Optical Depth Scatter

The optical depth to reionization is cosmology's most revised number, and its revisions have never settled into comfort. Tau measures the fraction of CMB photons rescattered by the reionized universe, anchoring when the first luminous objects ionized the cosmos and calibrating, through its degeneracies, the primordial amplitude, sigma_8, and the neutrino-mass bounds. Its history is a march of discrepant precision: WMAP's first year announced 0.17 (very early reionization), settling to 0.089 by the nine-year release; Planck's LFI gave 0.066; the HFI reanalysis dropped to 0.054; the SROLL2 and PR4 reprocessings have since drifted estimates between 0.051 and 0.063 depending on likelihood and dataset combination, while joint fits with large-scale structure prefer values higher still. Each shift exceeded the prior uncertainty; each was attributed to systematics newly excavated; and the current spread across defensible analyses, of order 20 percent of the value, remains wider than the quoted per-analysis errors.

The scatter matters doubly. Practically, tau's uncertainty is now the limiting systematic on the neutrino-mass bound and a lever on every growth-tension argument, so its instability propagates everywhere precision cosmology claims closure. Structurally, tau is a single number summarizing an entire epoch, and the model assumes that epoch was simple: one roughly monotonic reionization, characterized by one midpoint. If the true ionization history were structured, extended, multi-phase, or spatially patchy beyond the standard parameterization, different estimators weighting different scales would legitimately return different effective tau values, which is what the record shows.

The standing is an unstable foundation under a precision edifice: the scatter persists across the best available reprocessings, astrophysical reionization data (quasar spectra, JWST galaxy budgets) strain the simple history independently, and definitive low-ell polarization from LiteBIRD is the designated settlement.

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