The Primordial Sound of the Cosmos: Baryon Acoustic Oscillations and the Frozen Spectrum of Energy Quanta

This monograph presents a radical re-interpretation of Baryon Acoustic Oscillations (BAO) within the framework of Energy Quantum Theory (EQT)—a process-ontological physics that replaces static "entities" with the dynamics of the frequency-resolved energy quanta density field \rho(\mathbf{r}, t, f). We demonstrate that the CMB temperature fluctuations are not random primordial perturbations, but high-frequency gradient transients (\nabla \rho_H \neq 0) generated by the first astrophysical structures (e.g., Population III stars, primordial black holes). These transients drive a full-spectrum cascade via the nonlinear term k \rho_H^2, producing low-frequency energy quanta (f_L \sim 10^{-16}\,\text{Hz}) whose collective gradient flow manifests as the BAO "sound wave."

Crucially, we provide the first ab initio derivation of the sound speed c_s = c/\sqrt{3} from EQT’s master equation, showing it emerges from the balance between frequency-dependent diffusion (D(f) \propto f^{-1}) and dissipation (\Gamma(f) \propto f)—not from an ad hoc equation of state. The observed BAO scale (r_s \approx 150\,\text{Mpc}) is then identified as the freezing length of this wave at recombination (z \approx 1100), where the system transitions into a local pre-freezing state due to dissipation dominance (\Gamma > S).

This BAO mechanism is unified with the JWST "precocious galaxy" phenomenon: both arise from the same high-frequency driver, with different frequency modes freezing at distinct times according to the universal freezing spectrum t_{\text{freeze}}(f) \propto f^{-1}. Furthermore, the planar morphology of galaxies and the anisotropy of the BAO signal are explained by the cosmic web topology of the ultra-low-frequency dark energy field (\nu \lesssim 10^{-4}\,\text{Hz}), which guides the directional propagation of the gradient flow.

The work culminates in three falsifiable predictions: (1) BAO–CMB cross-correlation with significant dipole modulation (p < 0.01); (2) a high-redshift (z > 1100) 21cm BAO scale r_s < 147\,\text{Mpc}; (3) JWST galaxy spin axes aligned with DESI-identified filaments. By grounding BAO in a causal, cross-scale, and non-teleological process ontology, this monograph resolves the "time coincidence crisis" of early structure formation and establishes BAO not as a passive "standard ruler," but as the first audible heartbeat of the cosmic rhythm.