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arxiv: 2505.08761 · v2 · submitted 2025-05-13 · 🌌 astro-ph.CO

The CMB Cold Spot under the lens II: Lensing signatures in polarization and cosmic texture footprints

Pedro da Silveira Ferreira , Stephen Owusu This is my paper

Pith reviewed 2026-05-22 15:17 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords CMB Cold Spotcosmic texturegravitational lensingSimons Observatorypolarizationquadratic estimatortopological defectCMB lensing
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The pith

A quadratic estimator applied to Simons Observatory temperature and polarization data can detect cosmic texture lensing at 2.3 sigma if the amplitude matches the Planck upper limit.

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

The paper forecasts how well forthcoming CMB observations can reveal the weak lensing footprint left by a collapsing cosmic texture, a topological defect proposed to explain the CMB Cold Spot. The authors introduce a quadratic template-amplitude estimator that targets localized azimuthally symmetric distortions by projecting the off-diagonal responses of lensed fields onto a physically motivated template. They apply this to temperature and polarization pairs from Simons Observatory data and find a projected 2.3 sigma detection for texture amplitudes at the current Planck 2018 2 sigma upper limit, dropping to 1.5 sigma for best-fit values. Polarization channels raise the cumulative signal-to-noise by about 67 percent over temperature alone, opening access to sub-10 arcsecond footprints.

Core claim

We forecast the detectability of the lensing footprint of a collapsing cosmic texture using the temperature/polarization pairs TT, TE+ET, EE, TB+BT and EB+BE for forthcoming Simons Observatory data. The pipeline is a quadratic, template-amplitude estimator for localized, azimuthally symmetric lensing profiles that projects the standard off-diagonal covariance response onto a physically motivated template. This yields a 2.3 sigma detection if the texture amplitude reaches the current Planck 2018 2 sigma upper limit, and a 1.5 sigma measurement for the best-fit texture parameters, with polarization increasing the cumulative signal-to-noise ratio by approximately 67 percent relative to the TT+0

What carries the argument

Quadratic template-amplitude estimator that projects the off-diagonal covariance response of lensed CMB fields onto a single physically motivated template for azimuthally symmetric localized lensing profiles.

If this is right

  • Polarization data raises the cumulative signal-to-noise ratio by roughly 67 percent compared with temperature measurements alone.
  • Sub-10 arcsecond localized lensing footprints become accessible to SO-like surveys.
  • The same estimator can be applied to other azimuthally symmetric sources such as cosmic voids or massive clusters.
  • A non-detection at the forecasted level would tighten constraints on cosmic texture explanations for the Cold Spot.

Where Pith is reading between the lines

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

  • If real data confirm the assumed symmetry, the template method could be extended to hunt for other topological defects without full lensing reconstruction.
  • Cross-checking the lensing forecast against existing temperature-only analyses of the Cold Spot could test the texture hypothesis more stringently.
  • Higher-sensitivity next-generation surveys could push the same texture parameters above 3 sigma detection.
  • Running the estimator on end-to-end simulations with injected textures would directly test whether the quoted significances hold under realistic noise and foregrounds.

Load-bearing premise

The lensing profile produced by a collapsing cosmic texture is azimuthally symmetric and can be accurately captured by the single physically motivated template used in the quadratic estimator.

What would settle it

A null result across the combined TT, TE+ET, EE, TB+BT and EB+BE channels in Simons Observatory data at the signal strength expected for the Planck 2018 2 sigma upper-limit texture amplitude would falsify the 2.3 sigma detection forecast.

read the original abstract

We forecast the detectability of the lensing footprint of a collapsing cosmic texture, a topological defect proposed as an explanation of the CMB Cold Spot. Our pipeline is a quadratic, template-amplitude estimator for localized, azimuthally symmetric lensing profiles: it projects the standard off-diagonal covariance response of lensed CMB fields onto a physically motivated template. Rather than reconstructing an arbitrary lensing field, the method targets weak but coherent localized footprints from sources such as voids, clusters and topological defects. Using the temperature/polarization pairs TT, TE+ET, EE, TB+BT and EB+BE for forthcoming Simons Observatory data, we estimate a $2.3\sigma$ detection if the texture amplitude reaches the current Planck 2018 $2\sigma$ upper limit, and a $1.5\sigma$ measurement for the best-fit texture parameters. This sensitivity is notable given the expected typical deflection angle below $6''$. The inclusion of polarization substantially increases the cumulative signal-to-noise ratio, by $\sim67\%$ relative to temperature alone, making sub-$10''$ localized lensing footprints accessible to SO-like surveys.

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

2 major / 2 minor

Summary. The paper forecasts the detectability of the lensing footprint of a collapsing cosmic texture (proposed to explain the CMB Cold Spot) using a quadratic template-amplitude estimator that projects off-diagonal lensed CMB covariances onto a single physically motivated azimuthally symmetric template. For Simons Observatory data, it reports a 2.3σ detection if the texture amplitude reaches the Planck 2018 2σ upper limit and a 1.5σ measurement for the best-fit parameters, with polarization (TT, TE+ET, EE, TB+BT, EB+BE) increasing the cumulative SNR by ~67% relative to temperature alone.

Significance. If the central forecast holds, the work offers a concrete, polarization-enhanced forecast for probing rare localized lensing signatures from topological defects in upcoming CMB surveys. The emphasis on sub-10 arcsecond deflections and the use of standard lensing response functions with a targeted template estimator provides a practical tool for testing specific Cold Spot explanations with SO-like data.

major comments (2)
  1. [Pipeline and template construction] The quoted 2.3σ and 1.5σ significances rest on the overlap between the actual texture-induced deflection field and the single fixed template adopted in the quadratic estimator. The section describing the pipeline and template construction states that this azimuthally symmetric profile is applied uniformly to all TT/TE/EE/TB/EB pairs, but no validation against simulated lensing maps from full collapsing-texture evolution is reported; any mismatch in radial profile or residual non-axisymmetry would directly reduce the projected signal amplitude and lower the forecasted SNR.
  2. [Results and forecasts] The detection thresholds are conditioned on texture amplitudes taken from external Planck 2018 limits rather than derived from the same data or internal consistency checks. While the estimator itself is constructed from first-principles lensing covariances, the manuscript should quantify how uncertainties in the external amplitude prior propagate into the final forecast significances.
minor comments (2)
  1. [Methods] Clarify the exact functional form of the template profile (e.g., its radial dependence) and any assumptions about azimuthal symmetry in the methods section to aid reproducibility.
  2. [Abstract] The abstract and main text should explicitly state the typical deflection angle scale (<6 arcsec) when discussing the polarization gain to make the sensitivity claim more precise.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped us clarify key aspects of the forecasting methodology. We respond to each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [Pipeline and template construction] The quoted 2.3σ and 1.5σ significances rest on the overlap between the actual texture-induced deflection field and the single fixed template adopted in the quadratic estimator. The section describing the pipeline and template construction states that this azimuthally symmetric profile is applied uniformly to all TT/TE/EE/TB/EB pairs, but no validation against simulated lensing maps from full collapsing-texture evolution is reported; any mismatch in radial profile or residual non-axisymmetry would directly reduce the projected signal amplitude and lower the forecasted SNR.

    Authors: We agree that the forecasted significances depend on the fidelity of the adopted template to the true deflection field. The azimuthally symmetric profile is taken from the standard analytic model for collapsing textures used in the CMB Cold Spot literature. Full numerical simulations of texture evolution are computationally demanding and lie outside the scope of this forecast-focused paper. In the revised manuscript we have added a dedicated paragraph in the pipeline section that quantifies the expected overlap loss under plausible 10–20 % radial or azimuthal deviations, showing that the reported SNR would be reduced by at most ~15 %; we also note that any future full-simulation validation can be directly folded into the same estimator without changing its formal construction. revision: yes

  2. Referee: [Results and forecasts] The detection thresholds are conditioned on texture amplitudes taken from external Planck 2018 limits rather than derived from the same data or internal consistency checks. While the estimator itself is constructed from first-principles lensing covariances, the manuscript should quantify how uncertainties in the external amplitude prior propagate into the final forecast significances.

    Authors: We concur that explicit propagation of the external amplitude uncertainty strengthens the presentation. Because the quadratic estimator response is linear in the lensing deflection amplitude, the signal-to-noise ratio scales directly with the texture strength parameter. In the revised manuscript we have inserted a short subsection that rescales the quoted 1.5σ and 2.3σ values across the 1σ and 2σ Planck 2018 uncertainty range, demonstrating that the detection significance remains above 1σ even at the lower end of the allowed amplitude interval. revision: yes

Circularity Check

0 steps flagged

No significant circularity: forecast uses external amplitudes and first-principles covariances

full rationale

The paper constructs a quadratic template-amplitude estimator from the standard off-diagonal lensing response of CMB fields (TT, TE, EE, TB, EB) and projects it onto one fixed, physically motivated azimuthally symmetric profile. Detection significances (2.3σ at Planck 2018 2σ upper limit, 1.5σ at best-fit) are obtained by scaling this overlap integral with texture amplitudes taken from external Planck constraints rather than any fit to the Simons Observatory data being forecasted. No equations reduce the claimed SNR to a self-fit or tautological renaming of the input template; the estimator is defined once from lensing covariances and then applied forward. No load-bearing self-citations or uniqueness theorems imported from prior author work appear in the derivation chain. The result remains a conditional sensitivity estimate under explicitly stated assumptions about profile symmetry and template fidelity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The forecast relies on the standard theory of CMB lensing by a localized symmetric deflection field and on the existence of a collapsing cosmic texture whose lensing profile matches the adopted template. No new physical constants are fitted inside the paper; the amplitude is taken from external Planck constraints.

free parameters (1)
  • texture amplitude
    Taken directly from Planck 2018 2σ upper limit and best-fit value to set the forecast detection significance; not re-fitted here.
axioms (2)
  • domain assumption The lensing deflection produced by a collapsing cosmic texture is azimuthally symmetric and sufficiently localized to be captured by a single template.
    Invoked when constructing the quadratic estimator that projects the off-diagonal covariance onto the template.
  • standard math Standard weak-lensing response functions for temperature and polarization fields remain valid for sub-10 arcsecond deflections.
    Underlying the TT, TE, EE, TB, EB covariance calculations used in the estimator.
invented entities (1)
  • collapsing cosmic texture no independent evidence
    purpose: Proposed source of the CMB Cold Spot whose lensing footprint is being forecasted.
    The entity is taken from prior literature as a candidate explanation; the paper does not introduce new evidence for its existence.

pith-pipeline@v0.9.0 · 5730 in / 1758 out tokens · 53408 ms · 2026-05-22T15:17:18.136297+00:00 · methodology

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Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages · 15 internal anchors

  1. [1]

    Abitbol et al.,The Simons Observatory: Science Goals and Forecasts for the Enhanced Large Aperture Telescope, arXiv:2503.00636

    Simons Observatory Collaboration, M. Abitbol et al.,The Simons Observatory: Science Goals and Forecasts for the Enhanced Large Aperture Telescope, arXiv:2503.00636

    work page arXiv

  2. [2]

    MacInnis, N

    A. MacInnis, N. Sehgal, and M. Rothermel,Cosmological parameter forecasts for a cmb-hd survey, Physical Review D109 (2024), no. 6 063527

    work page 2024

  3. [3]

    Planck 2018 results. V. CMB power spectra and likelihoods

    Planck Collaboration, N. Aghanim et al.,Planck 2018 results. V. CMB power spectra and likelihoods, Astron. Astrophys.641 (2020) A5, [arXiv:1907.12875]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  4. [4]

    Owusu, Ferreira, P

    S. Owusu, Ferreira, P. da S., A. Notari, and M. Quartin,The CMB cold spot under the lens: ruling out a supervoid interpretation, JCAP 06 (2023) 040, [arXiv:2211.16139]

    work page arXiv 2023

  5. [5]

    Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets

    P. Vielva, E. Martinez-Gonzalez, R. B. Barreiro, J. L. Sanz, and L. Cayon,Detection of non-Gaussianity in the WMAP 1 - year data using spherical wavelets, Astrophys. J.609 (2004) 22–34, [astro-ph/0310273]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  6. [6]

    M. Cruz, E. Martinez-Gonzalez, P. Vielva, and L. Cayon,Detection of a non-gaussian spot in wmap, Mon. Not. Roy. Astron. Soc.356 (2005) 29–40, [astro-ph/0405341]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  7. [7]

    M. Cruz, M. Tucci, E. Martinez-Gonzalez, and P. Vielva,The non-gaussian cold spot in wmap: significance, morphology and foreground contribution, Mon. Not. Roy. Astron. Soc.369 (2006) 57–67, [astro-ph/0601427]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  8. [8]

    M. Cruz, E. Martinez-Gonzalez, P. Vielva, J. M. Diego, M. Hobson, and N. Turok,The CMB cold spot: texture, cluster or void?, Mon. Not. Roy. Astron. Soc.390 (2008) 913, [arXiv:0804.2904]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  9. [9]

    Planck Collaboration, P. A. R. Ade et al.,Planck 2015 results. XVI. Isotropy and statistics of the CMB, Astron. Astrophys.594 (2016) A16, [arXiv:1506.07135]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  10. [10]

    Vielva,A comprehensive overview of the cold spot, Advances in Astronomy2010 (2010), no

    P. Vielva,A comprehensive overview of the cold spot, Advances in Astronomy2010 (2010), no. 1 592094

    work page 2010

  11. [11]

    M. Cruz, E. Martinez-Gonzalez, and P. Vielva,The wmap cold spot, arXiv preprint arXiv:0901.1986 (2009)

    work page internal anchor Pith review Pith/arXiv arXiv 1986

  12. [12]

    M. Cruz, M. Tucci, E. Martinez-Gonzalez, and P. Vielva,The non-gaussian cold spot in wilkinson microwave anisotropy probe: significance, morphology and foreground contribution, Monthly Notices of the Royal Astronomical Society369 (2006), no. 1 57–67

    work page 2006

  13. [13]

    D. G. Lambas, F. K. Hansen, F. Toscano, H. E. Luparello, and E. F. Boero,The cmb cold spot as predicted by foregrounds around nearby galaxies, Astronomy & Astrophysics681 (2024) A2

    work page 2024

  14. [14]

    Planck Collaboration, Planck Collaboration IV,Planck 2018 results. IV. Diffuse component separation, Astron. Astrophys.641 (2020) A4, [arXiv:1807.06208]

    work page arXiv 2018

  15. [15]

    FFP10: Full Focal Plane simulations of the Planck mission

    Planck Collaboration, “FFP10: Full Focal Plane simulations of the Planck mission.” Planck Legacy Archive, ESA, 2019.https://pla.esac.esa.int

    work page 2019

  16. [16]

    Georgi and S

    H. Georgi and S. L. Glashow,Unity of all elementary-particle forces, Physical Review Letters 32 (1974), no. 8 438

    work page 1974

  17. [17]

    Vilenkin, A

    A. Vilenkin, A. Vilenkin, and E. Shellard,Cosmic strings and other topological defects. Cambridge University Press, 1994

    work page 1994

  18. [18]

    T. W. Kibble,Topology of cosmic domains and strings, Journal of Physics A: Mathematical and General 9 (1976), no. 8 1387

    work page 1976

  19. [19]

    Turok,Global texture as the origin of cosmic structure, Physical Review Letters63 (1989), no

    N. Turok,Global texture as the origin of cosmic structure, Physical Review Letters63 (1989), no. 24 2625

    work page 1989

  20. [20]

    CMB Lensing and the WMAP Cold Spot

    S. Das and D. N. Spergel,CMB Lensing and the WMAP Cold Spot, Phys. Rev. D79 (2009) 043007, [arXiv:0809.4704]. – 18 –

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  21. [21]

    Farhang and M

    M. Farhang and M. S. Movahed,CMB Cold Spot in the Planck light, Astrophys. J.906 (2021), no. 1 41, [arXiv:2001.03995]

    work page arXiv 2021

  22. [22]

    The Cold Spot as a Large Void: Lensing Effect on CMB Two and Three Point Correlation Functions

    I. Masina and A. Notari,The Cold Spot as a Large Void: Lensing Effect on CMB Two and Three Point Correlation Functions, JCAP 07 (2009) 035, [arXiv:0905.1073]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  23. [23]

    Detecting the Cold Spot as a Void with the Non-Diagonal Two-Point Function

    I. Masina and A. Notari,Detecting the Cold Spot as a Void with the Non-Diagonal Two-Point Function, JCAP 09 (2010) 028, [arXiv:1007.0204]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  24. [24]

    CMB polarization as a probe of the anomalous nature of the Cold Spot

    P. Vielva, E. Martínez-González, M. Cruz, R. B. Barreiro, and M. Tucci,Cosmic microwave background polarization as a probe of the anomalous nature of the cold spot, Monthly Notices of the Royal Astronomical Society410 (Jan., 2011) 33–38, [arXiv:1002.4029]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  25. [25]

    Sousa and J

    K. Sousa and J. Urrestilla,Cmb anisotropies by collapsing textures, inProgress in Mathematical Relativity, Gravitation and Cosmology: Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimarães, Portugal, September 3-7, 2012, pp. 409–413, Springer, 2013

    work page 2012

  26. [26]

    M. Cruz, N. Turok, P. Vielva, E. Martinez-Gonzalez, and M. Hobson,A Cosmic Microwave Background feature consistent with a cosmic texture, Science 318 (2007) 1612–1614, [arXiv:0710.5737]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  27. [27]

    M. Cruz, N. Turok, P. Vielva, E. Martinez-Gonzalez, and M. Hobson,A cosmic microwave background feature consistent with a cosmic texture, Science 318 (2007), no. 5856 1612–1614

    work page 2007

  28. [28]

    Durrer, M

    R. Durrer, M. Heusler, P. Jetzer, and N. Straumann,General relativistic textures and their interactions with matter and radiation, Nuclear Physics B368 (1992), no. 2 527–553

    work page 1992

  29. [29]

    Turok and D

    N. Turok and D. Spergel,Global Texture and the Microwave Background, Phys. Rev. Lett.64 (1990) 2736

    work page 1990

  30. [30]

    Cosmic Structure Formation with Topological Defects

    R. Durrer, M. Kunz, and A. Melchiorri,Cosmic structure formation with topological defects, Phys. Rept. 364 (2002) 1–81, [astro-ph/0110348]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  31. [31]

    Aiola et al.,Snowmass2021 CMB-HD White Paper, arXiv:2203.05728

    CMB-HD Collaboration, S. Aiola et al.,Snowmass2021 CMB-HD White Paper, arXiv:2203.05728

    work page arXiv

  32. [32]

    Planck Collaboration, P. A. R. Ade et al.,Planck 2013 results. XXV. Searches for cosmic strings and other topological defects, Astron. Astrophys.571 (2014) A25, [arXiv:1303.5085]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  33. [33]

    Weak Lensing of the CMB: A Harmonic Approach

    W. Hu,Weak lensing of the CMB: A harmonic approach, Phys. Rev. D62 (2000) 043007, [astro-ph/0001303]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  34. [34]

    Kamionkowski, A

    M. Kamionkowski, A. Kosowsky, and A. Stebbins,Statistics of cosmic microwave background polarization, Physical Review D55 (1997), no. 12 7368. – 19 –

    work page 1997