A Covariant Canvas Cosmology: Scalar–Tensor Dynamics, de Sitter Phase Structure, Perturbative Stability, Exact Einstein–Boltzmann Evolution, and Likelihood Confrontation

This paper constructs and audits the cosmological sector of the Emergence Canvas programme from a single frozen covariant action rather than from phenomenological modifications of the Friedmann equations. The common scalar potential is U(z)=Az-Bz^2+Cz^3,\qquad z=|\Phi|^2, with A,B,C>0 and B^2<4AC, and gravity is extended minimally through F(z)=M_*^2+\xi z. No bare cosmological constant, independent quintessence field, f(R) term, phenomenological dark-energy fluid, or separately chosen cosmological potential is inserted. The action is frozen before confronting observations—this is the central protocol rule. What the Paper Does The paper derives the exact Jordan-frame Friedmann and scalar equations for the homogeneous zero-charge branch, transforms to the Einstein frame, obtains the positive kinetic coefficient and c_T=1, and shows that the QFT vacuum \Phi=0 is Minkowski rather than de Sitter. Nonzero constant-field accelerated solutions are extrema of W=M_*^4V/F^2. Introducing m=\sqrt A,\qquad \kappa={AC\over B^2},\qquad \delta={m^2\over BM_*^2},\qquad u=\xi\delta,\qquad s={B\varphi^2\over m^2}, reduces the de Sitter condition exactly to a cubic polynomial: 1-\left(1+\frac u2\right)s+\frac{3\kappa}{4}s^2+\frac{u\kappa}{8}s^3=0. At minimal coupling, a maximum–minimum pair exists for 1/4<\kappa<1/3. At a stable root, {H_*^2\over m^2}=\delta\,{v(s_*)\over3f(s_*)}, exposing a scale tension: a particle-scale scalar with ordinary normalization produces curvature far above the observed late-time Hubble scale. The exact action was subsequently implemented in a Horndeski Einstein–Boltzmann solver using G_2=X-\mathcal M^2\left({\chi^2\over2}-{\chi^4\over4\delta}+{\kappa\chi^6\over8\delta^2}\right),\qquadG_4={1\over2}+{\xi\chi^2\over4},\qquad G_3=G_5=0. Stable low-coupling islands were found. Native Planck 2018 likelihoods, the official full-covariance DESI DR2 BAO vector, and Pantheon+ were evaluated. The best audited point in the restricted ensemble, (\delta,h)=(210,0.67660), at fixed low-coupling (\kappa,u)=(0.26,0.001), gives \chi^2_{\rm Canvas}=2436.6409,\qquad\Delta\chi^2_{\rm Canvas-GR}=-0.077, an essentially exact raw-likelihood tie with the identically assembled GR control. The dataset decomposition is: · Planck 2018: \chi^2_{\rm Planck}=1013.1666· DESI DR2 BAO: \chi^2_{\rm DESI}=19.8944· Pantheon+: \chi^2_{\rm Pantheon+}=1403.5799 For growth amplitude, S_8^{\rm Canvas}=0.8381 versus S_8^{\rm GR}=0.8375, showing the tested Canvas modification changes the Planck-calibrated growth amplitude only minimally. Complexity penalties, however, favor GR/\LambdaCDM. If Canvas is counted as having one additional effective parameter, \Delta{\rm AIC}\simeq+1.92 and \Delta{\rm BIC}\simeq+8.22. If three additional effective parameters are counted, \Delta{\rm AIC}\simeq+5.92 and \Delta{\rm BIC}\simeq+24.81. Thus penalized model comparison favors GR/\LambdaCDM. What This Paper Does Not Establish The present cosmology does not establish: · a primitive derivation of \kappa,u,\delta;· a primitive prediction of h,\omega_b,\omega_{\rm cdm},A_s,n_s,\tau;· a derived physical prior/stable-manifold measure;· a completed posterior and Bayesian evidence against identically sampled \LambdaCDM;· an independent weak-lensing likelihood;· a solution of the H_0 or S_8 tensions;· a proof that the cosmological scalar is the same physical pole as a particle-sector resonance;· a parameter-free prediction of the observed dark-energy density. Why This Matters The cosmology programme has progressed substantially beyond a correspondence argument. It possesses a frozen generally covariant action, exact background equations, a calculable de Sitter phase structure, explicit ghost and gradient conditions, a validated exact Einstein–Boltzmann implementation, and genuine likelihood evaluations against Planck, DESI DR2, and Pantheon+. The strongest empirical statement is deliberately modest: the effective cosmology is not empirically dead, but neither is it evidence for new physics. The main remaining problem is no longer "can the action produce a viable cosmic history?"—the answer to that existence question is yes within the conditional effective theory. The decisive questions are instead: derive the successful parameter measure from Canvas primitives, and perform a fully sampled, stability-aware evidence comparison. The work is best classified as a mathematically coherent and empirically competitive effective completion of the Canvas framework, not a parameter-free fundamental cosmological prediction. A completed posterior/evidence calculation with identically sampled \LambdaCDM, a derived stable-manifold measure, an independent weak-lensing likelihood, and primitive derivation of the successful cosmological parameters remain open. Keywords: canvas cosmology, scalar-tensor theory, de Sitter phase, Einstein-Boltzmann solver, Planck likelihood, DESI BAO, Pantheon+, Bayesian evidence, model comparison, covariant action