8.7 CMB Acoustic Peaks

This paper derives the positions of the Cosmic Microwave Background (CMB) acoustic peaks from the sound speed of the three-field coupling. The acoustic peak positions in the CMB temperature power spectrum are determined by the sound speed at recombination, and is derived from the steady-state distribution of the ℳ-ℐ sector coupling. Without dark matter, the first peak position is naturally given by the 𝒞-sector metric correction. The peak-height ratios are jointly determined by the baryon-to-photon ratio (Theorem 8.5.2.01) and the baryon asymmetry (Theorem 8.6.2.01). This paper provides the complete derivation of the sound speed from three-field coupling, the algebraic calculation of , the rigid prediction of the tensor-to-scalar ratio , and the algebraic origin of the scalar spectral index .