{"id":"ebe875d6-f4de-46c4-9c6e-89bb6d41e0a9","arxiv_id":"2504.20025","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"During reionization, the 21cm brightness field has a zero-linear-bias epoch, and if analyses reach its sampling noise floor, local primordial non-Gaussianity constraints could improve by roughly an order of magnitude.","lead":"This paper studies whether the 21cm radio glow from hydrogen during the universe's reionization era can reveal how the earliest density fluctuations were seeded. It finds a special 'zero-bias' moment that could give roughly ten times tighter constraints on primordial non-Gaussianity, but only if future surveys reach an idealized noise floor.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The exact zero-bias snapshot has zero Fisher information for fNL; the reported factor-10 gain is a near-zero-bias band-averaged effect, so the 6 MHz band-average forecast must be recomputed.","rationale":"The paper's strongest quantitative claim is the N4 forecast at the zero-bias epoch. The paper itself demonstrates in the Appendix that b1 = 0 is a Fisher minimum; combined with the single-snapshot treatment of a 6 MHz band, this means the reported sigma ~ 0.4 cannot be the Fisher information at the exact zero-crossing. The only way the number is meaningful is if it arises from averaging over the band's redshift evolution, which the main forecast does not do. This is more immediately load-bearing than the spin-temperature approximation: even granting Ts >> TCMB and neglecting velocity gradients, the exact-zero Fisher information vanishes. The spin-temperature issue is real and the paper caveats it (citing Ref. [22]), but it shifts the location of the crossing rather than changing the mathematical structure of the Fisher minimum. The reader's weakest_assumption focused on spin temperature, though the reader's rationale did list the band-average point as a condition, so agreement is partial. The recommended verdict remains conditional: the band-average test should be run, along with the reader's other conditions, before the factor-of-10 claim is taken at face value.","tokens_in":15074,"tokens_out":15675,"duration_ms":166122,"concrete_test":"Recompute the N4 forecast for a 6 MHz survey by integrating Eq. (13) over the full redshift extent of the band: use the sequence of simulation snapshots inside each band (or a smooth interpolation of b21_1(z), b21_phi(z), and N4(z)) and sum the per-slice Fisher matrices before inverting, for survey centers at the zero-crossing redshift and at +/-0.25 in z. Also evaluate Eq. (13) at the interpolated b21_1 = 0 redshift to confirm that F_fNL = 0 there. If the band-averaged sigma(fNL) for the zero-crossing-centered survey is not approximately 0.4, or if the minimum sigma shifts to a nonzero-bias survey center, then the headline 'zero-bias epoch' improvement is an artifact of the single-snapshot approximation and should be restated as a near-zero-bias band-averaging effect.","verdict_should_be":"UNCHANGED","load_bearing_attack":"At the exact zero-bias epoch, Eq. (13) gives F_fNL = 0 for any finite noise spectrum Ni, because the linear response to fNL is proportional to b21_1 * b21_phi * alpha(k) * P(k), while the covariance is (b21_1^2 P + Ni)^2. The paper's own Appendix notes that b1 = 0 is a Fisher minimum, with maxima at b1 = +/-sqrt(Ni/P). Thus the headline N4 improvement cannot come from the zero-crossing snapshot itself; it must come from nearby redshifts where b1 ~ sqrt(N4/P). However, the forecasts treat each 6 MHz survey as a single snapshot with constant properties: 'we take our fiducial survey setups centered at a simulation snapshot (with constant properties within that snapshot) to be a reasonable approximation.' Near the crossing, b1 changes sign across the band, so the band-averaged Fisher information is not equal to the central-snapshot Fisher information. In the single-snapshot approximation, centering exactly on b1 = 0 gives F = 0, yet the text reports sigma(fNL) ~ 0.4 at the zero-bias epoch for N4. This is an internal tension: either the reported gain is a band-averaging effect that has not actually been computed, or the forecast is evaluating a neighboring snapshot and mislabeling the zero-bias epoch. The claimed factor-of-10 improvement is therefore not yet supported by the calculation as written. A secondary algebra issue appears in the Appendix: Eq. (25) writes F = A b1^2/(1 + B/b1^2)^2, which behaves as b1^2 at large b1 rather than the correct 1/b1^2; the extrema quoted in the text are nevertheless the correct ones, but the discrepancy reinforces the need for a clean band-average computation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that during reionization there generically exists an epoch at which the linear bias of the 21cm brightness temperature field crosses zero, making 21cm radiation a natural 'zero-bias tracer' for local primordial non-Gaussianity in the sense of Castorina et al. Using the 21cmFAST OPT simulation, the author measures the evolution of the linear bias b21_1 and the PNG bias b21_phi via Separate Universe simulations, and defines four progressively optimistic noise spectra N1-N4 that model different analysis strategies from auto-power-spectrum to field-level/sampling-noise-limited. A Fisher forecast with 6 MHz bandwidth surveys centered on snapshots from z~7 to 15 yields sigma(fNL) as low as ~0.4 for the N4 noise model at the zero-bias epoch, a claimed factor-of-10 improvement over lower redshifts, while showing that the naive N1 analysis cannot reach sigma(fNL) <= 1. The paper concludes that reaching the sampling-noise floor is essential to exploit the zero-bias epoch.","tokens_in":15386,"tokens_out":9147,"duration_ms":89035,"significance":"If the central claim holds, the zero-bias epoch would provide a new observational target for 21cm surveys and for field-level analysis techniques, potentially improving local PNG constraints by an order of magnitude over conventional reionization-epoch forecasts. The work uses simulation-calibrated bias and noise coefficients rather than assumed values, computes b21_phi with Separate Universe techniques, and provides an analytic appendix that attempts to explain the structure of the forecast. The comparison with previous reionization simulations supports the qualitative existence of a zero-crossing. However, as detailed below, the exact-zero-bias Fisher pathology and the absence of an explicit band-averaged forecast currently undermine the headline factor-of-10 claim, and the spin-temperature assumption needs quantitative sensitivity testing. The underlying idea is timely and the methodology is largely sound, so the issues are fixable within the scope of a revision.","major_comments":[{"comment":"At b21_1 = 0 the integrand in Eq. (13) has a zero numerator and a finite denominator, so F_fNL = 0 identically for any finite noise spectrum Ni(k). The main text nevertheless reports sigma(fNL) ~ 0.4 at the zero-bias snapshot for the N4 analysis, which cannot arise from Eq. (13) evaluated at that snapshot. Either the forecast is actually evaluated at a neighboring snapshot with b21_1 != 0, or it implicitly averages over the 6 MHz band within which the bias changes sign; neither is described. The Appendix remark that finite snapshot sampling over-estimates the exact zero-bias Fisher information acknowledges the issue but does not reconcile it with the main-text presentation. Please recompute the band-averaged forecast with b1(z) varying across the survey window, or restate the claim as applying to the closest non-zero-bias snapshot with the resulting b1 value shown.","section":"The Fisher Matrix, Eq. (13), Fig. 3"},{"comment":"The algebraic form of the single-k Fisher information is incorrect. From Eq. (13) the k-dependent piece is proportional to b1^2 P^2/(b1^2 P + N)^2, which for constant P and N is A b1^2/(b1^2 + B)^2 = A/[b1^2 (1 + B/b1^2)^2] with B = N/P. The published expression A b1^2/(1 + B/b1^2)^2 behaves as A b1^2 at large |b1|, the opposite of Eq. (13) and of the trend in Fig. 3. The stated extrema at b1* = {-sqrt(B), 0, sqrt(B)} belong to the corrected expression, so the derivation should be redone and the corrected Laurent form used throughout.","section":"Appendix, Eq. (25)"},{"comment":"The zero-bias forecast assumes Ts >> TCMB and neglects velocity gradients, but at the claimed zero-bias epoch z ~ 10.3 the simulation gives Ts ~ 3 TCMB, so the factor (1 - TCMB/Ts) is order 2/3 and its fluctuations are not obviously negligible. Residual spin-temperature fluctuations can shift b21_1, modify b21_phi, and change all Ni(k), any of which can move or erase the zero-bias epoch on which the headline forecast depends. Citing Ref. [22] without a quantitative estimate is not sufficient; please add a sensitivity test, for example using the full Ts field from the same simulation or the approximations tested in Ref. [22].","section":"Time evolution of the 21cm linear bias; Fig. 1"}],"minor_comments":[{"comment":"There are several typographical errors, including 'marginalyl' in the Fisher Matrix section, 'satisfited' in the Appendix, and '21m radiation' instead of '21cm radiation' in the discussion of the N4 analysis; please correct these.","section":"Throughout"},{"comment":"The text says 'We have marginalized over the linear bias b21_1' but does not specify the prior or the implementation of the marginalization; please state whether this is a Gaussian prior with a given width or a flat projection, since the forecast near zero bias is sensitive to this choice.","section":"The Fisher Matrix"},{"comment":"The horizontal bars are described as the redshift range covered by the 6 MHz bandwidth, but it is not clear whether each forecast is centered on the simulation snapshot or on the band center; please clarify the placement of the band relative to the zero-bias snapshot.","section":"Fig. 3"},{"comment":"The abstract's statement that noise-like terms make sigma(fNL) <= 1 'unachievable even in simplified forecasts' applies to the N1 auto-power-spectrum analysis; please specify this more precisely to avoid the impression that it applies to the more sophisticated N2-N4 analyses.","section":"Abstract and Introduction"},{"comment":"The phrase 'zero-bias epoch to saturate Fisher information' is misleading because, as the Appendix shows, the exact zero-bias point is a Fisher minimum for finite noise; please rephrase to refer to the near-zero-bias regime or the sampling-noise-limited case.","section":"Conclusions"}],"recommendation":"major_revision","confidential_remarks":"The exact-zero Fisher issue is partially acknowledged in the Appendix, but the main-text presentation overstates the result and needs an explicit band-averaged calculation. The corrected Eq. (25) and a spin-temperature sensitivity test should be included in the revision. The overall idea is interesting and the simulation-based approach is a strength; no concerns about scholarship or attribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's real contribution is the systematic decomposition of 21cm noise into the N1–N4 ladder and the demonstration that naive power-spectrum analyses cannot reach sigma(fNL)<=1. That part is solid and worth taking seriously. The zero-bias epoch itself was already known from McQuinn & D'Aloisio and the Thesan-2 simulations, and the paper cites them properly; the novelty is the quantitative treatment of b2 noise and the radiation-background F(kλ) terms, using simulation-extracted bias and noise coefficients rather than assumed values.\n\nThe trouble is the central claim. The text says that at the zero-bias epoch an N4 analysis gives sigma(fNL)~0.4, a factor of ten better than lower redshifts. But Eq. (13) gives exactly zero Fisher information at b1=0 for any finite noise. The paper's own Appendix says the same: b1=0 is a Fisher minimum, with maxima at b1=±sqrt(N/P). So the quoted gain cannot come from the zero-crossing snapshot itself. It must come from neighboring snapshots or from band-averaging over the 6 MHz survey. The paper treats each band as a single snapshot with constant properties, which means the plotted point at the zero-bias epoch has, by construction, zero information if b1 is exactly zero. That is an internal contradiction between the main text and the Appendix, and it is load-bearing.\n\nThe fix is straightforward but necessary: compute the band-averaged Fisher information explicitly, marginalize over the noise parameters (A, B, bJ, lambdaJ) and the redshift evolution across the band, and report where the optimum actually sits — likely at b1 ~ ±sqrt(N/P), which is near but not exactly at zero. The qualitative idea still has merit: if analysis can reach the sampling floor, the error can be small in the neighborhood of the zero-crossing. But the factor-of-ten claim is not supported by the calculation as written.\n\nTwo other concerns are real but secondary. First, the Ts >> TCMB assumption is questionable at z~10, where Ts ~ 3 TCMB; residual spin-temperature fluctuations can shift the zero-crossing and alter all four noise curves. The paper notes this, but does not quantify the impact. Second, Eq. (25) has a typo: it should be A b1^2/(b1^2+B)^2, not A b1^2/(1+B/b1^2)^2. The stated extrema are correct, so this is minor, but it adds to the need for a clean analytic presentation.\n\nWho is this for? People working on 21cm PNG forecasts and on field-level analysis techniques for reionization surveys. The noise decomposition is a useful reference, and the negative result for power-spectrum-only analyses is an important caution. The paper deserves a serious referee, but the headline claim needs recomputation before it can be trusted.","headline":"Useful noise decomposition and a correct negative result, but the headline zero-bias gain contradicts the paper's own Fisher calculation and needs recomputation.","tokens_in":16019,"tokens_out":8255,"would_cite":true,"duration_ms":76421,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"During reionization, the 21cm field becomes a zero-bias tracer; at that epoch, a sampling-noise-limited analysis could constrain local primordial non-Gaussianity to sigma(f_NL) ~ 0.4.","keywords":["21cm cosmology","epoch of reionization","primordial non-Gaussianity","zero-bias tracer","scale-dependent bias","brightness temperature","Fisher forecast","intensity mapping noise"],"falsifier":"A reader could test the claim by measuring the 21cm power spectrum and its cross-correlation with galaxies across $z = 7$–$15$: if the brightness-temperature bias does not cross zero near a neutral fraction of about 0.85, or if the spin temperature at that epoch is not well above the CMB temperature, the predicted $\\sigma(f_{\\rm NL}^{\\rm loc}) \\sim 0.4$ gain is not realized. A Fisher forecast that includes the full $(1 - T_{\\rm CMB}/T_s)$ fluctuations and velocity-gradient terms would show whether the improvement survives.","tokens_in":14788,"feed_emoji":"📡","tokens_out":12083,"duration_ms":98949,"temperature":0.7,"pith_summary":"This paper argues that during the epoch of reionization there is a generic moment—when the universe is roughly 10–20% ionized—at which the 21cm brightness-temperature field becomes a 'zero-bias tracer': its linear bias crosses zero, so on large scales its fluctuations are uncorrelated with the dark matter density. At that moment the scale-dependent signature of local primordial non-Gaussianity (PNG) in the 21cm power spectrum has maximal sensitivity to the parameter $f_{\\rm NL}^{\\rm loc}$, because the PNG term is proportional to the product of the linear bias and the PNG bias. The paper shows, however, that this sensitivity is hidden unless the analysis can suppress noise-like contributions from nonlinear ionization bias and fluctuating radiation backgrounds: with a naive auto-power-spectrum analysis, $\\sigma(f_{\\rm NL}^{\\rm loc}) \\leq 1$ is unachievable and the zero-bias epoch is the least informative redshift. If a future analysis reaches the sampling-noise floor of the 21cm field, the forecast improves to $\\sigma(f_{\\rm NL}^{\\rm loc}) \\sim 0.4$, roughly ten times better than forecasts at lower redshifts that have been used previously. The result matters because $\\sigma(f_{\\rm NL}^{\\rm loc}) \\sim 1$ is the widely quoted threshold that separates single-field from multi-field inflation models.","feed_headline":"21cm zero-bias epoch promises tenfold tighter fNL bounds","feed_subtitle":"When 21cm bias crosses zero, sampling-floor analyses could reach sigma(fNL) ~ 0.4.","key_machinery":"The load-bearing mechanism is the redshift evolution of the 21cm linear bias, $b^{21}_1(z)$, and its relation to the PNG bias $b^{21}_\\phi$. Under the paper's approximations, the brightness-temperature field is a density-weighted neutral fraction, and the bias expansion yields $b^{21}_1(z) = \\bar{x}_H - (1-\\bar{x}_H)(b^x_1 - 2\\sigma^2 b^x_2)$; the first positive term and the second negative term guarantee a zero crossing near $\\bar{x}_H \\simeq 0.86$ regardless of the detailed astrophysics. Separately, the PNG bias is evaluated by Separate Universe simulations, which vary $\\sigma_8$ and take the derivative of the brightness temperature with respect to it, yielding $b^{21}_\\phi$. The forecast itself is carried by the Fisher information $F_{f_{\\rm NL}} = (2V/\\pi^2)\\int dk\\, k^2 [(b^{21}_1 b^{21}_\\phi \\alpha(k))^2 P(k)^2] / [(b^{21}_1)^2 P(k) + N_i(k)]^2$, with four noise spectra $N_i$ representing (1) the auto-power-spectrum stochasticity, (2) a field-level analysis that removes $b_2$ noise, (3) a further removal of fluctuating-radiation-background noise, and (4) the pure sampling noise of ionized bubbles. The analytic single-$k$ limit shows the Fisher information has maxima at $b_1 = \\pm\\sqrt{B}$ for finite noise $B = N/P$, explaining why the zero-bias point is only optimal when the noise is at the sampling floor.","core_discovery":"The central discovery is that the 21cm brightness temperature is a naturally occurring zero-bias tracer, with the zero crossing occurring early in reionization rather than at a fine-tuned astrophysical moment. In the approximation of saturated spin temperature and negligible velocity gradients, $\\delta T_b = T_0\\, x_H\\,(1+\\delta_m)$, and expanding the neutral-hydrogen fraction in a biased-tracer expansion gives the linear bias $b^{21}_1(z) = \\bar{x}_H - (1-\\bar{x}_H)(b^x_1 - 2\\sigma^2 b^x_2)$. The positive term from neutral gas tracing matter and the negative term from ionized regions anti-correlating with density force a zero crossing near $\\bar{x}_H \\simeq 0.86$; the paper finds this crossing in its fiducial simulation and notes that previous, physically different reionization simulations also cross near $\\bar{x}_H \\sim 0.8$–$0.9$. The PNG bias $b^{21}_\\phi$ is measured with Separate Universe simulations and follows a universality-style relation $b_\\phi = \\delta_B(b_1 - 1)$ until late reionization. A Fisher forecast that compares the PNG signal with four increasingly optimistic noise spectra then shows that only the sampling-noise-limited analysis (Noise 4) converts the zero-bias epoch into a $\\sigma(f_{\\rm NL}^{\\rm loc}) \\sim 0.4$ constraint.","pith_inferences":["Editorial inference: the same noise taxonomy ($N_1$–$N_4$) should apply to other line-intensity tracers that transition from tracing to anti-tracing the matter field, such as CO or [CII] during reionization; each would have its own zero-bias epoch and its own sampling floor.","Editorial inference: the zero-bias redshift itself could be measured empirically as the vanishing of the 21cm–galaxy cross-power spectrum, turning the bias crossing into a calibration point for reionization astrophysics.","Editorial inference: if spin-temperature fluctuations are not negligible at $z \\sim 10$, they may not simply add noise; cross-correlating the brightness temperature with the CMB or with galaxy density could isolate $(1 - T_{\\rm CMB}/T_s)$ fluctuations and actually locate the true zero-bias epoch, converting the paper's weakest assumption into a measurement."],"forward_implications":["If the zero-bias epoch is real, a 21cm survey that can locate it—for example by cross-correlating with high-redshift galaxy surveys—gains a specific redshift target where $f_{\\rm NL}^{\\rm loc}$ constraints are maximized.","Power-spectrum-only analyses will not be enough: without field-level or higher-order statistics to remove $b_2$ noise, the zero-bias epoch is the worst place to measure PNG, and $\\sigma(f_{\\rm NL}^{\\rm loc}) \\leq 1$ remains out of reach.","An analysis that reaches the sampling-noise floor of the 21cm field would see roughly a tenfold reduction in $\\sigma(f_{\\rm NL}^{\\rm loc})$ near the zero-bias epoch compared with lower redshifts, even with foreground-motivated large-scale cuts.","If a future galaxy survey detects $f_{\\rm NL}^{\\rm loc}$, the zero-bias 21cm epoch provides an independent cross-check targeting the same parameter with different systematics.","Because the zero crossing occurs early in reionization ($\\bar{x}_H \\sim 0.2$), the symmetries-based perturbative bias expansion used for the forecast is still valid there, unlike late in reionization."],"supporting_citations":[{"why":"Defines the zero-bias tracer concept and the Fisher-information argument that b1 = 0 maximizes PNG sensitivity in the negligible-noise limit.","marker":"[1]"},{"why":"Supplies the symmetries-based biased-tracer expansion of the 21cm field and previously noted the zero-crossing of the linear bias in simulations.","marker":"[23]"},{"why":"Provides the analytic excursion-set calculation of the PNG bias b_phi for 21cm fluctuations that the Separate Universe measurement is compared with.","marker":"[16]"},{"why":"Provides the seminumerical 21cm simulation code used to generate the fiducial brightness-temperature, ionization, and spin-temperature fields.","marker":"[17, 18]"},{"why":"Defines the fiducial astrophysical scenario whose reionization history is consistent with current observations and sets the simulation parameters.","marker":"[19]"},{"why":"Documents the approximation of neglecting spin-temperature fluctuations and velocity gradients, the key caveat on which the zero-bias epoch forecast rests.","marker":"[22]"},{"why":"Gives the earlier 21cm power-spectrum PNG forecast at average redshift z ~ 8 that this paper improves upon near the zero-bias epoch.","marker":"[14]"},{"why":"Shows how large-scale fluctuations in ionizing and radiation backgrounds enter the bias expansion as a scale-dependent term that can mimic local PNG.","marker":"[51]"},{"why":"Supplies the analytic ionized-bubble mass function used to compute the sampling-noise floor (Noise 4) for the 21cm field.","marker":"[25]"}],"fun_headline_variants":["Zero-bias 21cm: a new window to primordial non-Gaussianity","21cm zero-crossing could slash fNL error bars tenfold","Zero-bias 21cm epoch: tenfold reduction in fNL errors","Early reionization's zero-bias 21cm for fNL precision","Zero-bias 21cm: key to fNL constraints at 0.4"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The forecast assumes that during the zero-bias epoch the spin temperature of neutral hydrogen is much larger than the cosmic microwave background temperature, so fluctuations in spin temperature and gas velocity can be neglected; at $z \\sim 10$ the fiducial simulation has $T_s \\simeq 3 T_{\\rm CMB}$, where that assumption is not automatically safe.","fun_headline_variants_meta":{"raw":{"variants":["Zero-bias 21cm: a new window to primordial non-Gaussianity","21cm zero-crossing could slash fNL error bars tenfold","Zero-bias 21cm epoch: tenfold reduction in fNL errors","Early reionization's zero-bias 21cm for fNL precision","Zero-bias 21cm: key to fNL constraints at 0.4"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001248,"raw_usage":{"total_tokens":5194,"prompt_tokens":1097,"completion_tokens":4097,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":713,"completion_tokens_details":{"reasoning_tokens":3995}},"tokens_in":713,"tokens_out":4097,"duration_ms":25795,"temperature":1.0,"reasoning_tokens":3995,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:38:51.845079+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A reader could test the claim by measuring the 21cm power spectrum and its cross-correlation with galaxies across $z = 7$–$15$: if the brightness-temperature bias does not cross zero near a neutral fraction of about 0.85, or if the spin temperature at that epoch is not well above the CMB temperature, the predicted $\\sigma(f_{\\rm NL}^{\\rm loc}) \\sim 0.4$ gain is not realized. A Fisher forecast that includes the full $(1 - T_{\\rm CMB}/T_s)$ fluctuations and velocity-gradient terms would show whether the improvement survives.","supporting_citations":[{"cited_title":"McQuinn and A","cited_arxiv_id":null,"evidence_quote":"Supplies the symmetries-based biased-tracer expansion of the 21cm field and previously noted the zero-crossing of the linear bias in simulations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the analytic excursion-set calculation of the PNG bias b_phi for 21cm fluctuations that the Separate Universe measurement is compared with."},{"cited_title":"Testing common approximations to predict the 21cm signal at the Epoch of Reionization and Cosmic Dawn","cited_arxiv_id":"2404.08042","evidence_quote":"Documents the approximation of neglecting spin-temperature fluctuations and velocity gradients, the key caveat on which the zero-bias epoch forecast rests."},{"cited_title":"A new scale in the bias expansion","cited_arxiv_id":"1812.02731","evidence_quote":"Shows how large-scale fluctuations in ionizing and radiation backgrounds enter the bias expansion as a scale-dependent term that can mimic local PNG."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the analytic ionized-bubble mass function used to compute the sampling-noise floor (Noise 4) for the 21cm field."}],"review_version":1}