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arxiv: 2607.06526 · v1 · pith:YQWQKIVQ · submitted 2026-07-07 · astro-ph.CO

One with HI: Modelling HI Intensity Mapping one-point statistics including systematics

Bernhard Vos-Gines , Cora Uhlemann This is my paper

Reviewed by Pith2026-07-08 02:49 UTCglm-5.2pith:YQWQKIVQopen to challenge →

classification astro-ph.CO
keywords intensitystatisticssystematicsadditionalbeambiasdarkhydrogen
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The pith

HI density PDF survives telescope systematics and breaks cosmological degeneracies

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

The paper builds a theoretical model for the one-point probability density function (PDF) of neutral hydrogen (HI) intensity in spherical cells, starting from large-deviation statistics and spherical collapse for dark matter, then layering on a quadratic bias model and non-Poissonian stochasticity for the HI-dark matter connection. The central achievement is incorporating two dominant observational systematics — the telescope beam (angular smoothing) and foreground removal (radial mode suppression) — directly into the rate function that determines the PDF shape, by replacing the power spectrum inside the variance integral with a systematics-modulated version. The authors validate this model against high-resolution simulations at percent-level accuracy across three smoothing scales (15.5, 24.8, and 31.0 Mpc/h) at redshift z = 1.32, finding that the telescope beam is the most impactful systematic, reducing the PDF variance substantially while foreground removal and thermal noise play smaller roles. The paper then performs Fisher forecasts showing that, even after systematics degrade the signal, the HI PDF retains non-Gaussian cosmological information that the power spectrum alone cannot access. When combined with the power spectrum, the PDF breaks the degeneracy between the matter density parameter Omega_M and the fluctuation amplitude sigma_8 (up to 64% and 49% uncertainty reductions respectively), and also helps disentangle sigma_8 from the linear bias b_1, because the PDF skewness depends on the bias ratio rather than the product sigma_8 * b_1 that the power spectrum constrains.

Core claim

The HI one-point PDF, modelled via large-deviation statistics with a quadratic Eulerian bias and non-Poissonian stochasticity, retains non-Gaussian cosmological information even after telescope beam and foreground-removal systematics are included. The key mechanism is that the PDF's skewness carries information about the linear bias b_1 that is largely independent of sigma_8, while the power spectrum constrains only their product sigma_8 * b_1. Combining the two statistics therefore breaks the degeneracy. The complementarity depends on smoothing scale: larger scales (R = 31 Mpc/h) are most effective for constraining Omega_M and sigma_8 because their degeneracy direction is most misaligned, w

What carries the argument

Large-deviation theory (LDT) rate function for the matter PDF in spherical cells, combined with a conditional distribution P(delta_HI | delta_m) parameterised by quadratic Eulerian bias and non-Poissonian stochasticity. Systematics enter through a modified power spectrum in the variance integral and an effective volume correction. The full model is implemented using the CosMomentum code.

Load-bearing premise

The skewness of the matter PDF in the presence of anisotropic systematics (beam plus foreground removal) is approximated by simply inserting the systematics-modulated power spectrum into the standard spherical-cell skewness formula. This overestimates the skewness relative to simulations, requiring an ad hoc Edgeworth correction, and leaves residual parameter biases of 0.5–1 sigma that would grow proportionally with the larger survey volume of the full SKA.

What would settle it

If the skewness discrepancy between the approximate and true systematics-modulated PDF grows beyond what the Edgeworth correction can absorb when scaled to full SKA survey volume, the parameter biases would exceed 1 sigma and the forecasted constraints would be unreliable.

Figures

Figures reproduced from arXiv: 2607.06526 by Bernhard Vos-Gines, Cora Uhlemann.

Figure 1
Figure 1. Figure 1: —: Left: We represent ρHI = 1 + ∆THI/T¯ b on a 5 Mpc/h slice of the HI intensity map without observational systematics obtained from the simulation box UNIT1 at redshift z = 1.321. Overlaid on this, we show 0.5 percent of the HI galaxies as yellow stars with a size proportional to their HI mass. Right: Same slice from an HI Intensity map with systematics included. 2.4. Summary statistics In this work we co… view at source ↗
Figure 2
Figure 2. Figure 2: —: Normalised one-point probability density function (PDF) of our HI Intensity Maps at redshift z = 1.321 smoothed with a top hat kernel with smoothing radius R = 15.5 Mpc/h (left) and R = 31.0 Mpc/h (right) as a function of the HI temperature ∆THI = T¯ bδHI. Black solid lines represent the PDF without systematics, dot-dashed lines include the foreground removal effect and blue lines include the telescope … view at source ↗
Figure 3
Figure 3. Figure 3: —: Top: Conditional distribution of HI given dark matter density contrast, computed at a smoothing scale of R = 24.8 Mpc/h. The mean HI overdensity and the scatter, ⟨δHI|δm⟩ ± p ⟨δ 2 HI|δm⟩, are represented as magenta solid and dashed lines, respectively. Bottom: Ratio between the best-fit quadratic models for the mean HI density and the same quantity obtained from simulations (magenta) as well as the rati… view at source ↗
Figure 4
Figure 4. Figure 4: —: Top: Simulation-based HI PDFs with smoothing radii of R = 15.5, 24.8, and 31.0 Mpc/h from HI Intensity maps at z = 1.321 are shown as points, plotted as a function of the temperature fluctuations ∆THI. The corresponding theory PDFs obtained with CosMomentum, are shown as solid lines. Bottom: Ratio between the theoretical and simulated PDFs, with the jackknife-based 1σ uncertainty shown as shaded regions… view at source ↗
Figure 5
Figure 5. Figure 5: —: Top left: Comparison between UNIT and model HI power spectra. The shot noise constant power spectrum, computed using equation 26, is shown as an orange horizontal solid line. The thermal power spectrum, obtained from equation 28, is shown as a magenta line. UNIT HI power spectra without and with observational systematics are represented as black and blue points with 1 − σ errorbars, respectively. Error … view at source ↗
Figure 6
Figure 6. Figure 6: —: Left: Jackknife correlation matrix (removing SSC, equation 34) for the power spectrum and PDFs smoothed at R = 15.5 and 31.0 Mpc/h considering telescope beam (Rbeam = 38.45 Mpc/h) and foreground-removal (kFG = 3.64 × 10−3 h/Mpc) systematics. Right: Covariance diagonal amplitudes for all previous smoothing scales and including R = 24.8 Mpc/h: solid (dashed) lines consider super-sample covariance (removal… view at source ↗
Figure 7
Figure 7. Figure 7: —: Derivatives of the summary statistics with respect to the cosmological parameters θ = {ΩM, σ8, b1}, multiplied by the matrix-square root of the inverse covariance matrix. In this subsection, we analyze how our summary statistics depend on cosmological parameters. In subsubsection 4.1.2 we provided theoretical predictions for Ptheory,sys(k) and P(δHI), where we assume in both cases a particular cosmology… view at source ↗
Figure 8
Figure 8. Figure 8: —: {ΩM, σ8} Fisher forecast where we show 1σ and 2σ contours for the HI power spectrum alone P(k) (black) and its combination with the PDF (P(k) + P(∆THI) at R = 15.5,31.0 Mpc/h) in blue and red ellipses, respectively. Colored stars represent the parameter bias recovered due to differences between UNIT-based and model statistics, which are colored accordingly. Colored pentagons indicate the parameter bias … view at source ↗
Figure 9
Figure 9. Figure 9: —: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: —: Ratio between the smoothed variance calculated by integrating the theoretical power spectrum P(k) of both dark matter and HI catalogues with and without systematics (see Equation A1 and Equation A2) and its corresponding variance calculated using UNIT simulations. The 1% region is shown as a grey shaded area. Black star markers indicate the smoothing scales used in this work. A.1. Variance In this appe… view at source ↗
Figure 11
Figure 11. Figure 11: —: Cosmological parameter θ ={ΩM, σ8, b1} dependence between variance ratios with and without systematics as a function of θ/θfid, for smoothing radius R = 15.5, 24.8, 31.0 Mpc/h. A.2. Skewness In addition to the change in the variances, the presence of the beam and foreground removal systematics cause an associated change in the reduced skewness defined as S3(R) = ⟨δ 3 R⟩/⟨δ 2 R⟩ 2 . If we consider a smo… view at source ↗
Figure 12
Figure 12. Figure 12: —: Top: Simulation-based DM PDFs with smoothing radii of R = 15.5, 24.8, and 31.0 Mpc/h from DM Intensity maps at z = 1.321 are shown as colored points, plotted as a function of the temperature fluctuations ∆Tm(,sys). The corresponding PDFs obtained with CosMomentum, are shown as solid lines. Bottom: Ratio between the theoretical and simulated PDFs, with the jackknife-based 1σ uncertainty shown as shaded … view at source ↗
Figure 13
Figure 13. Figure 13: —: χ 2 distribution from the data (blue histogram) for the PDF alone (right) and its combination with the power spectrum (left) compared to a χ 2 distribution with the appropriate number of degrees of freedom (dof) as expected for an underlying Gaussian distribution of data points (black solid line) [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: —: UNIT-based shot noise as a function of dark matter overdensity with systematics for three different smoothing scales are shown as points. Quadratic best fits are shown as solid lines. The black dotted horizontal line, α = 1, represents Poissonian shot noise [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
read the original abstract

Neutral hydrogen (HI) traces the dark matter distribution of the Universe. Upcoming surveys such as the Square Kilometre Array Observatory (SKAO) will trace neutral hydrogen up to z < 6 using several detection techniques including Intensity Mapping, which offers a unique window to explore the post-reionization Universe. Beyond two-point statistics promise to extract additional non-Gaussian information but require an accurate modelling of observational systematics such as foregrounds and the telescope beam. This work develops a theoretical model for the HI one-point probability density function (PDF) in spherical cells based on large-deviation statistics and spherical collapse for dark matter along with a nonlinear tracer bias and stochasticity parameterisation. It incorporates foreground removal and telescope beam effects that are validated against high-resolution simulations. We show that, despite these observational systematics, the HI PDF is able to capture additional non-Gaussian information from HI intensity maps compared to the power spectrum and can thus tighten constraints on cosmological parameters, breaking the degeneracy between the linear bias and the clustering amplitude.

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 / 8 minor

Summary. This manuscript develops a theoretical model for the one-point probability density function (PDF) of neutral hydrogen (HI) intensity mapping data, based on large-deviation statistics (LDT) for the matter field combined with a quadratic Eulerian bias and non-Poissonian stochasticity model for HI. The framework incorporates telescope beam smoothing, foreground removal, and thermal noise. The model is validated against UNIT simulations at z=1.321 at three smoothing scales (R=15.5, 24.8, 31.0 Mpc/h), achieving percent-level agreement for the PDF (up to ~4% without systematics, ~3% with systematics at the smallest scale) and within 1-sigma for the power spectrum at k<k_max=0.097 h/Mpc. A Fisher forecast demonstrates that combining the PDF with the power spectrum breaks degeneracies between Omega_M and sigma_8 (up to 64% and 49% uncertainty reduction, respectively) and between sigma_8 and the linear bias b_1. The treatment of the matter PDF skewness under anisotropic systematics is approximate and patched with an Edgeworth correction.

Significance. The paper provides a timely and well-structured first attempt at incorporating realistic HI intensity mapping systematics (beam, foreground removal, thermal noise) into an LDT-based one-point PDF framework. The use of the publicly available CosMomentum code and validation against high-resolution UNIT simulations are strengths. The demonstration that the PDF retains complementary non-Gaussian information even after systematics, and specifically that the sigma_8-b_1 degeneracy can be broken via the skewness scaling S_3,HI ~ S_3,m/b_1, is a concrete and falsifiable result. The systematic exploration of which smoothing scale is optimal for which parameter degeneracy (large R for Omega_M-sigma_8; small R for sigma_8-b_1) is a useful design insight for future SKA analyses.

major comments (3)
  1. Section 5.4, Table 2, and the discussion following Eq. (32): The parameter biases delta_theta are computed using the simulation-volume covariance (V=1 Gpc/h^3), yielding biases of 0.5-1 sigma for Omega_M. The manuscript acknowledges (p. 16-17) that rescaling to the SKA survey volume (V_s=16.3 Gpc/h^3, Eq. 37) would amplify these biases by ~sqrt(V_sky/V_sim) ~ 4x, producing 2-4 sigma biases on Omega_M. This directly undermines the quantitative forecast for Omega_M shown in Figure 8 (the 64% uncertainty reduction). The Edgeworth correction (Eq. A8) only partially mitigates this (Table 2: from -0.71 sigma to -0.59 sigma at R=15.5). The manuscript should either (a) explicitly state that the Omega_M forecast is an upper bound and quantify the expected bias at SKA volume, or (b) improve the skewness model to bring the residual bias below 1 sigma even after volume rescaling. As written, the 64%
  2. Section 5.1, Eq. (30), and Section 5.4: The Fisher forecast treats the nuisance parameters (b_2, alpha_0, alpha_1, alpha_2) as fixed rather than marginalized over. The manuscript acknowledges this limitation in the Conclusion (p. 17, 'marginalisation of shot noise parameters'). However, these parameters are load-bearing for the PDF model and are scale-dependent (Table 1 shows large variations across R). Since the forecast combines PDFs at different smoothing scales, holding these fixed could substantially overstate the constraining power. The authors should at minimum provide a robustness check: repeat the forecast with nuisance parameters shifted by their fit uncertainties and report the degradation in the Omega_M and sigma_8 constraints. If this is not feasible, the forecast constraints should be explicitly framed as optimistic upper bounds.
  3. Appendix A.2, Eqs. (A5)-(A8), and Table 3: The skewness approximation under anisotropic systematics replaces P(k) with P(k)*S_eff^2(k) inside the variance integral (Eq. A5 applied to Eq. A2), which overestimates the reduced skewness by ~3% at R=15.5 (Table 3: 4.47 vs 4.34 simulated). The Edgeworth correction (Eq. A8) is then applied to force the PDF to match the tree-level bispectrum result S_3^{tree,B} (Table 3, column 5: 4.22). However, the tree-level result itself underestimates the simulated skewness (4.22 vs 4.34), so the corrected PDF is being matched to a value that is ~3% below the simulation. The authors should clarify whether matching to the tree-level value (rather than the simulated value) is the correct target, and discuss the residual impact of this mismatch on the PDF shape and the resulting Fisher biases.
minor comments (8)
  1. Table 1 caption: 'S_sim_{3,m}' and 'S_th_{3,m}' labels are ambiguous; clarify that these are the reduced skewness of the matter field with and without systematics.
  2. Section 3.3, p. 6: The sentence 'its contribution is greatly reduced after spherical smoothing to .' has a missing value after 'to'. Please complete this statement.
  3. Figure 2: The legend labels for the different systematics combinations (FG, Beam, FG+Beam, FG+Beam+Thermal Noise) are somewhat hard to distinguish in the printed version. Consider using more distinct line styles or colors.
  4. Section 4.1.2, Eq. (21): The effective volume V_eff increases 'by a factor 32 to 9' — this should likely read 'by a factor of 3 to 9' or 'by a factor of 3.2 to 9'. Please clarify.
  5. Section 5.2, Eq. (34): The super-sample covariance (SSC) correction subtracts the subbox mean. It would be helpful to state explicitly whether this correction is applied only to the covariance or also to the model predictions used in the Fisher derivatives.
  6. Figure 8: The y-axis label 'sigma_8 i' is unclear; presumably 'i' stands for 'inferred' or similar. Please clarify or remove.
  7. The reference to 'Majumdar et al. (2026)' (arXiv:2606.30200) appears to be a future-dated preprint. Please verify the citation.
  8. Section 2.3: The statement 'we use cubic voxels due to the finite resolution of numerical simulations' could note that real surveys have anisotropic voxels, and briefly mention whether this affects the systematics modelling.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for a careful and constructive report. The three major comments all identify legitimate limitations of our Fisher forecast that we agree should be addressed more transparently in the revised manuscript. We provide point-by-point responses below. In brief: (1) we will explicitly reframe the Omega_M forecast as an upper bound and quantify the expected SKA-volume bias; (2) we will add a robustness check varying nuisance parameters within their fit uncertainties and frame the constraints as optimistic if marginalization is not included; (3) we will clarify the skewness matching target and discuss the residual impact on the PDF shape and Fisher biases. All three points require revisions to the manuscript text and figures.

read point-by-point responses

  1. Referee: Section 5.4, Table 2, and the discussion following Eq. (32): The parameter biases delta_theta are computed using the simulation-volume covariance (V=1 Gpc/h^3), yielding biases of 0.5-1 sigma for Omega_M. The manuscript acknowledges (p. 16-17) that rescaling to the SKA survey volume (V_s=16.3 Gpc/h^3, Eq. 37) would amplify these biases by ~sqrt(V_sky/V_sim) ~ 4x, producing 2-4 sigma biases on Omega_M. This directly undermines the quantitative forecast for Omega_M shown in Figure 8 (the 64% uncertainty reduction). The Edgeworth correction (Eq. A8) only partially mitigates this (Table 2: from -0.71 sigma to -0.59 sigma at R=15.5). The manuscript should either (a) explicitly state that the Omega_M forecast is an upper bound and quantify the expected bias at SKA volume, or (b) improve the skewness model to bring the residual bias below 1 sigma even after volume rescaling. As written, the 64%

    Authors: The referee is correct that the simulation-volume covariance understates the relative bias that would be encountered at SKA survey volume. We agree that option (a) is the appropriate path: we will explicitly reframe the Omega_M forecast as an upper bound on the constraining power and quantify the expected bias at SKA volume. Specifically, we will add a sentence in Section 5.4 stating that at the SKA survey volume (V_s = 16.3 (Gpc/h)^3), the relative biases on Omega_M would be amplified by a factor of approximately sqrt(V_s/V_sim) ~ 4.04, yielding biases of approximately 2-4 sigma for Omega_M depending on the smoothing scale and skewness treatment. We will note that the Edgeworth correction reduces but does not eliminate this bias (e.g., from -0.71 sigma to -0.59 sigma at R=15.5 Mpc/h at simulation volume, which would rescale to approximately -2.4 sigma and -2.0 sigma respectively at SKA volume). We will add a clarifying statement that the 64% uncertainty reduction on Omega_M should therefore be interpreted as an optimistic upper bound on the achievable constraining power, contingent on further improvements to the skewness modelling in the presence of anisotropic systematics. We agree that improving the skewness model itself (option b) is the physically preferred long-term solution, but this requires a full derivation of the rate function for anisotropic filters, which is beyond the scope of this first attempt at incorporating systematics into the LDT-based PDF framework. We will state this explicitly as a limitation and as future work. revision: yes

  2. Referee: Section 5.1, Eq. (30), and Section 5.4: The Fisher forecast treats the nuisance parameters (b_2, alpha_0, alpha_1, alpha_2) as fixed rather than marginalized over. The manuscript acknowledges this limitation in the Conclusion (p. 17, 'marginalisation of shot noise parameters'). However, these parameters are load-bearing for the PDF model and are scale-dependent (Table 1 shows large variations across R). Since the forecast combines PDFs at different smoothing scales, holding these fixed could substantially overstate the constraining power. The authors should at minimum provide a robustness check: repeat the forecast with nuisance parameters shifted by their fit uncertainties and report the degradation in the Omega_M and sigma_8 constraints. If this is not feasible, the forecast constraints should be explicitly framed as optimistic upper bounds.

    Authors: The referee correctly identifies that holding the nuisance parameters (b_2, alpha_0, alpha_1, alpha_2) fixed is a significant simplification, particularly given their scale-dependence as shown in Table 1. We agree that a robustness check is the minimum requirement. In the revised manuscript, we will perform the following check: for each nuisance parameter, we will shift its value by the 1-sigma uncertainty from the conditional mean and variance fits (estimated from the jackknife scatter across the four UNIT simulation boxes) and recompute the Fisher forecast constraints on Omega_M and sigma_8. We will report the degradation in the constraints in a new table or as an addition to the text in Section 5.4. We expect the degradation to be non-negligible, particularly for the combination of PDFs at multiple smoothing scales where the scale-dependent nuisance parameters introduce additional freedom. Regardless of the magnitude of the degradation, we will explicitly frame the forecast constraints as optimistic upper bounds on the constraining power, pending a full marginalization over nuisance parameters. We will also note in the revised text that a full marginalization would require computing derivatives of the summary statistics with respect to each nuisance parameter, which is feasible within the CosMomentum framework but was beyond the scope of this initial study. revision: yes

  3. Referee: Appendix A.2, Eqs. (A5)-(A8), and Table 3: The skewness approximation under anisotropic systematics replaces P(k) with P(k)*S_eff^2(k) inside the variance integral (Eq. A5 applied to Eq. A2), which overestimates the reduced skewness by ~3% at R=15.5 (Table 3: 4.47 vs 4.34 simulated). The Edgeworth correction (Eq. A8) is then applied to force the PDF to match the tree-level bispectrum result S_3^{tree,B} (Table 3, column 5: 4.22). However, the tree-level result itself underestimates the simulated skewness (4.22 vs 4.34), so the corrected PDF is being matched to a value that is ~3% below the simulation. The authors should clarify whether matching to the tree-level value (rather than the simulated value) is the correct target, and discuss the residual impact of this mismatch on the PDF shape and the resulting Fisher biases.

    Authors: The referee raises a valid and important point. The choice to match to the tree-level bispectrum result S_3^{tree,B} = 4.22 rather than the simulated value S_3^{sim} = 4.34 was motivated by the desire to use a theoretically self-consistent prediction rather than fitting to the simulation. However, as the referee notes, the tree-level result itself underestimates the simulated skewness by approximately 3% at R=15.5 Mpc/h, which means the Edgeworth-corrected PDF is being matched to a value that is below the simulation truth. We will clarify this point in the revised Appendix A.2. Specifically, we will add a discussion of the following points: (1) The tree-level bispectrum result is the correct theoretical target in the sense that it is the analytically computable prediction at leading order in perturbation theory, and it properly accounts for the anisotropic filter shape via Eq. (A7). The simplified approach of replacing P(k) with P(k)*S_eff^2(k) inside the skewness integral (Eq. A5 applied to Eq. A2) is an approximation that does not correctly capture the angular structure of the combined filter, leading to the overestimate (4.47 vs 4.22). (2) The residual 3% mismatch between the tree-level value (4.22) and the simulation (4.34) is expected because tree-level perturbation theory itself is approximate at the mildly nonlinear scales probed by R=15.5 Mpc/h. At larger smoothing scales (R=31.0 Mpc/h), the tree-level result (3.57) agrees much better with the simulation (3.58), confirming that the approximation improves in the more linear regime. (3) We will discuss the residual impact on the PDF shape: the 3% skewness mismatch at R=15.5 Mpc/h propagates to a small but non-negligible distortion of the PDF tails, which contributes to the residual Fisher biases reported in Table revision: no

  4. Referee: The referee raises a valid and important point. The choice to match to the tree-level bispectrum result S_3^{tree,B} = 4.22 rather than the simulated value S_3^{sim} = 4.34 was motivated by the desire to use a theoretically self-consistent prediction rather than fitting to the simulation. However, as the referee notes, the tree-level result itself underestimates the simulated skewness by approximately 3% at R=15.5 Mpc/h, which means the Edgeworth-corrected PDF is being matched to a value that is below the simulation truth. We will clarify this point in the revised Appendix A.2. Specifically, we will add a discussion of the following points: (1) The tree-level bispectrum result is the correct theoretical target in the sense that it is the analytically computable prediction at leading order in perturbation theory, and it properly accounts for the anisotropic filter shape via Eq. (A7). The

    Authors: This appears to be a duplicate of the third major comment. Our response is as above: we will clarify in the revised Appendix A.2 that the tree-level bispectrum result is the theoretically self-consistent target, explain the residual 3% mismatch as expected tree-level PT inaccuracy at mildly nonlinear scales, and discuss its impact on the PDF shape and Fisher biases. We will also note that matching to the simulated skewness would be an alternative approach, but it would sacrifice the predictive nature of the model and require simulation calibration at each cosmology, which defeats the purpose of the theoretical framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity: the LDT framework is externally grounded, CosMomentum is public, and bias parameters fitted to simulations are used for validation, not presented as first-principles predictions.

full rationale

The paper's central derivation chain is largely self-contained against external benchmarks. The matter PDF framework (Eqs. 14-19) is grounded in Large Deviation Theory with citations to Bernardeau (1994), Bernardeau et al. (2014), and Uhlemann et al. (2016) — these are independent prior results, not self-citations by the current paper's authors. The CosMomentum code (Friedrich et al. 2025) is publicly released and independently maintained. The bias parameters (b1, b2, alpha_0, alpha_1, alpha_2) are fitted to UNIT simulations (Table 1, Section 4.1.2) and used to validate the model against the same simulations (Figure 4), but the paper does not present these fitted parameters as first-principles predictions — they are explicitly treated as nuisance parameters calibrated to simulations. The Fisher forecast (Section 5) computes derivatives around a fiducial cosmology using the theoretical model, not by fitting to the simulation data vector. The skewness approximation under anisotropic systematics (Eq. A5 applied to A2) is acknowledged as approximate and corrected via an Edgeworth expansion (Eq. A8), with residual biases reported honestly (Table 2). While co-author Uhlemann appears in several cited works, these citations provide independent mathematical frameworks (LDT, spherical collapse) that are not themselves unverified ansätze — they are established results in the literature. The one minor concern is that the skewness correction (Eq. A8) patches the model to match a tree-level bispectrum calculation, which could be seen as fitting the PDF shape to a known perturbative result, but this is a standard modeling choice rather than a circular definition. No step in the derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

6 free parameters · 7 axioms · 0 invented entities

No new physical entities, particles, forces, or dimensions are introduced. The model uses existing theoretical frameworks (LDT, spherical collapse, Eulerian bias) and existing simulation products (UNIT, SAGE). The free parameters are all fitted to simulations rather than predicted from first principles, which is standard practice for tracer bias modelling but limits the model's predictive power.

free parameters (6)
  • b1 (linear bias) = 1.469–1.509 (Table 1, varies with R)
    Fitted to the HI-matter cross-power spectrum on scales 0.01<k<0.1 h/Mpc (Section 4.2.1).
  • b2 (quadratic bias) = −0.265 to −0.329 (no sys), −0.428 to −0.459 (with sys)
    Fitted to the conditional mean <delta_HI|delta_m> from simulations (Eq. 22, Table 1).
  • alpha_0, alpha_1, alpha_2 (stochasticity) = 0.838–2.347 / 0.196–2.913 / 2.829–7.452 (Table 1)
    Fitted to the conditional variance ratio from simulations (Eq. 23, Table 1). Six parameters total across three smoothing scales.
  • b1^sys, b2^sys, alpha_0^sys, alpha_1^sys, alpha_2^sys = See Table 1 (with systematics)
    Separate bias and stochasticity parameters fitted with systematics included. Six additional fitted sets.
  • N_parallel (=2) = 2
    Foreground removal parameter chosen to emulate FastICA with N_IC=4 (Section 3.1, citing Soares et al. 2021). Not fitted in this paper but adopted from prior calibration.
  • R_mol (=0.4) = 0.4
    Molecular-to-atomic ratio, constant, adopted from Zoldan et al. 2016 (Eq. 1).
axioms (7)
  • domain assumption Large Deviation Principle holds for the matter density PDF in spherical cells at mildly nonlinear scales
    Invoked in Section 4.1.1 (Eq. 14–16). Standard in the LDT cosmology literature (Bernardeau & Reimberg 2016). Validated against simulations in Appendix A.3.
  • domain assumption Spherical collapse provides the most probable mapping from linear to nonlinear density
    Used in Eq. 16 via the contraction principle. Standard assumption in LDT PDF modelling (Valageas 2002).
  • domain assumption The saddle-point approximation is valid for sigma_NL(R) << 1
    Invoked in Eq. 18. Stated to hold for the smoothing scales considered (R=15.5–31.0 Mpc/h). Standard in Uhlemann et al. 2016.
  • domain assumption HI can be modelled as a biased tracer of dark matter with a quadratic Eulerian bias and non-Poissonian stochasticity
    Eqs. 22–23. Adopted from Friedrich et al. 2022 and McCarthy Gould et al. 2025. The paper finds up to 4% deviations at the smallest scale, suggesting higher-order terms may be needed.
  • ad hoc to paper Foregrounds are smooth in frequency and can be removed by a simple exponential suppression (Eq. 3)
    Section 3.1. The paper acknowledges this 'neglects some effects like mode mixing induced by the instrument or residual contamination after cleaning' but argues it captures the dominant behaviour.
  • domain assumption The telescope beam can be approximated as a Gaussian convolution with fixed width
    Section 3.2, Eq. 4. Standard first-order approximation for single-dish IM.
  • ad hoc to paper Redshift-space distortions can be neglected for the purposes of this controlled study
    Section 3.3. The paper explicitly states RSD are left for future work and that this is a controlled setting. This is a significant simplification for any realistic forecast.

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