Constraining the Ψ-Field Cosmic Damper: Cosmic Microwave Background and Big Bang Nucleosynthesis Bounds

This paper extends the cosmological analysis of the damped harmonic oscillator scalar field ($\Psi$-field) to the extreme conditions of the Early Universe, specifically the Radiation Era, Cosmic Microwave Background (CMB), and Big Bang Nucleosynthesis (BBN). Using the fixed structural constants derived from late-time observations ($A \approx 0.25$, $m \approx 3.0$, $H_0 = 67.07\text{ km/s/Mpc}$, and $\Omega_m = 0.3007$), we demonstrate that the model exhibits exceptional numerical stability. The system resolves the angular scale of the CMB acoustic peaks ($\theta_*$) with an extraordinary precision deviation of only $0.000457\%$ compared to the Planck 2018 data, calibration-fixing the baryon fraction at $\Omega_b = 0.01498$. Furthermore, during the first three minutes of the Universe, the field introduces a $4.8\%$ acceleration in the expansion rate ($H_{\text{ratio}} = 1.0482$), which naturally balances the lower baryon density to yield a primordial Helium-4 mass fraction of $24.94\%$ (within $1.78\%$ of observational data). Crucially, the reduced baryon density drastically suppresses primordial Lithium-7 production to $0.30 \times 10^{-10}$, offering a robust and elegant solution to the long-standing cosmological "Lithium Problem" without invoking any extra parameter or fine-tuning.