The CMB power spectrum's acoustic peaks sit at specific angular scales that depend on the geometry of the universe and the sound speed of acoustic oscillations in the primordial plasma. Joint fits show subtle systematic offsets between the inferred acoustic-scale standard ruler and other cosmological parameters (Addison 2018; Planck 2018). DESI BAO measures r_d ≈ 147 Mpc; Planck CMB gives r_d ≈ 150 Mpc, a 2.3σ mismatch.
The standard model assumes the BAO scale is set by a single universal sound horizon at the drag epoch, propagated forward through a constant-Λ FRW expansion. Pre-recombination sound speed c_s² = 1 / [3(1 + R)] places the baryon-loading term R in the denominator. Once the plasma composition is fixed, the model produces one r_d value and demands every probe agree.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, the bulk acoustic-peak structure follows from the Plasma Equivalence Theorem: once the cascade-thermalized plasma reaches its post-thermalization thermodynamic state, its subsequent acoustic evolution is governed by the same six-parameter framework as ΛCDM (P29, P30). Two plasmas that arrive at the same thermodynamic state by different paths produce acoustically identical CMB power spectra, regardless of origin.
SCT's cascade-thermalized plasma reaches the standard six-parameter state {T_dec, η, Y_p, τ_reion, k_eq, r_s} through a different history than ΛCDM's hot-dense origin, but the resulting spectrum is acoustically identical at multipoles l > 30 (P30). The cascade terminates well before t ≈ 1 second (P40), so BBN proceeds at thermal equilibrium under standard Standard Model thermodynamics (P42), reproducing the observed light-element abundances. The acoustic peak positions in SCT therefore reproduce the ΛCDM predictions to standard precision unless a post-cascade modification intervenes.
Two such modifications produce the observed mild offsets. First, the CAR formula c_s² = (1 + R_b)/3 (paper 4216) inverts the baryon-loading position, with R_b in the numerator as a coherent-amplification term (P45); CAMB integrated under CAR gives r_d ≈ 149.1 Mpc, between DESI's 147 and Planck's 150, reducing the inter-dataset tension (cross-link to recid 8). Second, the dynamical Λ_eff(x,t) field locally modifies the angular-diameter distance to last scattering when the line of sight passes through underdense regions like the KBC supervoid (P17, P19). The combined effect is at the sub-percent level, exactly the size of the observed offsets.
If precision Planck or CMB-S4 reanalysis finds the acoustic peak positions inconsistent with the Plasma Equivalence Theorem prediction at greater than 3σ (i.e., the bulk l > 30 spectrum requires a non-standard six-parameter framework not reducible to {T_dec, η, Y_p, τ_reion, k_eq, r_s}), the M2 framework fails. Equivalently, if DESI Year 5 measures r_d outside [146, 152] Mpc at greater than 3σ, the CAR-modified sound horizon is refuted.