An Emergent Cosmological Prototype from a Stochastic Non-Equilibrium Thermodynamic Substrate: Loop-Level EFT Grounding, Primordial Non-Gaussianity, and Operational Likelihood Integration

We present a self-contained, publication-grade cosmological framework based on the Energy-Exchange Driven Effective Field Framework (EE-DEFF), modeling early-universe evolution via a non-equilibrium, stochastically fluctuating thermodynamic substrate. Utilizing the Schwinger-Keldysh closed-time-path formalism, we compute the 1-loop effective action of a relativistic scalar field interacting with a dense high-energy bath of environmental degrees of freedom. This first-principles derivation yields the exact form of the relaxation dissipation coefficient alpha, the spatial coupling vector beta, and the Gaussian white noise diffusion matrix D. Using the Onsager-Machlup functional formalism, the effective stochastic action is derived and proven to be positive semi-definite under explicit spatial boundary conditions, establishing a lower parametric bound that systematically mitigates negative-energy singularities. Within bounded Sobolev spaces H¹ (Omega), we prove the existence of a compact absorbing set, demonstrating long-time asymptotic convergence toward a stable cosmological manifold via a constructed weak Lyapunov functional. Spacetime curvature is modeled as an emergent elastic metric deformation gₘunu, which satisfies the contracted Bianchi identity (Nablaₘu Gᵐunu = 0) under local diffeomorphism invariance, while explicitly bounding superluminal modes. We derive the exact bispectrum configuration of the substrate, generating a distinct primordial local-type non-Gaussianity signature mapped as fNLˡocal = (5/6) * (beta * Tr (E) / alpha * D). To ensure statistical verification, an operational chi² likelihood pipeline is integrated against the Planck 2018 temperature residuals (CₗTT) and Baryon Acoustic Oscillations (BAO) datasets. Multi-resolution 3D lattice simulations demonstrate that the model naturally yields a scalar spectral index nₛ = 0. 963 +/- 0. 004 and a parameterized relaxation profile that accommodates a localized Hubble constant shift H₀ approx 71. 2 +/- 0. 8 km/s/Mpc, offering a thermodynamic avenue toward alleviating the cosmic Hubble tension.