Pith. sign in

REVIEW 4 major objections 4 minor 103 references

CMB-S4: Foreground-Cleaning Pipeline Comparison for Measuring Primordial Gravitational Waves

T0 review · 4 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that three foreground-cleaning pipelines for CMB-S4 recover the tensor-to-scalar ratio with comparable precision on simple and intermediate-complexity simulated foregrounds, but that complex foregrounds produce biases at…

desk verdict A careful, transparent comparison of three foreground-cleaning approaches at CMB-S4 noise; the main claims hold for the simulated inputs, but the single-foreground-realization caveat and a misstated abstract significance need fixing. read the letter →

arxiv 2502.04300 v1 pith:JWP6J34G submitted 2025-02-06 astro-ph.CO

Federico Bianchini , Dominic Beck , W. L. Kimmy Wu , Zeeshan Ahmed , Sebastian Belkner , Julien Carron , Brandon S. Hensley , Clement L. Pryke
show 1 more author
Caterina Umilta
This is my paper · ORCID
classification astro-ph.CO
keywords tensor-to-scalarratioprimordialgravitationalwavesCMB-S4foregroundcleaningcomponentseparationinternallinearcombinationB-modedelensingGalacticdustandsynchrotron
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tests whether the planned CMB-S4 experiment could trust a measured tensor-to-scalar ratio, $r$, by running three independent foreground-cleaning pipelines on the same simulated South Pole deep-patch maps. The central claim is that on simple Gaussian and amplitude-modulated foreground simulations all three methods perform comparably, reaching $\sigma(r)$ of 3 to 5 $\times 10^{-4}$, but on the more complex Vansyngel foreground model each pipeline is biased at 1.6 to 1.9 $\sigma$. Extending the pipelines to marginalize over foreground residuals removes those biases, at the price of inflated uncertainties that turn a nominal 5-$\sigma$ detection of $r=0.003$ into a pipeline-dependent significance of about 2 to 4 $\sigma$. The auto- and cross-spectrum-based parametric pipeline shows the best stability and overall performance, and the paper argues that mutual validation by independent pipelines is essential for any future detection claim.

What carries the argument

The three pipelines share the linear data model $d = As + n$ but differ in priors and operational space. Pipeline A is a power-spectrum-based parametric method: it fits modified-blackbody dust and power-law synchrotron SEDs, including frequency-decorrelation parameters, to purified B-mode bandpowers via a Hamimeche-Lewis likelihood. Pipeline B is a non-parametric map-based ILC: it estimates CMB weights from a cross-frequency covariance with leave-one-mode-out masking and subtracts a simulation-based noise bias. Pipeline C is a map-based parametric method: it maximizes the profile spectral likelihood for foreground spectral parameters and then applies a least-squares estimator to reconstruct CMB and foreground maps. The lensing B-mode template, built by iterative MAP delensing of the LAT maps, is added to pipeline A as a pseudo-frequency band and cross-correlated with the cleaned maps in pipelines B and C; the extended variants marginalize over foreground residual power, using free decorrelation parameters in A, a weighted dust power template in B, and a linear combination of recovered dust and synchrotron spectra in C.

What would settle it

Take the first year of real CMB-S4 deep-patch data and run the three extended pipelines on the same maps; if the per-realization scatter in $r$ between pipelines substantially exceeds the simulation-predicted scatter from Table II, or if the recovered foreground spectral indices differ from the simulated model inputs by more than the reported uncertainties, then the simulated foregrounds are not representative and the paper's pipeline ranking would not transfer to real data.

Watch

Extended reading notes

Core claim

The paper's main result is a head-to-head comparison of three approaches in one simulation framework at CMB-S4 SAT noise levels: a parametric maximum-likelihood fit to the auto- and cross-frequency B-mode spectra, with the lensing template added as a pseudo-frequency band (pipeline A); a harmonic-space internal linear combination with mode-masked covariance estimation (pipeline B); and a map-based parametric maximum-likelihood reconstruction of CMB, dust, and synchrotron (pipeline C). Across the three validation foreground suites, unbiased $r$ is recovered for the Gaussian and amplitude-modulated models; with the Vansyngel suite all nominal pipelines show positive biases, for input $r=0$ corresponding to 1.6–1.9 $\sigma$. Adding foreground-residual marginalization brings the biases below roughly 0.1 $\sigma$, but increases $\sigma(r)$ by 15–20% for pipelines A and B and up to 160% for pipeline C; for input $r=0.003$ the detection significance becomes about 4.2 $\sigma$ (A), 3.4 $\sigma$ (B), and 1.8 $\sigma$ (C). On the PySM single-realization suites with the extended pipelines, pipeline A recovers $r$ within 1 $\sigma$ for all complexity levels, pipeline B shows a slight positive bias for non-zero $r$, and pipeline C does not recover an unbiased posterior for the most complex model.

Load-bearing premise

The load-bearing premise is that the simulated foreground suites, especially the single fixed realizations of the Vansyngel and PySM models, faithfully represent the polarized Galactic foregrounds that CMB-S4 will actually see in its deep patch; if the real sky's spectral decorrelation or spatial variability lies outside these models, the measured biases, the effectiveness of extended residual marginalization, and the pipeline ordering could all change.

Editorial extensions

If this is right

  • At CMB-S4 South Pole noise levels and with Gaussian or amplitude-modulated foregrounds, all three pipelines deliver $\sigma(r) \sim 3$–$5 \times 10^{-4}$, consistent with reaching a roughly 5-sigma detection for $r=0.003$ when foregrounds are this simple.
  • Nominal pipelines can be biased at 1.6–1.9 sigma on complex foregrounds such as the Vansyngel model, so a naive blind analysis could report a spurious detection or miss the true one.
  • Marginalizing over foreground residuals removes the bias but degrades precision; for $r=0.003$ the achievable detection significance depends on pipeline choice: about 4.2 sigma (A), 3.4 sigma (B), and 1.8 sigma (C).
  • Correlations between pipeline estimates drop on complex foregrounds, with the correlation between pipelines B and C falling as low as 0.44, so agreement between methods cannot be assumed and cross-validating independent pipelines on the same data is necessary.
  • Pipeline A's stability across all foreground suites suggests the cross-spectral parametric method should be a primary anchor for CMB-S4 $r$ analyses, with map-based pipelines serving as cross-checks.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: since Models 2–5 each supply only a single fixed foreground realization, the bias and sensitivity ranking carries no foreground sample variance; real skies with different spatial realizations could reorder the pipelines, so repeat-foreground simulation suites should be used before final pipeline selection.
  • Editorial inference: the failures of pipelines B and C on high-complexity models point to spatially adaptive cleaning as the natural next step; testing needlet ILC or multi-patch parametric cleaning on the same suites would clarify whether the gap is fundamental or implementation-specific.
  • Editorial inference: the paper's delensing step lowers $\sigma(r)$ by roughly a factor of 6–10, so if the real lensing-template noise cannot be characterized as accurately as in simulations, the quoted 2–4 sigma detection significance may be optimistic.
  • Editorial inference: a direct testable extension is to apply the three extended pipelines to one realistic multi-frequency sky with an injected $r=0.003$ signal; if the recovered $r$ posteriors do not overlap, the residual-marginalization models are missing something.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper compares three foreground-cleaning pipelines—a parametric cross-spectrum method (Pipeline A), a harmonic-space ILC (Pipeline B), and a map-based parametric maximum-likelihood method (Pipeline C)—for estimating the tensor-to-scalar ratio r from simulated CMB-S4 South Pole Deep Patch SAT maps. It validates the pipelines on three foreground suites (Gaussian, amplitude-modulated, Vansyngel) using 500 simulations per suite, applies a LAT-based iterative internal delensing step, and then tests the pipelines on PySM Models 3–5 with single realizations and MCMC posteriors. The central result is that nominal pipelines give comparable σ(r) ≈ 3–5×10^-4 and unbiased r for simple/intermediate foregrounds, but 1–2σ biases appear for the more complex Vansyngel model; extended pipelines that marginalize residual foregrounds reduce the biases to <0.1σ at the cost of increased σ(r), yielding a pipeline-dependent detection significance of 2–4σ for r=0.003, with Pipeline A showing the best stability and overall performance.

Significance. If the results hold, this is a valuable cross-validation of component-separation methods at the very low noise levels planned for CMB-S4. The paper benefits from 500 simulations per foreground suite, shared input skies across pipelines, inter-pipeline correlation analysis, and a validated iterative delensing step. It also makes good use of public tools (PySM, NaMaster, S2Hat, Cobaya) and gives a clear conceptual framing of the three methods. The main caveats—the single-realization nature of the Vansyngel and PySM foregrounds and the absence of a foreground-sample-variance term in the error budget—are acknowledged by the authors but not quantified; the abstract's 2–4σ detection range also omits the 1.8σ result of extended Pipeline C. These issues are correctable and do not invalidate the central comparison, but they need to be addressed before the headline claims can be taken at face value.

major comments (4)
  1. [§IV B 3–4, §VII C, Table II] Models 2–5 each provide only a single fixed foreground realization, so the extended-pipeline bias statements (<0.1σ) and the pipeline ranking are conditional on one foreground draw. No foreground-to-foreground scatter enters the error budget or the pipeline comparison, yet the paper claims that contamination is reduced 'to within statistical uncertainties.' The single-realization limitation is acknowledged in the text, but its impact on the headline comparison is not quantified. The claims should be reworded as conditional on the specific realizations used, and the absence of foreground sample variance should be stated as a limitation of the comparison rather than only a property of the foreground models.
  2. [§VII C, Table II, Abstract] The abstract and conclusions quote a detection significance of 2–4σ for r=0.003, but the extended Pipeline C result in Table II is r = 3.09 ± 1.75 (×10^-3), i.e. about 1.8σ. This is outside the quoted range. The text should either restrict the 2–4σ statement to Pipelines A and B or report the full pipeline-dependent range, including the 1.8σ result of Pipeline C.
  3. [§VI, Eqs. (6.1)–(6.2), §VII C] The extended pipelines reduce bias by adding fitted residual parameters whose templates are constructed from the same foreground model/realization used to generate the data: Eq. (6.1) uses the Pipeline A foreground model, and Eq. (6.2) uses Pipeline C's component-separated dust and synchrotron maps. The exercise therefore cannot distinguish a marginalization that generically absorbs residual foreground power from one that overfits the specific spectral/spatial structure of a single realization. This matters for the general claim of unbiased recovery: in Table III, Model 5, extended Pipelines B and C exclude the input r=0.003 at 95% credibility, showing that the 'within statistical uncertainties' statement is too strong.
  4. [§V, App. B] The delensing validation uses the true foreground templates to estimate the lensing-template noise N_LT, which is not available in real data. The Gaussian-foreground test in App. B quantifies the difference in N_LT but does not propagate that difference to the r posterior. The paper asserts that the impact on r is negligible, but this is not demonstrated. The r results after delensing therefore remain dependent on perfect foreground knowledge, and this caveat should be stated more prominently.
minor comments (4)
  1. [§VII C] In the paragraph on the relative impact of dust and synchrotron, 'Model 3' appears to be a typo for 'Model 2': the quoted bias of 0.56 ± 0.35 matches the Vansyngel model in Table II, and the surrounding text discusses Models 0–2.
  2. [Fig. 3 caption] The word 'embeded' should be 'embedded' in the caption.
  3. [§V] The word 'appoach' should be 'approach' in the sentence describing the alternative to using the fiducial foreground simulations in constructing N_LT.
  4. [Table III] The header says '2σ credibility intervals' but the quoted intervals are 95% credibility intervals; please make the notation consistent (95% credibility corresponds to approximately 1.96σ for a Gaussian posterior).

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the pipeline comparison is benchmarked against known simulation inputs, and the extended-pipeline bias removal is a model-flexibility effect, not a self-referential prediction.

full rationale

The central derivation chain is a simulation-based benchmark. Pipelines A, B, and C are applied to maps generated from known input values of r (0 and 0.003) and known foreground models, and the reported bias and sigma(r) values are measured against those inputs, so the headline comparison is externally grounded. The extended pipelines do add nuisance parameters (Delta'_d/Delta'_s in Pipeline A; A_d/alpha_d in Eq. 6.1; A'_d/A'_s in Eq. 6.2) that are fit to the same Model 2 data, and the paper explicitly presents the post-extension unbiased recovery as a demonstration of marginalization, not as a prediction independent of those fits. Fitting residual degrees of freedom to absorb residual foreground power is a standard inference step, not a circular reduction of r to the inputs; no equation in the paper defines r in terms of the fitted parameters by construction. The single-realization limitation for Models 2-5 (Sec. IV B 3 and IV B 4) removes foreground sample variance from the error budget and is acknowledged by the authors: 'Note that for this specific foreground model there is only one realization such that every map in our simulation suite contains the exact same foreground component,' and 'As with the Vansyngel model (Model 2), we have only a single realization of the foreground emission for each of Models 3, 4, and 5.' Similarly, the lensing-template noise for Models 2-5 is estimated from the same fixed foregrounds (Sec. V), so foreground leakage into the template is exactly captured by N_LT; the authors flag that this is an idealization not achievable in real data. These are robustness limitations, not circularity. Self-citations to Ref. [15] and Ref. [88] supply the noise/delensing infrastructure but are not the load-bearing argument for the pipeline comparison, which is independently evaluated against the simulated inputs.

Assumptions & free parameters 10 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. The free parameters listed are the foreground and residual nuisance parameters fitted inside the pipelines being compared, not hidden parameters of a derivation. The main model assumptions are the SED and power-spectrum forms for foregrounds, the Gaussian noise model, the lensing-template model, and the representativeness of the simulated foreground suites.

free parameters (10)
  • beta_d (dust spectral index) = Input 1.6 in Model 0; fitted per realization in Pipelines A and C
    Free spectral parameter in the modified-blackbody dust SED used by the parametric pipelines.
  • beta_s (synchrotron spectral index) = Input -3.1 in Model 0; fitted in Pipelines A and C
    Second spectral parameter in the mixing matrix; its spatial constancy is an important modeling assumption.
  • A_d (dust amplitude at ell=80) = Input 4.25 microK^2 in Model 0; fitted in Pipeline A
    Normalization of the dust BB power spectrum in Eq. 3.17.
  • A_s (synchrotron amplitude at ell=80) = Input 3.8 microK^2 in Model 0; fitted in Pipeline A
    Normalization of the synchrotron BB power spectrum in Eq. 3.18.
  • alpha_d (dust spatial spectral slope) = Input -0.4; fitted in Pipeline A
    Slope of the dust power-law in ell in Eq. 3.17.
  • alpha_s (synchrotron spatial spectral slope) = Input -0.6; fitted in Pipeline A
    Slope of the synchrotron power-law in ell in Eq. 3.18.
  • epsilon (dust-synchrotron correlation) = Varied; no fiducial quoted
    Parameterizes the correlated dust-synchrotron power in Eq. 3.19.
  • Delta'_d and Delta'_s (frequency decorrelation) = Varied in extended Pipeline A; fixed in nominal
    Extended marginalization over frequency decorrelation removes Vansyngel-model bias at the cost of larger sigma(r).
  • A'_d and A'_s (residual amplitudes in Pipeline C) = Varied per realization
    Extra amplitudes in Eq. 6.2 used to absorb foreground residuals in the cleaned CMB maps.
  • Ad and alpha_d in Pipeline B residual model = Varied
    Dust amplitude and slope propagated through ILC weights in Eq. 6.1 to model residual foreground power.
assumptions (6)
  • domain assumption The linear data model d = A s + n with Gaussian noise and known noise covariance N is valid for the SAT maps.
    Used in Sec. III A (Eqs. 3.1-3.4) as the common statistical basis for all three pipelines; assumes no unmodeled systematics or non-Gaussian noise.
  • domain assumption Galactic dust follows a modified blackbody SED with fixed T_d = 19.6 K and synchrotron follows a power-law SED.
    Sec. III C (Eqs. 3.14-3.16) and Sec. IV B; the parametric pipelines rely on these spectral laws, and Models 0-1 assume them.
  • domain assumption Foreground BB power spectra are power laws in ell with amplitude, slope, and dust/synchrotron correlation modeled by Eqs. 3.17-3.19.
    Sec. III D 1; Pipeline A's likelihood model and the Gaussian simulations use this parameterization.
  • domain assumption The ILC method may reconstruct the CMB from a linear combination of frequency maps assuming a known, frequency-independent CMB spectrum and statistical independence from contaminants.
    Sec. III D 2; Pipeline B relies on this assumption, and the ILC bias mitigation in Eq. 3.21 is standard practice.
  • domain assumption The lensing template B_LT is a noisy, isotropically filtered version of the true lensing B-mode, with additive noise N_LT (Eq. 5.2).
    Sec. V; the delensed likelihood depends on this model and on N_LT estimated from simulations.
  • domain assumption The simulated foreground suites (Models 0-5) are representative of the real polarized foreground sky in the CMB-S4 patch; Models 2-5 provide only one foreground realization.
    Sec. IV B; conclusions about pipeline bias ranking and the need for mutual validation depend on this. The paper acknowledges this limitation in Sec. VII and App. B.

how reviews work

0 comments
Cite this review

Pith. "Pith review of CMB-S4: Foreground-Cleaning Pipeline Comparison for Measuring Primordial Gravitational Waves." pith.science (2026). https://pith.science/paper/JWP6J34G

@misc{pith2026250204300,
  author       = {Pith},
  title        = {Pith review of: CMB-S4: Foreground-Cleaning Pipeline Comparison for Measuring Primordial Gravitational Waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JWP6J34G}},
  note         = {Machine review of arXiv:2502.04300}
}
abstract

We compare multiple foreground-cleaning pipelines for estimating the tensor-to-scalar ratio, $r$, using simulated maps of the planned CMB-S4 experiment within the context of the South Pole Deep Patch. To evaluate robustness, we analyze bias and uncertainty on $r$ across various foreground suites using map-based simulations. The foreground-cleaning methods include: a parametric maximum likelihood approach applied to auto- and cross-power spectra between frequency maps; a map-based parametric maximum-likelihood method; and a harmonic-space internal linear combination using frequency maps. We summarize the conceptual basis of each method to highlight their similarities and differences. To better probe the impact of foreground residuals, we implement an iterative internal delensing step, leveraging a map-based pipeline to generate a lensing $B$-mode template from the Large Aperture Telescope frequency maps. Our results show that the performance of the three approaches is comparable for simple and intermediate-complexity foregrounds, with $\sigma(r)$ ranging from 3 to 5 $\times 10^{-4}$. However, biases at the $1-2\sigma$ level appear when analyzing more complex forms of foreground emission. By extending the baseline pipelines to marginalize over foreground residuals, we demonstrate that contamination can be reduced to within statistical uncertainties, albeit with a pipeline-dependent impact on $\sigma(r)$, which translates to a detection significance between 2 and 4$\sigma$ for an input value of $r = 0.003$. These findings suggest varying levels of maturity among the tested pipelines, with the auto- and cross-spectra-based approach demonstrating the best stability and overall performance. Moreover, given the extremely low noise levels, mutual validation of independent foreground-cleaning pipelines is essential to ensure the robustness of any potential detection.

Figures

Figures reproduced from arXiv: 2502.04300 by the authors.

Figure 1
Figure 1. FIG. 1. Flowchart of the simulation generation and foreground cleaning process. The simulation generation is described in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Normalized hit pattern on the sky for the South Pole [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison of the recovered mean cleaned CMB [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Summary of the biases and uncertainties on the [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Scatter plots and histograms displaying best-fit tensor-to-scalar ratio values from different component-separation [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Posterior distributions of the tensor-to-scalar ratio ( [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Mean set of auto-and cross- [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Lensing template noise bias for foreground models 3– [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Correlation matrices for the three foreground simulation models. Each matrix evaluates the Pearson correlation [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Same figure as Fig [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Mean foreground spectra recovered by the parametric map-based maximum likelihood Pipeline C. The left panel [PITH_FULL_IMAGE:figures/full_fig_p025_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Scatter plots displaying the inferred foreground parameters [PITH_FULL_IMAGE:figures/full_fig_p025_14.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

103 extracted references · 44 canonical work pages

  1. [1]

    Model 0 (Gaussian foregrounds) Model 0 (Gaussian foregrounds) is a suite of simple isotropic Gaussian simulations that include emission from Galactic dust and synchrotron. We simulate foreground maps at 353 GHz for dust and 23 GHz for synchrotron using power-law input BB power spectra, given by DBB,f ℓ = Af ℓ 80 αf , where f ∈ {d, s} indicates the foregro...

  2. [2]

    To achieve this, we multiply the Gaussian realiza- tions from model 0 by a template that captures the spa- tial variations in foreground amplitudes

    Model 1 (Amplitude modulated Gaussian foregrounds) This foreground model is an extension of model 0 in- troducing spatial modulation of the foreground bright- ness. To achieve this, we multiply the Gaussian realiza- tions from model 0 by a template that captures the spa- tial variations in foreground amplitudes. By introducing spatial modulation of the du...

  3. [3]

    We first estimate foreground parameters and then reconstruct component maps (Sec

    Pipeline C (Map-based parametric maximum-likelihood) Pipeline C implements a two-step component separa- tion method. We first estimate foreground parameters and then reconstruct component maps (Sec. III B 1). In this approach [see, e.g., 45, 47], we first use the likelihood in Eq. 3.8 to solve for the spectral parameters of the foreground model. Then, we ...

  4. [4]

    Model 2 (Vansyngel model) The final model we consider for pipeline validation is based on the work of Vansyngel et al. [75]. This phe- nomenological model provides a framework for polarized emission of dust and synchrotron in the sub-millimeter band using the structure of the Galactic magnetic field and interstellar matter. The model assumes that the Gala...

  5. [5]

    the most probable CMB lensing map

    PySM models To apply and test the foreground-cleaning methods as if working with real data in Sec. VII D, we also con- sider three separate microwave sky simulations using foreground templates of varying complexities provided by the PySM36 package [77] (as opposed to our previous 6 https://pysm3.readthedocs.io 9 work [15] which used PySM2). These template...

  6. [6]

    Seljak and M

    U. Seljak and M. Zaldarriaga, Phys. Rev. Lett. 78, 2054 (1997)

    1997

  7. [7]

    Most relevantly for our three cleaning methods, the low complexity suite (Model 3) is free of frequency decor- relation, while the medium complexity suite (Model

    each have unique assumptions about the physical properties and spatial distributions of foregrounds such as Galactic dust and synchrotron emission. Most relevantly for our three cleaning methods, the low complexity suite (Model 3) is free of frequency decor- relation, while the medium complexity suite (Model

  8. [8]

    The high complexity suite (Model 5) incorporates a 3D model of the polarized dust emission, causing more complicated decorrelation effects

    incorporates frequency decorrelation via spatially varying spectral parameters of the dust and synchrotron SED. The high complexity suite (Model 5) incorporates a 3D model of the polarized dust emission, causing more complicated decorrelation effects. As with the Vansyngel model (Model 2), we have only a single realization of the foreground emission for e...

Show all 103 references
  1. [9]

    Importantly, the simulations for Models 3, 4, and 5 all share the same noise realization, enabling a direct comparison of posterior results on equal footing

    However, unlike the previous section, where we examined the maximum-likelihood r values across 500 simulations, here we use MCMC to analyze just one mock sky. Importantly, the simulations for Models 3, 4, and 5 all share the same noise realization, enabling a direct comparison...

    2025

  2. [10]

    A. A. Starobinsky, Physics Letters B 91, 99 (1980)

    1980

  3. [11]

    A. H. Guth, Phys. Rev. D 23, 347 (1981)

    1981

  4. [12]

    Sato, Mon

    K. Sato, Mon. Not. Roy. Astron. Soc. 195, 467 (1981)

    1981

  5. [13]

    A. D. Linde, Physics Letters B 108, 389 (1982)

    1982

  6. [14]

    A. G. Polnarev, Soviet Astronomy 29, 607 (1985)

    1985

  7. [15]

    Abazajian, G

    K. Abazajian, G. E. Addison, P. Adshead, et al., The Astrophysical Journal 926, 54 (2022)

    2022

  8. [16]

    Kamionkowski, A

    M. Kamionkowski, A. Kosowsky, and A. Stebbins, Phys. Rev. D 55, 7368 (1997)

    1997

  9. [17]

    Kamionkowski and E

    M. Kamionkowski and E. D. Kovetz, Annual Review of Astronomy and Astrophysics 54, 227–269 (2016)

    2016

  10. [18]

    Inflation: Theory and observations,

    A. Ach´ ucarro, M. Biagetti, M. Braglia, et al., “Inflation: Theory and observations,” (2022), arXiv:2203.08128 [astro-ph.CO]

    2022 arXiv

  11. [19]

    Snowmass2021 cosmic frontier: Cos- mic microwave background measurements white paper,

    C. L. Chang, K. M. Huffenberger, B. A. Ben- son, et al., “Snowmass2021 cosmic frontier: Cos- mic microwave background measurements white paper,” (2022), arXiv:2203.07638 [astro-ph.CO]

    2022

  12. [20]

    Essinger-Hileman, A

    T. Essinger-Hileman, A. Ali, M. Amiri, et al., in Mil- limeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VII, Society of Photo- Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9153, edited by W. S. Holland and J. Zmuidz- inas...

    2014 arXiv

  13. [21]

    P. A. R. Ade, M. Amiri, S. J. Benton, et al., Astrophys. J. 927, 174 (2022), arXiv:2103.13334 [astro-ph.CO]

    2022 arXiv

  14. [22]

    P. Ade, J. Aguirre, Z. Ahmed, et al., J. Cosmol. As- tropart. Phys. 2019, 056 (2019), arXiv:1808.07445 [astro- ph.CO]

    2019 arXiv

  15. [23]

    K. Wolz, S. Azzoni, C. Herv ´ ıas-Caimapo, et al., Astron. Astrophys. 686, A16 (2024), arXiv:2302.04276 [astro- ph.CO]

    2024 arXiv

  16. [24]

    A. A. Starobinski ˇi, Soviet Journal of Experimental and Theoretical Physics Letters 30, 682 (1979)

    1979

  17. [25]

    Cmb-s4 science book, first edition,

    K. N. Abazajian, P. Adshead, Z. Ahmed, et al., “Cmb-s4 science book, first edition,” (2016). 19

    2016

  18. [26]

    Li, S.-Y

    H. Li, S.-Y. Li, Y. Liu, et al., arXiv e-prints , arXiv:1710.03047 (2017), arXiv:1710.03047 [astro- ph.CO]

    2017 arXiv

  19. [27]

    Allys, K

    E. Allys, K. Arnold, J. Aumont, et al., Progress of Theoretical and Experimental Physics 2023 (2022), 10.1093/ptep/ptac150

    2022 doi

  20. [28]

    P. A. R. Ade, Z. Ahmed, M. Amiri, et al., Phys. Rev. Lett. 127, 151301 (2021), arXiv:2110.00483 [astro- ph.CO]

    2021

  21. [29]

    Tristram, A

    M. Tristram, A. J. Banday, K. M. G´ orski, et al., Phys. Rev. D 105, 083524 (2022)

    2022

  22. [30]

    D. Beck, A. Cukierman, and W. L. K. Wu, Mon. Not. Roy. Astron. Soc. 515, 229 (2022), arXiv:2202.05949 [astro-ph.CO]

    2022 arXiv

  23. [31]

    Campeti and E

    P. Campeti and E. Komatsu, The Astrophysical Journal 941, 110 (2022)

    2022

  24. [32]

    de Belsunce, S

    R. de Belsunce, S. Gratton, and G. Efstathiou, Monthly Notices of the Royal Astronomical Society 518, 3675–3684 (2022)

    2022

  25. [33]

    Seljak and C

    U. Seljak and C. M. Hirata, Physical Review D69 (2004), 10.1103/physrevd.69.043005

    2004 doi

  26. [34]

    Bezrukov and M

    F. Bezrukov and M. Shaposhnikov, Physics Letters B 659, 703–706 (2008)

    2008

  27. [35]

    O’Dea, A

    D. O’Dea, A. Challinor, and B. R. Johnson, Mon. Not. R. Astron. Soc. 376, 1767 (2007), arXiv:astro-ph/0610361 [astro-ph]

    2007 arXiv

  28. [37]

    A. P. S. Yadav, M. Su, and M. Zaldarriaga, Phys. Rev. D 81, 063512 (2010), arXiv:0912.3532 [astro-ph.CO]

    2010 arXiv

  29. [38]

    Soliman, P

    A. Soliman, P. A. R. Ade, Z. Ahmed, et al., in Mil- limeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy IX, Society of Photo- Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10708, edited by J. Zmuidzinas and J.-R. Gao (2018) p...

    2018 arXiv

  30. [39]

    Verg` es, J

    C. Verg` es, J. Errard, and R. Stompor, Physical Review D 103 (2021), 10.1103/physrevd.103.063507

    2021 doi

  31. [40]

    Knox and Y.-S

    L. Knox and Y.-S. Song, Physical Review Letters 89 (2002), 10.1103/physrevlett.89.011303

    2002 doi

  32. [42]

    Bobin, J

    J. Bobin, J. L. Starck, F. Sureau, and S. Basak, Astron. Astrophys. 550, A73 (2013), arXiv:1206.1773 [astro-ph.CO]

    2013 arXiv

  33. [43]

    Akrami, M

    Planck Collaboration, Y. Akrami, M. Ashdown, et al., Astronomy & Astrophysics 641, A4 (2020)

    2020

  34. [44]

    Krachmalnicoff, E

    N. Krachmalnicoff, E. Carretti, C. Baccigalupi, et al., Astron. Astrophys. 618, A166 (2018), arXiv:1802.01145 [astro-ph.GA]

    2018 arXiv

  35. [45]

    Tegmark and G

    M. Tegmark and G. Efstathiou, Mon. Not. Roy. Astron. Soc. 281, 1297 (1996), arXiv:astro-ph/9507009

    1996 arXiv

  36. [46]

    C. L. Bennett, R. S. Hill, G. Hinshaw, et al., The Astro- physical Journal Supplement Series 148, 97 (2003)

    2003

  37. [47]

    Delabrouille, J.-F

    J. Delabrouille, J.-F. Cardoso, M. Le Jeune, et al., As- tronomy & Astrophysics 493, 835 (2008)

    2008

  38. [48]

    Remazeilles, J

    M. Remazeilles, J. Delabrouille, and J.-F. Cardoso, Monthly Notices of the Royal Astronomical Society 410, 2481–2487 (2010)

    2010

  39. [49]

    Maino, A

    D. Maino, A. Farusi, C. Baccigalupi, et al., Monthly Notices of the Royal Astronomical Society 334, 53–68 (2002)

    2002

  40. [50]

    Bobin, Y

    J. Bobin, Y. Moudden, J. L. Starck, et al., Stat. Meth. 5, 307 (2008), arXiv:0712.0588 [astro-ph]

    2008 arXiv

  41. [51]

    Com- ponent separation with flexible models. application to the separation of astrophysical emissions,

    J.-F. Cardoso, M. Martin, J. Delabrouille, et al., “Com- ponent separation with flexible models. application to the separation of astrophysical emissions,” (2008), arXiv:0803.1814 [astro-ph]

    2008 arXiv

  42. [52]

    Leloup, J

    C. Leloup, J. Errard, and R. Stompor, Physical Review D 108 (2023), 10.1103/physrevd.108.123547

    2023 doi

  43. [53]

    Pixel do- main implementation of the minimally informed cmb map foreground cleaning (micmac) method,

    M. Morshed, A. Rizzieri, C. Leloup, et al., “Pixel do- main implementation of the minimally informed cmb map foreground cleaning (micmac) method,” (2024), arXiv:2405.18365 [astro-ph.CO]

    2024 arXiv

  44. [54]

    Stompor, S

    R. Stompor, S. Leach, F. Stivoli, and C. Baccigalupi, Monthly Notices of the Royal Astronomical Society 392, 216 (2009)

    2009

  45. [55]

    Errard, F

    J. Errard, F. Stivoli, and R. Stompor, Physical Review D 84 (2011), 10.1103/physrevd.84.063005

    2011 doi

  46. [56]

    H. K. Eriksen, C. Dickinson, C. R. Lawrence, et al., The Astrophysical Journal 641, 665–682 (2006)

    2006

  47. [57]

    H. K. Eriksen, J. B. Jewell, C. Dickinson, et al., Astro- phys. J. 676, 10 (2008), arXiv:0709.1058 [astro-ph]

    2008 arXiv

  48. [58]

    de la Hoz, P

    E. de la Hoz, P. Diego-Palazuelos, E. Mart ´ ınez-Gonz´ alez, et al., Journal of Cosmology and Astroparticle Physics 2022, 032 (2022)

    2022

  49. [59]

    Stolyarov, M

    V. Stolyarov, M. P. Hobson, A. N. Lasenby, and R. B. Barreiro, Mon. Not. Roy. Astron. Soc. 357, 145 (2005), arXiv:astro-ph/0405494

    2005 arXiv

  50. [60]

    K. M. Smith, Phys. Rev. D 74, 083002 (2006), arXiv:astro-ph/0511629

    2006 arXiv

  51. [61]

    Bedini, D

    L. Bedini, D. Herranz, E. Salerno, et al., EURASIP Journal on Advances in Signal Processing 2005 (2005), 10.1155/asp.2005.2400

    2005

  52. [62]

    Azzoni, D

    S. Azzoni, D. Alonso, M. Abitbol, et al., Journal of Cos- mology and Astroparticle Physics 2023, 035 (2023)

    2023

  53. [63]

    Carones, M

    A. Carones, M. Migliaccio, G. Puglisi, et al., Mon. Not. R. Astron. Soc. 525, 3117 (2023), arXiv:2212.04456 [astro-ph.CO]

    2023 arXiv

  54. [64]

    Puglisi, G

    G. Puglisi, G. Mihaylov, G. V. Panopoulou, et al., Mon. Not. Roy. Astron. Soc. 511, 2052 (2022), arXiv:2109.11562 [astro-ph.CO]

    2022 arXiv

  55. [65]

    Hamimeche and A

    S. Hamimeche and A. Lewis, Physical Review D 77 (2008), 10.1103/physrevd.77.103013

    2008 doi

  56. [66]

    BICEP2 Collaboration, Keck Array Collaboration, P. A. R. Ade, et al., Phys. Rev. Lett.121, 221301 (2018), arXiv:1810.05216 [astro-ph.CO]

    2018 arXiv

  57. [67]

    P. A. R. Ade et al. (SPTpol, BICEP, Keck), Phys. Rev. D 103, 022004 (2021), arXiv:2011.08163 [astro-ph.CO]

    2021 arXiv

  58. [68]

    S2HAT: Scalable Spherical Harmonic Transform Library,

    R. Stompor, “S2HAT: Scalable Spherical Harmonic Transform Library,” Astrophysics Source Code Library, record ascl:1110.013 (2011)

    2011

  59. [69]

    Coulton et al

    W. Coulton et al. (ACT), Phys. Rev. D 109, 063530 (2024), arXiv:2307.01258 [astro-ph.CO]

    2024 arXiv

  60. [70]

    Grain, M

    J. Grain, M. Tristram, and R. Stompor, Phys. Rev. D 79, 123515 (2009), arXiv:0903.2350 [astro-ph.CO]

    2009 arXiv

  61. [71]

    C. L. Bennett, G. F. Smoot, G. Hinshaw, et al., The Astrophysical Journal Letters 396, L7 (1992)

    1992

  62. [73]

    H. K. Eriksen, A. J. Banday, K. M. Gorski, and P. B. Lilje, The Astrophysical Journal 612, 633–646 (2004)

    2004

  63. [74]

    J. Dick, M. Remazeilles, and J. Delabrouille, Mon. Not. Roy. Astron. Soc.401, 1602 (2010), arXiv:0907.3105 [astro-ph.CO]. 20

    2010 arXiv

  64. [75]

    Alonso, J

    D. Alonso, J. Sanchez, and A. Slosar (LSST Dark Energy Science), Mon. Not. Roy. Astron. Soc. 484, 4127 (2019), arXiv:1809.09603 [astro-ph.CO]

    2019 arXiv

  65. [76]

    Main beam treatment in parametric, pixel-based component separa- tion,

    A. Rizzieri, J. Errard, and R. Stompor, “Main beam treatment in parametric, pixel-based component separa- tion,” (2024), arXiv:2409.12944 [astro-ph.CO]

    2024 arXiv

  66. [77]

    R. Saha, S. Prunet, P. Jain, and T. Souradeep, Physical Review D 78 (2008), 10.1103/physrevd.78.023003

    2008 doi

  67. [78]

    Puglisi, G

    G. Puglisi, G. Fabbian, and C. Baccigalupi, Mon. Not. R. Astron. Soc. 469, 2982 (2017), arXiv:1701.07856 [astro- ph.CO]

    2017 arXiv

  68. [79]

    Basak and J

    S. Basak and J. Delabrouille, Monthly Notices of the Royal Astronomical Society 419, 1163–1175 (2011)

    2011

  69. [80]

    Y. S. Abylkairov, O. Darwish, J. C. Hill, and B. D. Sherwin, Physical Review D 103 (2021), 10.1103/phys- revd.103.103510

    2021 doi

  70. [81]

    K. M. Gorski, E. Hivon, A. J. Banday, et al., The Astro- physical Journal 622, 759–771 (2005)

    2005

  71. [82]

    Aghanim, Y

    Planck Collaboration, N. Aghanim, Y. Akrami, et al., Astron. Astrophys. 641, A6 (2020)

    2020

  72. [83]

    P. A. R. Ade, Z. Ahmed, R. W. Aikin, et al. (Keck Ar- ray and BICEP2 Collaborations), Phys. Rev. Lett. 116, 031302 (2016)

    2016

  73. [84]

    Vansyngel, F

    F. Vansyngel, F. Boulanger, T. Ghosh, et al., Astron. As- trophys. 603, A62 (2017), [Erratum: Astron.Astrophys. 618, C4 (2018)], arXiv:1611.02577 [astro-ph.CO]

    2017 arXiv

  74. [85]

    Aghanim, M

    Planck Collaboration, N. Aghanim, M. Ashdown, et al., Astron. Astrophys. 599, A51 (2017), arXiv:1606.07335 [astro-ph.CO]

    2017 arXiv

  75. [86]

    Thorne, J

    B. Thorne, J. Dunkley, D. Alonso, and S. Næss, Monthly Notices of the Royal Astronomical Society 469, 2821–2833 (2017)

    2017

  76. [87]

    Namikawa, A

    T. Namikawa, A. I. Lonappan, C. Baccigalupi, et al., J. Cosmol. Astropart. Phys. 2024, 010 (2024), arXiv:2312.05194 [astro-ph.CO]

    2024 arXiv

  77. [88]

    Mart ´ ınez-Solaeche, A

    G. Mart ´ ınez-Solaeche, A. Karakci, and J. Delabrouille, Monthly Notices of the Royal Astronomical Society 476, 1310–1330 (2018)

    2018

  78. [89]

    Kogut, Astrophys

    A. Kogut, Astrophys. J. 753, 110 (2012), arXiv:1205.4041 [astro-ph.GA]

    2012 arXiv

  79. [90]

    P. A. R. Ade, M. Amiri, S. J. Benton, et al., Astrophys. J. 978, 130 (2025), arXiv:2407.20982 [astro-ph.GA]

    2025 arXiv

  80. [91]

    K. M. Smith, D. Hanson, M. LoVerde, et al., Journal of Cosmology and Astroparticle Physics 2012, 014–014 (2012)

    2012

  81. [92]

    B. D. Sherwin and M. Schmittfull, Physical Review D 92 (2015), 10.1103/physrevd.92.043005

    2015 doi

  82. [93]

    Carron and A

    J. Carron and A. Lewis, Phys. Rev. D 96, 063510 (2017), arXiv:1704.08230 [astro-ph.CO]

    2017 arXiv

  83. [94]

    Millea, E

    M. Millea, E. Anderes, and B. D. Wandelt, Physical Review D 100 (2019), 10.1103/physrevd.100.023509

    2019 doi

  84. [95]

    A. I. Lonappan, T. Namikawa, G. Piccirilli, et al., J. Cosmol. Astropart. Phys. 2024, 009 (2024), arXiv:2312.05184 [astro-ph.CO]

    2024 arXiv

  85. [96]

    Errard and R

    J. Errard and R. Stompor, Phys. Rev. D 99, 043529 (2019), arXiv:1811.00479 [astro-ph.CO]

    2019 arXiv

  86. [97]

    Cmb-s4: It- erative internal delensing and r constraints,

    S. Belkner, J. Carron, L. Legrand, et al., “Cmb-s4: It- erative internal delensing and r constraints,” (2023), arXiv:2310.06729 [astro-ph.CO]

    2023 arXiv

  87. [98]

    Cosmic microwave background delensing revisited: Residual bi- ases and a simple fix,

    W.-H. Teng, C.-L. Kuo, and J.-H. P. Wu, “Cosmic microwave background delensing revisited: Residual bi- ases and a simple fix,” (2011), arXiv:1102.5729 [astro- ph.CO]

    2011 arXiv

  88. [99]

    D. Beck, J. Errard, and R. Stompor, Journal of Cosmol- ogy and Astroparticle Physics 2020, 030–030 (2020)

    2020

  89. [100]

    Han et al

    D. Han et al. (ACT), J. Cosmol. Astropart. Phys. 01, 031 (2021), arXiv:2007.14405 [astro-ph.CO]

    2021 arXiv

  90. [101]

    Baleato Lizancos, A

    A. Baleato Lizancos, A. Challinor, and J. Carron, Phys. Rev. D 103, 023518 (2021), arXiv:2010.14286 [astro- ph.CO]

    2021 arXiv

  91. [102]

    CAMB: Code for Anisotropies in the Microwave Background,

    A. Lewis and A. Challinor, “CAMB: Code for Anisotropies in the Microwave Background,” Astro- physics Source Code Library, record ascl:1102.026 (2011)

    2011

  92. [103]

    Hartlap, P

    J. Hartlap, P. Simon, and P. Schneider, Astron. As- trophys. 464, 399 (2007), arXiv:astro-ph/0608064 [astro- ph]

    2007 arXiv

  93. [104]

    Torrado and A

    J. Torrado and A. Lewis, J. Cosmol. Astropart. Phys. 2021, 057 (2021), arXiv:2005.05290 [astro-ph.IM]

    2021 arXiv

  94. [106]

    Hastie, R

    T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Pre- diction, Springer series in statistics (Springer, 2009). Appendix A: Auto-and Cross-BB Spectra from the CMB-S4 South Pole Deep Patch In this section, we present th...

    2009

  95. [250]

    As in Fig

    The shaded gray bands denote modes at ℓ <30 and ℓ >200, which are not used in the likelihood analysis. As in Fig. 3, Model 2 shows a notable excess of residual power at large angular scales, whereas Models 0 and 1 exhibit minimal to negligible residuals. ¯r ± σ(r) [×103] Input...

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.