Numerical and Observational Tests of QIMG Thermalisation: BBN, CMB, Entropy, and Radiation-Density Constraints

Quantum-Informational Metric Genesis Cosmology (QIMG Cosmology) and its associated thermalisation framework propose a layered transition from pre-FRW informational initial conditions to a physically realised hot early universe. In the preceding microscopic thermalisation work, the residual QIMG stress-energy representation \[ Tʳᵉˢμν = (1-Θₜₕ) Tⁱⁿᶠᵒμν \] was identified as the object undergoing thermalisation, and the effective action-level chain \[ Sₜₕ Jᵗʰν Γ_i(T) Θₜₕ(t) \] was introduced. That construction supplied a microscopic origin for the transfer current and for the temperature-dependent channel rates into radiation, matter, and plasma response sectors. However, it did not yet test whether the resulting thermalisation dynamics can generate a viable Hot Big Bang history compatible with observational constraints. The present work develops the next layer of the QIMG programme by formulating a numerical and observational testing framework for QIMG thermalisation. Its central aim is to evolve the thermalisation system from the microscopic channel rates \(Γ_i(T)\) into cosmological observables and consistency variables, \[ ρrad(t), T(t), s(t), η_b(t), P_ζ(k), C_ . \] Here \(ρrad(t)\) is the radiation-density history, \(T(t)\) is the temperature evolution, \(s(t)\) is the entropy-density evolution, \(η_b(t)\) is the baryon-to-photon ratio, \(P_ζ(k)\) is the primordial curvature spectrum, and \(C_\) is the CMB angular power spectrum. The framework begins from the rate equation \[ Θ̇ₜₕ = (1-Θₜₕ) Γₜₒₜ(T), Γₜₒₜ(T) = ∑_i Γ_i(T), \] and couples it to background evolution equations for the residual, radiation, matter, and plasma sectors. Since the densities are treated as mass-density-like quantities, while the channel transfer rates \(Q_i\) are energy-density transfer rates, the source terms enter the density equations through \(Q_i/c^2\). This convention preserves consistency with \[ Q_i = Γ_i(T)ρᵣₑₛc^2. \] The paper then defines the conditions under which QIMG thermalisation can recover a standard radiation-dominated hot phase before Big Bang nucleosynthesis. These conditions include completion of thermalisation, \[ Θₜₕ→1, \] positive radiation production, \[ ρrad(t)>0, \] non-negative entropy production, \[ ∇_μ s^μ≥0, \] and compatibility with BBN-sensitive quantities such as \(T(t)\), \(s(t)\), \(η_b(t)\), and the effective radiation density. In addition to background evolution, the work outlines how perturbations in the residual QIMG sector may be transferred into radiation and matter perturbations. This provides the basis for connecting QIMG thermalisation to the primordial curvature spectrum \(P_ζ(k)\) and, ultimately, to CMB observables \(C_\). The present paper does not claim to perform a final Boltzmann-code-level comparison with observational data. Instead, it establishes the numerical system, consistency tests, parameter-space criteria, and failure modes required for such a comparison. The central question addressed is therefore not whether QIMG thermalisation is assumed to be viable, but whether its rate-driven evolution can be tested against standard early-universe constraints. In this sense, the present work converts the microscopic QIMG thermalisation framework into a falsifiable numerical and observational programme.