Lorentz-Stable Dynamics and Emergent Structure in a Two-Component Environmental\\ Quantum Field Theory (TCPE–QFT v2.0)

We present TCPE–QFT v2.0, a nonperturbative, environment-coupled quantum field theory formulated in (3+1)-dimensional spacetime and embedded in a cosmological FLRW background. The model extends previous frameworks Theory of Coherent Physical Encoding (TCPE and TCPE v1.0) by incorporating dynamic feedback between a primary scalar field φ(x,t) and an auxiliary environment field χ(x,t), leading to the emergence of spatially coherent structures, mode-selective amplification, and observable phase transitions.Key advancements include a full Lorentz-invariant Lagrangian with ultraviolet stability, a reformulated Euclidean instanton analysis using variational techniques, and a numerical implementation that enables real-time simulations in both 1D and spherically symmetric 3D regimes. Quantitative observables—such as the spectral power P(k,t), correlation length ξ(t), spectral entropy Sₖ(t), and total energy E(t)—validate the theory’s predictive capacity and internal consistency.The model is compared against known benchmarks from lattice-based reheating and preheating dynamics (Frolov, Kofman, Podolsky), and its predictions for cosmological observables Ω_φ(z) and w(z) remain within 1σ bounds of Planck and SN Ia data. TCPE–QFT v2.0 thus offers a falsifiable, structurally grounded alternative to ΛCDM, with implications for the study of quantum decoherence, emergent structure, and early-universe dynamics.