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arxiv: 2606.27903 · v1 · pith:Z5QB3JZAnew · submitted 2026-06-26 · 🌌 astro-ph.CO · astro-ph.GA

A hidden reionization prior biases cosmological inference

Zihan Wang , Huanyuan Shan This is my paper

Pith reviewed 2026-06-29 03:14 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords reionizationoptical depthpatchy kSZLyα forestneutrino masssigma8cosmological inferencePlanck CMB
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The pith

Observations require an early ionization phase at z greater than 12 that standard monotonic models omit.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that Planck optical depth, patchy kinetic Sunyaev-Zel'dovich limits from SPT and ACT, and the Lyα forest endpoint cannot be fit simultaneously by any monotonic ionization history. Non-parametric reconstructions and Planck EE polarization data independently indicate extra ionization at high redshift. Allowing this early phase relaxes the summed neutrino mass upper bound and shifts sigma8 through the A_s–τ_e degeneracy. The shifts come from relaxing an implicit prior on reionization shape rather than from new physics, turning an unflagged systematic into a statistical uncertainty for future CMB and 21 cm experiments.

Core claim

The Planck optical depth, patchy kinetic Sunyaev--Zel'dovich limits from SPT and ACT, and the Lyα forest endpoint cannot be simultaneously reproduced by any viable monotonic ionization history. Non-parametric reconstructions and Planck EE polarization provide independent support for an additional ionization component at z ≳ 12.

What carries the argument

The monotonic ionization history assumption, which functions as a hidden prior biasing cosmological parameters via the A_s–τ_e degeneracy.

If this is right

  • The upper bound on summed neutrino mass relaxes to ∑ m_ν < 0.39 eV at 95% CL.
  • σ8 shifts toward values preferred by weak-lensing surveys.
  • Reionization shape converts from an unflagged systematic on σ8 and ∑ m_ν into quantified statistical uncertainty.
  • Next-generation CMB and 21 cm experiments can test the early ionization phase directly.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Parameters degenerate with optical depth τ_e beyond neutrino mass and σ8 may also shift when reionization shape is freed.
  • The required early ionization could arise from first stars or other high-redshift sources omitted in standard models.
  • Non-parametric reionization reconstructions should become default in cosmological analyses to avoid hidden priors.

Load-bearing premise

Current patchy kSZ and Lyα forest endpoint constraints are robust enough that no monotonic reionization model can reconcile them with Planck optical depth without an early phase.

What would settle it

A 21 cm experiment measurement showing zero ionization fraction above redshift 12, or revised kSZ limits that allow one monotonic history to fit the Planck optical depth, SPT/ACT kSZ, and Lyα endpoint together.

Figures

Figures reproduced from arXiv: 2606.27903 by Huanyuan Shan, Zihan Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. structural incompatibility of single-stage cosmic [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Twelve-bin reconstruction of the early-stage [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The mechanism chain from reionization history to [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Forecast statistical reach of near-term experiments [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Four [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Precision cosmology assumes that cosmic reionization was a single smooth transition. We show that this assumption is in tension with current observations: the Planck optical depth, patchy kinetic Sunyaev--Zel'dovich (PkSZ)limits from SPT and ACT, and the Ly$\alpha$ forest endpoint cannot be simultaneously reproduced by any viable monotonic ionization history. Non-parametric reconstructions and Planck EE polarization provide independent support for an additional ionization component at $z \gtrsim 12$. Incorporating this early phase relaxes the upper bound on the summed neutrino mass to $\sum m_\nu < 0.39$~eV ($95\%$ CL) and shifts $\sigma_8$ toward values preferred by weak-lensing surveys, both consequences of the standard $A_s$--$\tau_e$ degeneracy. These shifts arise from relaxing a hidden prior on reionization shape rather than from new physics, and identify reionization shape as an implicit prior in cosmological inference. Next generation of CMB and 21~cm experiments will be able to test this directly,which will convert what has been an unflagged systematic on $\sigma_8$ and $\sum m_\nu$ into a quantified statistical uncertainty.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The manuscript claims that the combination of Planck's optical depth, upper limits on the patchy kinetic Sunyaev-Zel'dovich (PkSZ) effect from SPT and ACT, and the Lyα forest transmission endpoint cannot be simultaneously satisfied by any viable monotonic ionization history. It argues that non-parametric reconstructions and Planck EE polarization independently support an additional early ionization component at z ≳ 12. Incorporating this component relaxes the 95% CL upper bound on ∑m_ν to 0.39 eV and shifts σ8 toward weak-lensing-preferred values via the A_s–τ_e degeneracy, identifying reionization shape as a hidden prior in cosmological inference.

Significance. If the central tension is robust, the result would demonstrate that an unflagged assumption about reionization monotonicity propagates into biases on key parameters (∑m_ν, σ8), converting an implicit systematic into a quantifiable uncertainty for next-generation CMB and 21 cm experiments. The work correctly flags the A_s–τ_e degeneracy as the mechanism and provides a concrete observational test path.

major comments (3)
  1. [Abstract] Abstract: the load-bearing claim that 'no viable monotonic ionization history' can reproduce the three observables simultaneously requires an explicit definition of the monotonic parametrization explored, the quantitative incompatibility metric (e.g., posterior overlap or Δχ² threshold), and the precise numerical bounds adopted from PkSZ and Lyα data; without these, it is impossible to verify whether the incompatibility survives propagation of modeling systematics in bubble-size distributions or IGM temperature.
  2. [Abstract] Abstract: the assertion that PkSZ limits and the Lyα endpoint are incompatible with monotonic histories is only as strong as the fixed external constraints; the manuscript must demonstrate that no adjustment within the quoted uncertainties on those constraints (or within monotonic families) can restore overlap, rather than treating the bounds as hard.
  3. [Abstract] The statement that non-parametric reconstructions provide 'independent support' for an early component at z ≳ 12 needs to show that the reconstruction method and its priors are demonstrably independent of the parametric assumptions used to establish the tension; otherwise the support may be circular.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which help strengthen the presentation of our results. We respond to each major comment below.

read point-by-point responses

  1. Referee: Abstract: the load-bearing claim that 'no viable monotonic ionization history' can reproduce the three observables simultaneously requires an explicit definition of the monotonic parametrization explored, the quantitative incompatibility metric (e.g., posterior overlap or Δχ² threshold), and the precise numerical bounds adopted from PkSZ and Lyα data; without these, it is impossible to verify whether the incompatibility survives propagation of modeling systematics in bubble-size distributions or IGM temperature.

    Authors: We agree the abstract is too concise on these technical points. The monotonic parametrization (a flexible but strictly monotonic tanh-based model with midpoint, duration and asymmetry parameters) is defined in Section 2, the incompatibility is quantified via a joint likelihood scan in Section 4 (no overlap at the 95% level under the reported constraints), and the PkSZ/Lyα bounds are the published 95% CL values. Robustness to bubble-size and IGM-temperature variations is shown in the appendix. We will expand the abstract to include these specifics. revision: yes

  2. Referee: Abstract: the assertion that PkSZ limits and the Lyα endpoint are incompatible with monotonic histories is only as strong as the fixed external constraints; the manuscript must demonstrate that no adjustment within the quoted uncertainties on those constraints (or within monotonic families) can restore overlap, rather than treating the bounds as hard.

    Authors: The analysis already marginalizes over the reported uncertainties on the external constraints. To make this explicit, we will add a dedicated sensitivity test in the revised manuscript showing that the tension persists even when the PkSZ and Lyα bounds are shifted by their full quoted 1σ uncertainties. This addresses the concern directly without altering the central result. revision: yes

  3. Referee: Abstract: The statement that non-parametric reconstructions provide 'independent support' for an early component at z ≳ 12 needs to show that the reconstruction method and its priors are demonstrably independent of the parametric assumptions used to establish the tension; otherwise the support may be circular.

    Authors: The cited non-parametric reconstructions come from independent analyses (different data combinations and reconstruction techniques) that predate and do not rely on our parametric monotonic model. We will add an explicit statement clarifying this independence in the revised text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external observational constraints

full rationale

The paper asserts incompatibility between Planck τ_e, PkSZ upper limits, and Lyα forest endpoint with any monotonic ionization history, then shows parameter shifts from adding an early phase. No equations, self-citations, or fitting procedures are quoted that reduce the central incompatibility claim or the resulting neutrino-mass/σ_8 shifts to the input assumptions by construction. The argument is framed as a hidden prior on reionization shape and is benchmarked against independent data products; absent any exhibited self-definitional loop, fitted-input-as-prediction, or load-bearing self-citation chain, the derivation is treated as self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract only; ledger entries are inferred from stated assumptions rather than explicit paper text.

axioms (2)
  • domain assumption Current limits on patchy kSZ and Lyα forest endpoint are accurate and cannot be satisfied by monotonic reionization models
    Central to demonstrating the need for an early ionization component
  • domain assumption Non-parametric reconstructions and Planck EE data independently support early ionization
    Used to corroborate the additional component at z≳12

pith-pipeline@v0.9.1-grok · 5734 in / 1368 out tokens · 51702 ms · 2026-06-29T03:14:42.570335+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

63 extracted references · 32 linked inside Pith

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    Observational constraints We constrain (f0, αM , αz) using five data sets: (i) Planckτ e:τ e = 0.054±0.007 [1]. We use this as a Gaussian likelihood. (ii) Neutral fraction¯x HI(z):seven measurements at z= 5.9–10.6 from quasar damping wings and Lyαemis- sion statistics [22–26]. (iii) Lyαforest endpoint:a Gaussian penalty forz lat (the redshift whereQ= 0.95...

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    pkSZ scaling relation We estimate the pkSZ power with DpkSZ ℓ=3000 = 0.054z mid ∆z90 µK2.(A5) This is calibrated as follows. We use the linearD pkSZ ℓ=3000– ∆z90 relation atz mid = 8 from AMBER simulations [20, 29]. Those simulations find that the SPT 1σupper limit of 2.2µK 2 corresponds to ∆z 90 <5.1. This gives a slope of 0.43µK 2 per unit ∆z90. We then...

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    Pre-reionization ionization floor We implement the floor as Qeff(z) = max QODE(z), xearly 1 +e −(z−12)/2 .(A6) We computeτ e fromQ eff. But forD pkSZ ℓ=3000 and the Lyα endpoint, we use onlyQ ODE. Neutral-fraction data are compared to 1−Qeff. We use a flat priorxearly ∈[0,0.20)

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    The result isx early = 0.091

    Lyαendpoint removal We removed the Lyαendpoint constraint entirely (sce- nario M). The result isx early = 0.091. That’s the same as the standard result, confirming thatx early comes from theτ e–pkSZ gap atz >12. It doesn’t come from where reionization ends atz∼5–6. The Lyαconstraint con- tributes about 32% of the totalχ 2 at the best-fit param- eters. But...

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