Reionization history

Reionization history — DCT predicts a 15% upward τ shift, consistent at 0.43σ.

Prediction	\(\tau\) shifted upward by \(\sim 15\%\) (Avrami-enhanced early structure)
Measured	Planck PR3 \(\tau = 0.054 \pm 0.007\) + JWST z>10 ionising photons
Residual	0.43σ
Status	PASS
Source paper	DCT-CMB-01

Mechanism

DCT crystallisation enables earlier and brighter star formation at \(z = 10\)–\(13\) (see /observables/jwst-early-galaxies/), giving a \(\sim 15\%\) upward shift in the reionisation optical depth \(\tau\). Consistent with Planck PR3 + JWST joint analysis.

Derivation

The growth-of-structure equation in the Jordan frame picks up a late-time correction from the Avrami profile: \(\delta'' + 2H\delta' - 4\pi G \rho_m P_{\rm eff} \delta = 0\) with \(P_{\rm eff} \to 1\) at high redshift and a mild \((1 - P_0)\) suppression at \(z = 0\). Under the canonical constant-\(P_0\) treatment this gives \(S_8 \approx 0.776\) against KiDS-Legacy 2025 \(0.815 \pm 0.022\), a \(\sim\!1.8\sigma\) tension; an interim Avrami-extended branch that closed the tension at \(S_8 = 0.811\) was reverted on (see Updates).

Python verification

The verification script for this observable is cmb_analysis.py. Run it with python3 cmb_analysis.py to reproduce the canonical DCT result against the public-archive measurement source listed above.

Methodology

Domain	Cosmology (COS)
Input data source	See "References" below for the canonical public-archive citation. The verification script consumes the published value (or the public dataset, where applicable) and compares against the DCT closed-form prediction.
Measurement procedure	The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference; no internal recalibration is applied.
Acceptance threshold	HIT: residual within 1σ of measurement. SOFT: directional agreement, residual within bracketing range. OPEN: untested or unresolved.
Falsification threshold	MISS: prediction excluded at ≥3σ by the canonical measurement under the corpus-canonical (constant-\(P_0\)) treatment.
Current status	See the verdict pill in the prediction table above.

Cross-references

Related observables in the same domain: planck-ee-tau · jwst-early-galaxies.

Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.

Audit notes

Status post-: this observable's verdict above reflects the corpus-canonical (constant-\(P_0\)) treatment. Any prior interim Avrami-extension framing has been reverted (see /updates/ for the change log). The cluster-paper deep-link above (DCT-COS-01) is the canonical source of the derivation chain.

References

Back to all observables or the predictions table.