Optical Depth Scatter

The optical depth to reionization τ is constrained from multiple independent observables — the CMB EE polarization bump amplitude, the Lyman-alpha forest transmission statistics, and the kinematic Sunyaev-Zel'dovich effect from galaxy clusters — but these constraints do not all converge on the same value. The scatter between different τ estimates, at the level of Δτ ~ 0.01–0.02, exceeds what ΛCDM's simple reionization model predicts and suggests either a complex or extended reionization history, or unresolved systematic errors in multiple independent measurements. In SCT, the scatter in τ measurements is expected because different observables probe different aspects of an inherently complex reionization process. The pre-existing matter in the colliding pockets means that reionization proceeded in at least two phases: an early phase driven by the thermalization of pre-existing ionizing sources at high redshift, and a later phase driven by the first generation of post-collision Population II and III stars.

Each observable is sensitive to a different combination of these phases: the polarization bump probes the total column integral of the ionized fraction weighted by the CMB quadrupole amplitude, the Lyman-alpha forest probes the ionized fraction at z ~ 5–6 from the ground up, and the kSZ probes the line-of-sight velocity-weighted free electron column in the local universe. Because these observables weight the reionization history differently, a two-phase reionization gives them systematically different effective τ values. The apparent scatter is therefore not observational noise or systematic error but a genuine physical signal encoding the two-component structure of SCT's reionization history — a prediction that can be tested by future 21 cm cosmology surveys sensitive to the neutral hydrogen distribution at z > 10.