/6)². On a Friedmann-Lemaître-Robertson-Walker background, we derive the modified Friedmann equation and prove that the gravitational-wave propagation speed equals the speed of light exactly (c_T = c), consistent with the GW170817/GRB 170817A constraint. De Sitter space is an exact solution satisfying the Higuchi stability bound. At the present cosmological epoch, the fractional correction to the Hubble rate is δH²/H² ≈ 1.28 × 10⁻⁶⁴, rendering the theory trivially consistent with all precision cosmology data.