The CMB optical depth to reionization τ is supposed to be a single global parameter tightly linked to a smooth ionization history. Different analysis pipelines and different combinations with external datasets (BAO, LSS) yield discrepant or scattered τ estimates (Kaplinghat 2003; Planck VI 2020; White 2021). The scatter hints that reionization is more complex than the simple single-epoch templates assume.
The standard model assumes a single smooth reionization epoch around z ≈ 6 to 8 produced by the first stars, parameterized by one optical depth value. Recovering scatter across analysis pipelines within the model requires either pixel-level systematic improvements or invoking patchy reionization, neither of which is parsimonious within minimal ΛCDM.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, reionization is naturally multi-epoch rather than a single smooth event. Post-collision reheating events (P47) operate at staggered times across the cosmological era between cascade termination (P40) and the first-star epoch, re-ionizing localized regions on different timescales. Different sky directions therefore traverse different reionization histories and accumulate slightly different optical depths.
The Plasma Equivalence Theorem (P29, P30) governs the bulk plasma evolution at l > 30, fixing the global average τ. The directional scatter at the 1 to 2% level emerges from the multi-phase reheating distribution, with optical depth correlated with cosmic-web environment (denser regions reheat earlier, voids later). Pre-existing matter from prior cascade cycles (P25) supplies the baryon budget that reheats; the cascade-axis geometry (P22, P36, P64) introduces a weak directional preference at the cascade-axis alignment level.
The same M2 framework that resolves the polarization-bump anomaly (recid 39) and the heated-CMB-term signature (recid 40) accounts for the optical-depth scatter as one more observational projection of multi-phase reheating. There is no need to invoke pipeline systematics or to posit a single fine-tuned reionization history that cannot account for the directional variation. The scatter is the predicted signature, not the noise.
If 21-cm tomography (HERA, SKA) finds reionization proceeded smoothly from a single redshift onset across all sky directions (no environmental or directional dependence at the 1% level), the M2 multi-phase reheating prediction fails. Equivalently, if cross-correlating τ estimates with cosmic-web environment finds zero correlation at greater than 2σ, the directional-scatter prediction is refuted.