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arxiv: 2605.14572 · v2 · pith:3EEVP7WZnew · submitted 2026-05-14 · 🌀 gr-qc · astro-ph.CO

Modifications of CMB Temperature and Polarization Quadrupole Signals in Thurston Spacetimes

Tanay Gupta , Sukanta Panda , Rajib Saha This is my paper

Pith reviewed 2026-05-20 21:24 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.CO
keywords CMB anisotropyThurston geometriesStokes parametersquadrupole signalspolarization patternscosmic isotropy violationanisotropic spacetimes
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The pith

Thurston spacetimes generate distinguishable symmetries in CMB temperature and polarization quadrupole signals through Stokes parameters.

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

The paper explores anisotropic Thurston geometries as a possible explanation for observed violations of large-scale isotropy in the cosmic microwave background. It sets up Thurston spacetimes as background models, constructs transfer equations for each geometry, and solves them to track the time evolution of temperature and polarization amplitudes. These amplitudes are expressed using the Stokes parameters P, Q, U, and V, with the goal of identifying unique symmetry patterns that could isolate one geometry from another. A reader would care because such patterns might offer a direct observational test for non-standard cosmic topologies or curvatures that standard isotropic models cannot accommodate.

Core claim

By introducing Thurston spacetimes as background models and constructing transfer equations relative to each geometry, the resulting Stokes-parameter patterns exhibit distinguishable symmetries. Solving these equations shows the evolution of temperature and polarization amplitudes at different timestamps, allowing attempts to isolate individual Thurston geometries while highlighting the role of spatial curvature in the FLRW limiting cases.

What carries the argument

Transfer equations solved relative to each Thurston spacetime background to produce time-evolved Stokes-parameter patterns (P, Q, U, V) in CMB quadrupole signals.

If this is right

  • Each Thurston geometry produces a unique time-dependent signature in the CMB Stokes parameters.
  • Spatial curvature effects become visible in the patterns when comparing to standard FLRW limits.
  • Symmetry properties of the patterns can be used to establish general results across the family of models.
  • The approach provides a framework for testing anisotropic backgrounds against CMB data.

Where Pith is reading between the lines

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

  • Detection of these patterns in real data could narrow the range of viable global topologies for the universe.
  • The method might be extended to compare predictions against multipole data from existing surveys.
  • Similar transfer-equation techniques could apply to other anisotropic or topologically nontrivial metrics.

Load-bearing premise

The Stokes-parameter patterns produced by the transfer equations for different Thurston backgrounds will display symmetries distinct enough to isolate each geometry from observations.

What would settle it

CMB observations showing either identical quadrupole patterns across all Thurston geometries or no match to any of the predicted Stokes-parameter symmetry evolutions would falsify the ability to isolate individual geometries.

Figures

Figures reproduced from arXiv: 2605.14572 by Rajib Saha, Sukanta Panda, Tanay Gupta.

Figure 1
Figure 1. Figure 1: Ideal linear polarization ∂f ∂t + ˙q ∂f ∂q + ˙p ∂f ∂p = 0 (3.10) where pa = ∂xa/∂λ is the four-momentum of the photon, λ being the affine parameter along the photon path (geodesic proper distance/ conformal time). Equation (3.10) can be promoted to relativistic form, given the theory of radiative transfer (see [46]) as p α ∂f ∂xα − Γ α βγp β p γ ∂f ∂pα = 0 (3.11) where the first term is the same as equatio… view at source ↗
Figure 2
Figure 2. Figure 2: Mechanism of polarization generation from gravitational field [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Temperature and polarization signals for [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Temperature and polarization signals for [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Temperature and polarization signals for [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Temperature and polarization signals for [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Temperature and polarization signals for [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Temperature and polarization signals for [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Temperature and polarization signals for Nil geometry. Cosmic (physical) time increases from [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Temperature and polarization signals for Solv geometry. Cosmic (physical) time increases from [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
read the original abstract

Recent cosmological tests have discovered a fresh new set of anomalies in the large-scale isotropy of the universe. Motivated thus by the numerous pieces of evidence for large-scale cosmic isotropy violation with the advent of the 'precision cosmology' era, we are led to explore the viability of anisotropic Thurston geometries, described in William Thurston's geometrization conjecture. In this work, we examine the coherent temperature and polarization signals generated in the CMB sky by such geometries. We begin with introducing Thurston spacetimes as our background model and the formalism we use to obtain the patterns. We then construct a set of transfer equations relative to a given background and solve them for each spacetime geometry. We finally discuss the role of spatial curvature in these FLRW limiting models along with their underlying geometry, and attempt to establish some general results on the symmetries of the patterns produced by their time evolution in terms of the Stokes parameters P, Q, U and V. We show the evolution of temperature and polarization amplitudes in terms of such Stokes parameters at different timestamps and attempt to isolate individual Thurston geometries.

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 / 3 minor

Summary. The manuscript examines CMB temperature and polarization quadrupole signals in anisotropic Thurston spacetimes as potential explanations for observed large-scale isotropy violations. It introduces Thurston geometries as backgrounds, constructs and solves transfer equations for the Stokes parameters (P, Q, U, V) in each case, analyzes the resulting patterns' symmetries and time evolution, and attempts to isolate individual geometries through their distinguishable features.

Significance. If the derived Stokes-parameter patterns prove distinguishable by symmetry and evolution, the work provides a concrete framework linking Thurston geometries to observable CMB anomalies. The explicit transfer-equation construction and discussion of curvature effects in FLRW limits represent a useful technical contribution, though quantitative validation against data would strengthen its impact.

major comments (2)
  1. The central claim that individual Thurston geometries can be isolated rests on the symmetries of the solved Stokes-parameter patterns, yet the manuscript provides no quantitative metric (e.g., overlap integrals, chi-squared distinguishability, or multipole-by-multipole comparison) to demonstrate that the patterns are observationally separable; this weakens the isolation result in the final section.
  2. The transfer equations are stated to be constructed relative to each Thurston background, but the explicit modifications to the standard Boltzmann hierarchy (e.g., changes to the geodesic deviation or polarization transport terms) are not derived or referenced to a numbered equation, making it difficult to verify the adaptation for non-FLRW curvature.
minor comments (3)
  1. The abstract outlines the procedure but does not preview any specific numerical results or symmetry classifications; a sentence summarizing the key distinguishable features would improve clarity.
  2. Figure captions for the time-evolution plots should specify the exact timestamps, normalization conventions for the Stokes amplitudes, and the coordinate system used for the quadrupole.
  3. A brief comparison table listing the dominant symmetry properties (e.g., parity or rotational invariance) for each Thurston geometry would aid readers in following the isolation argument.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We address each major comment below and have made revisions to strengthen the paper accordingly.

read point-by-point responses

  1. Referee: The central claim that individual Thurston geometries can be isolated rests on the symmetries of the solved Stokes-parameter patterns, yet the manuscript provides no quantitative metric (e.g., overlap integrals, chi-squared distinguishability, or multipole-by-multipole comparison) to demonstrate that the patterns are observationally separable; this weakens the isolation result in the final section.

    Authors: We agree that quantitative metrics would enhance the robustness of our isolation claims. Although the distinct symmetry patterns in the Stokes parameters (P, Q, U, V) for each Thurston geometry, as derived from the time evolution, allow for qualitative differentiation, we have added in the revised manuscript a quantitative comparison using overlap integrals between the quadrupole patterns of different geometries. This demonstrates their separability at a level sufficient for observational distinction, addressing the concern directly. revision: yes

  2. Referee: The transfer equations are stated to be constructed relative to each Thurston background, but the explicit modifications to the standard Boltzmann hierarchy (e.g., changes to the geodesic deviation or polarization transport terms) are not derived or referenced to a numbered equation, making it difficult to verify the adaptation for non-FLRW curvature.

    Authors: We acknowledge that the explicit form of the modifications to the Boltzmann hierarchy was not sufficiently detailed in the original submission. The adaptations involve incorporating the specific curvature effects of each Thurston spacetime into the geodesic deviation equation and the polarization transport terms. In the revised version, we have added a dedicated subsection deriving these modifications step by step, with references to the corresponding numbered equations in the main text and an appendix for full details. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard transfer formalism applied to new backgrounds

full rationale

The paper introduces Thurston spacetimes as background models, constructs transfer equations for the Stokes parameters relative to each given background, solves them explicitly for the geometries, and derives the resulting temperature and polarization patterns along with their symmetries and time evolution. These steps rely on the standard cosmological transfer formalism applied to the new anisotropic backgrounds; the patterns and their distinguishability are outputs of the solved equations rather than inputs by definition or self-citation. No load-bearing step reduces to a fitted parameter renamed as prediction, a self-definitional loop, or an ansatz smuggled via prior self-work. The central claim of isolatable geometries follows directly from the explicit solutions and symmetry analysis presented.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the central modeling step rests on the domain assumption that Thurston geometries can serve as viable cosmological backgrounds and that their transfer equations admit solvable patterns with identifiable symmetries.

axioms (1)
  • domain assumption Thurston spacetimes can be used as background models for the universe in place of FLRW
    The paper begins by introducing these geometries as the background for CMB calculations.

pith-pipeline@v0.9.0 · 5724 in / 1226 out tokens · 59121 ms · 2026-05-20T21:24:40.987499+00:00 · methodology

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Works this paper leans on

78 extracted references · 78 canonical work pages · 7 internal anchors

  1. [1]

    These are:

    Solv These eight maximal geometries can be said to form the building blocks of all compact 3-manifolds and are referred to asThurston geometries. These are:

    work page

  2. [2]

    FLRW spacetimes R3/H3/S3 (3) ds2 =−dt 2 +a 2(t){dχ2 +S 2 κ(χ)dΩ2}(2.1)

    work page

  3. [3]

    FLRW spacetimes in 2D with a third flat anisotropic axis R×H 2/S2 (2) ds2 =−dt 2 +a 2(t){dz2 +dχ 2 +S 2 κ(χ)dϕ2}(2.2) {z∈R is orthogonal to (χ,ϕ) plane} where Sκ(χ) =    sin(χ√κ)√κ , κ >0 (S 3,R×S 2) χ, κ= 0 sinh(χ√−κ)√−κ , κ <0 (H 3,R×H 2) (2.3) whereκis the curvature parameter of the universe and is related to the radius of curvature of each Thur...

    work page

  4. [4]

    Universal cover of the unit tangent bundle of the hyperbolic plane ^U(H2) (1) ds2 =−dt 2 +a 2(t) n dx2 + cosh2 x √ −κ dy2 + dz+ sinh x √ −κ dy 2o (2.5)

    work page

  5. [5]

    Nilpotent subgroup of an extension of the group of isometries (abb.Nil)(1) ds2 =−dt 2 +a 2(t) dx2 + 1−κ x 2 dy2 +dz 2 −2x √ −κ dy dz (2.6)

    work page

  6. [6]

    Solvable Lie group (abb.Solv)(1) ds2 =−dt 2 +a 2(t){e2z√−κdx2 +e −2z√−κdy2 +dz 2}(2.7) As is evident, all the anisotropic Thurston geometries (2.2), (2.5) - (2.7) reduce to flat FLRW in the limit κ→0. 2 3 Evolution equations To analyze photon geodesics in each of our geometries, we introduce a tetrad basis constructed from a local coordinate systemx α [45...

    work page

  7. [7]

    Desi 2024 vi: cosmological constraints from the measurements of baryon acoustic oscillations.Journal of Cosmology and Astroparticle Physics, 2025(02):021, 2025

    AG Adame, J Aguilar, S Ahlen, Se Alam, DM Alexander, M Alvarez, O Alves, A Anand, U Andrade, E Armengaud, et al. Desi 2024 vi: cosmological constraints from the measurements of baryon acoustic oscillations.Journal of Cosmology and Astroparticle Physics, 2025(02):021, 2025

    work page 2024

  8. [8]

    Planck 2018 results-v

    Nabila Aghanim, Yashar Akrami, Mark Ashdown, J Aumont, Carlo Baccigalupi, M Ballardini, An- thony J Banday, RB Barreiro, N Bartolo, S Basak, et al. Planck 2018 results-v. cmb power spectra and likelihoods.Astronomy & Astrophysics, 641:A5, 2020

    work page 2018

  9. [9]

    First cosmology results using type ia supernovae from the dark energy survey: constraints on cosmological parameters.The Astrophysical Journal Letters, 872(2):L30, 2019

    TMC Abbott, S Allam, P Andersen, Charlotte Angus, J Asorey, A Avelino, S Avila, BA Bassett, K Bechtol, GM Bernstein, et al. First cosmology results using type ia supernovae from the dark energy survey: constraints on cosmological parameters.The Astrophysical Journal Letters, 872(2):L30, 2019

    work page 2019

  10. [10]

    Shadab Alam, Metin Ata, Stephen Bailey, Florian Beutler, Dmitry Bizyaev, Jonathan A Blazek, Adam S Bolton, Joel R Brownstein, Angela Burden, Chia-Hsun Chuang, et al. The clustering of galaxies in the completed sdss-iii baryon oscillation spectroscopic survey: cosmological analysis of the dr12 galaxy sample.Monthly Notices of the Royal Astronomical Society...

    work page 2017

  11. [11]

    Large-scale geometry of the universe.Journal of Cosmology and Astroparticle Physics, 2024(01):010, 2024

    Yassir Awwad and Tomislav Prokopec. Large-scale geometry of the universe.Journal of Cosmology and Astroparticle Physics, 2024(01):010, 2024

    work page 2024

  12. [12]

    Three dimensional manifolds, kleinian groups and hyperbolic geometry

    William P Thurston. Three dimensional manifolds, kleinian groups and hyperbolic geometry. 1982

    work page 1982

  13. [13]

    The entropy formula for the Ricci flow and its geometric applications

    Grisha Perelman. The entropy formula for the ricci flow and its geometric applications.arXiv preprint math/0211159, 2002

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  14. [14]

    Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

    Grisha Perelman. Finite extinction time for the solutions to the ricci flow on certain three-manifolds. arXiv preprint math/0307245, 2003

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  15. [15]

    Ricci flow with surgery on three-manifolds

    Grisha Perelman. Ricci flow with surgery on three-manifolds.arXiv preprint math/0303109, 2003

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  16. [16]

    Asymmetry of the cmb map: local and global anomalies.Journal of Cosmology and Astroparticle Physics, 2021(03):103, 2021

    James Creswell and Pavel Naselsky. Asymmetry of the cmb map: local and global anomalies.Journal of Cosmology and Astroparticle Physics, 2021(03):103, 2021

    work page 2021

  17. [17]

    Anomalous cmb north-south asymmetry.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 78(6):063531, 2008

    Armando Bernui. Anomalous cmb north-south asymmetry.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 78(6):063531, 2008

    work page 2008

  18. [18]

    Scale-dependent non-gaussianity and the cmb power asym- metry.Journal of Cosmology and Astroparticle Physics, 2015(07):007–007, 2015

    Christian T Byrnes and Ewan RM Tarrant. Scale-dependent non-gaussianity and the cmb power asym- metry.Journal of Cosmology and Astroparticle Physics, 2015(07):007–007, 2015

    work page 2015

  19. [19]

    Symmetry and antisymmetry of the cmb anisotropy pattern.Advances in Astronomy, 2012(1):960509, 2012

    Jaiseung Kim, Pavel Naselsky, and Martin Hansen. Symmetry and antisymmetry of the cmb anisotropy pattern.Advances in Astronomy, 2012(1):960509, 2012

    work page 2012

  20. [20]

    Directional dependence of cmb parity asymmetry.Physical Review D, 89(2):023010, 2014

    Wen Zhao. Directional dependence of cmb parity asymmetry.Physical Review D, 89(2):023010, 2014

    work page 2014

  21. [21]

    Spectral distortions of the cmb dipole.The Astrophysical Journal, 810(2):131, 2015

    SA Balashev, EE Kholupenko, J Chluba, AV Ivanchik, and DA Varshalovich. Spectral distortions of the cmb dipole.The Astrophysical Journal, 810(2):131, 2015

    work page 2015

  22. [22]

    Superposition of blackbodies and the dipole anisotropy: A possibility to calibrate cmb experiments.Astronomy & Astrophysics, 424(2):389–408, 2004

    Jens Chluba and RA Sunyaev. Superposition of blackbodies and the dipole anisotropy: A possibility to calibrate cmb experiments.Astronomy & Astrophysics, 424(2):389–408, 2004

    work page 2004

  23. [23]

    The cmb cold spot as predicted by foregrounds around nearby galaxies.Astronomy & Astrophysics, 681:A2, 2024

    Diego Garcia Lambas, Frode K Hansen, Facundo Toscano, Heliana E Luparello, and Ezequiel F Boero. The cmb cold spot as predicted by foregrounds around nearby galaxies.Astronomy & Astrophysics, 681:A2, 2024

    work page 2024

  24. [24]

    Cmb cold spot in the planck light.The Astrophysical Journal, 906(1):41, 2021

    Marzieh Farhang and SMS Movahed. Cmb cold spot in the planck light.The Astrophysical Journal, 906(1):41, 2021

    work page 2021

  25. [25]

    Is the cold spot responsible for the cmb north-south asymmetry?Physical Review D—Particles, Fields, Gravitation, and Cosmology, 80(12):123010, 2009

    Armando Bernui. Is the cold spot responsible for the cmb north-south asymmetry?Physical Review D—Particles, Fields, Gravitation, and Cosmology, 80(12):123010, 2009

    work page 2009

  26. [26]

    Lack-of-correlation anomaly in cmb large scale polarisation maps.Journal of Cosmology and Astropar- ticle Physics, 2021(08):015, 2021

    Caterina Chiocchetta, Alessandro Gruppuso, Massimiliano Lattanzi, Paolo Natoli, and Luca Pagano. Lack-of-correlation anomaly in cmb large scale polarisation maps.Journal of Cosmology and Astropar- ticle Physics, 2021(08):015, 2021

    work page 2021

  27. [27]

    Planck 2018 results-vii

    Yashar Akrami, M Ashdown, Jonathan Aumont, Carlo Baccigalupi, M Ballardini, Anthony J Banday, RB Barreiro, Nicola Bartolo, S Basak, K Benabed, et al. Planck 2018 results-vii. isotropy and statistics of the cmb.Astronomy & Astrophysics, 641:A7, 2020

    work page 2018

  28. [28]

    Planck intermediate results-xlvi

    Nabila Aghanim, Mark Ashdown, Jonathan Aumont, Carlo Baccigalupi, Mario Ballardini, AJ Banday, RB Barreiro, Nicola Bartolo, Suman Basak, R Battye, et al. Planck intermediate results-xlvi. reduction of large-scale systematic effects in hfi polarization maps and estimation of the reionization optical depth. Astronomy & Astrophysics, 596:A107, 2016

    work page 2016

  29. [29]

    Testing cosmic microwave background anomalies in e-mode polarization with current and future data.The Astrophysical Journal, 945(1):79, 2023

    Rui Shi, Tobias A Marriage, John W Appel, Charles L Bennett, David T Chuss, Joseph Cleary, Joseph R Eimer, Sumit Dahal, Rahul Datta, Francisco Espinoza, et al. Testing cosmic microwave background anomalies in e-mode polarization with current and future data.The Astrophysical Journal, 945(1):79, 2023. 19

    work page 2023

  30. [30]

    Cmb anomalies after planck.Classical and Quantum Gravity, 33(18):184001, 2016

    Dominik J Schwarz, Craig J Copi, Dragan Huterer, and Glenn D Starkman. Cmb anomalies after planck.Classical and Quantum Gravity, 33(18):184001, 2016

    work page 2016

  31. [31]

    First-year wilkinson microwave anisotropy probe (wmap) observations: determination of cosmological parameters.The Astrophysical Journal Supplement Series, 148(1):175–194, 2003

    David N Spergel, Licia Verde, Hiranya V Peiris, Eiichiro Komatsu, MR Nolta, Charles L Bennett, Mark Halpern, Gary Hinshaw, Norman Jarosik, Alan Kogut, et al. First-year wilkinson microwave anisotropy probe (wmap) observations: determination of cosmological parameters.The Astrophysical Journal Supplement Series, 148(1):175–194, 2003

    work page 2003

  32. [32]

    The des view of the eridanus supervoid and the cmb cold spot.Monthly Notices of the Royal Astronomical Society, 510(1):216–229, 2022

    András Kovács, Niall Jeffrey, Marco Gatti, Chihway Chang, Lorne Whiteway, Nico Hamaus, Ofer Lahav, Giorgia Pollina, David Bacon, Tomasz Kacprzak, et al. The des view of the eridanus supervoid and the cmb cold spot.Monthly Notices of the Royal Astronomical Society, 510(1):216–229, 2022

    work page 2022

  33. [33]

    Evidence against a supervoid causing the cmb cold spot.Monthly Notices of the Royal Astronomical Society, 470(2):2328–2338, 2017

    Ruari Mackenzie, Tom Shanks, Malcolm N Bremer, Yan-Chuan Cai, Madusha LP Gunawardhana, András Kovács, Peder Norberg, and Istvan Szapudi. Evidence against a supervoid causing the cmb cold spot.Monthly Notices of the Royal Astronomical Society, 470(2):2328–2338, 2017

    work page 2017

  34. [34]

    Forecasts of CMB $E$-mode anomalies for AliCPT-1

    Jiazheng Dou and Wen Zhao. Forecasts of cmbe-mode anomalies for alicpt-1.arXiv preprint arXiv:2604.20699, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  35. [35]

    Geometric origin of cmb large-angle anomalies from discrete vacuum nucleation, 2026

    Raghu Kulkarni. Geometric origin of cmb large-angle anomalies from discrete vacuum nucleation, 2026

    work page 2026

  36. [36]

    The cmb axis of evil as a holographic projection effect: An observer-dependent inter- pretation

    Marcel Krüger. The cmb axis of evil as a holographic projection effect: An observer-dependent inter- pretation

    work page

  37. [37]

    The joint large-scale foreground-cmb posteriors of the 3 year wmap data.The Astrophysical Journal Letters, 672(2):L87–L90, 2008

    HK Eriksen, C Dickinson, JB Jewell, AJ Banday, KM Górski, and CR Lawrence. The joint large-scale foreground-cmb posteriors of the 3 year wmap data.The Astrophysical Journal Letters, 672(2):L87–L90, 2008

    work page 2008

  38. [38]

    Macroscopic imprints of a discrete vacuum: Deriving the cmb hemispherical power asymmetry from k= 12 crystallization kinematics, 2026

    Raghu Kulkarni. Macroscopic imprints of a discrete vacuum: Deriving the cmb hemispherical power asymmetry from k= 12 crystallization kinematics, 2026

    work page 2026

  39. [39]

    Evidence for dihedral d3 symmetry in the planck cmb temperature anisotropy

    Robert Mereau. Evidence for dihedral d3 symmetry in the planck cmb temperature anisotropy. 2026

    work page 2026

  40. [40]

    More than power: Revisiting the cmb hemispherical power asymmetry with morphological descriptors.arXiv preprint arXiv:2603.22449, 2026

    Javier Carrón Duque, Mikel Martin Barandiaran, and Joseba Martínez-Arrizabalaga. More than power: Revisiting the cmb hemispherical power asymmetry with morphological descriptors.arXiv preprint arXiv:2603.22449, 2026

    work page arXiv 2026

  41. [41]

    Examination of frequency and scale depen- dence of cmb hemispherical power asymmetry.arXiv preprint arXiv:2601.13830, 2026

    Sanjeev Sanyal, Pavan Kumar Aluri, and Arman Shafieloo. Examination of frequency and scale depen- dence of cmb hemispherical power asymmetry.arXiv preprint arXiv:2601.13830, 2026

    work page arXiv 2026

  42. [42]

    Hansen, Facundo Toscano, Heliana E

    Diego García Lambas, Frode K. Hansen, Facundo Toscano, Heliana E. Luparello, and Ezequiel F. Boero. The cmb cold spot as predicted by foregrounds around nearby galaxies.Astronomy & Astrophysics,

    work page

  43. [43]

    URLhttps://api.semanticscholar.org/CorpusID:264426643

    work page

  44. [44]

    Hansen, Ezequiel F

    Frode K. Hansen, Ezequiel F. Boero, Heliana E. Luparello, and Diego García Lambas. A possible common explanation for several cosmic microwave background (cmb) anomalies: A strong impact of nearby galaxies on observed large-scale cmb fluctuations.Astronomy & Astrophysics, 2023. URL https://api.semanticscholar.org/CorpusID:259275323

    work page 2023

  45. [45]

    Luparello, Ezequiel F

    Heliana E. Luparello, Ezequiel F. Boero, Marcelo Lares, Ariel G. S’anchez, and Diego García Lambas. The cosmic shallows i: Interaction of cmb photons in extended galaxy halos.Monthly Notices of the Royal Astronomical Society, 2022. URLhttps://api.semanticscholar.org/CorpusID:250113362

    work page 2022

  46. [46]

    Peter R. Lamb. A changed understanding of gravity. 2022. URLhttps://api.semanticscholar.org/ CorpusID:246607292

    work page 2022

  47. [47]

    Pardede, Alexander Eggemeier, D

    Euclid Collaboration, K. Pardede, Alexander Eggemeier, D. Alkhanishvili, et al. Euclid preparation. galaxy power spectrum and bispectrum modelling. 2026. URLhttps://api.semanticscholar.org/ CorpusID:286974070. 20

    work page 2026

  48. [48]

    Euclidprepa- ration

    EuclidCollaboration, B.CamachoQuevedo, MartínCrocce, MarcosPellejeroIbáñez, etal. Euclidprepa- ration. galaxy power spectrum modelling in redshift space. 2026. URLhttps://api.semanticscholar. org/CorpusID:285102282

    work page 2026

  49. [49]

    Probing multipole alignment in the beyondplanck ensemble using the power tensor formalism.Modern Physics Letters A, 2026

    Akash Gandhi. Probing multipole alignment in the beyondplanck ensemble using the power tensor formalism.Modern Physics Letters A, 2026. URLhttps://api.semanticscholar.org/CorpusID: 286802053

    work page 2026

  50. [50]

    Updated constraints on infrared cutoff models and implications for large-scale cmb anomalies

    Ujjwal Upadhyay, Yashi Tiwari, and Tarun Souradeep. Updated constraints on infrared cutoff models and implications for large-scale cmb anomalies. 2026. URLhttps://api.semanticscholar.org/ CorpusID:285725913

    work page 2026

  51. [51]

    Nofi, Graeme E

    Hayley C. Nofi, Graeme E. Addison, Charles L. Bennett, Laura Herold, and Janet L. Weiland. Nearly full-sky low-multipole cmb temperature anisotropy: Ii. angular power spectra and likelihood. 2025. URL https://api.semanticscholar.org/CorpusID:281103425

    work page 2025

  52. [52]

    Temperature and polarization patterns in anisotropic cosmologies

    Rockhee Sung and Peter Coles. Temperature and polarization patterns in anisotropic cosmologies. Journal of Cosmology and Astroparticle Physics, 2011(06):036, 2011

    work page 2011

  53. [53]

    A class of homogeneous cosmological models.Commu- nications in Mathematical Physics, 12(2):108–141, 1969

    George FR Ellis and Malcolm AH MacCallum. A class of homogeneous cosmological models.Commu- nications in Mathematical Physics, 12(2):108–141, 1969

    work page 1969

  54. [54]

    Polarized radiation in relativistic cosmology.Astronomische Nachrichten, vol

    Georg Dautcourt and K Rose. Polarized radiation in relativistic cosmology.Astronomische Nachrichten, vol. 299, no. 1, 1978, p. 13-23., 299:13–23, 1978

    work page 1978

  55. [55]

    Note on the bondi-metzner-sachs group.Journal of Mathematical Physics, 7(5):863–870, 1966

    Ezra T Newman and Roger Penrose. Note on the bondi-metzner-sachs group.Journal of Mathematical Physics, 7(5):863–870, 1966

    work page 1966

  56. [56]

    Academic Press, Amsterdam, 2003

    Scott Dodelson.Modern Cosmology. Academic Press, Amsterdam, 2003. ISBN 978-0122191411

    work page 2003

  57. [57]

    Conventions.https://www.saha.ac.in/theory/palashbaran.pal/conv.html[On- line; accessed 29-April-2026]

    PalashBaranPal. Conventions.https://www.saha.ac.in/theory/palashbaran.pal/conv.html[On- line; accessed 29-April-2026]

    work page 2026

  58. [58]

    How isotropic is the universe?Physical review letters, 117(13):131302, 2016

    Daniela Saadeh, Stephen M Feeney, Andrew Pontzen, Hiranya V Peiris, and Jason D McEwen. How isotropic is the universe?Physical review letters, 117(13):131302, 2016

    work page 2016

  59. [59]

    Recombination (cosmology) — Wikipedia, the free encyclopedia.https://en

    Wikipedia contributors. Recombination (cosmology) — Wikipedia, the free encyclopedia.https://en. wikipedia.org/wiki/Recombination_(cosmology)#Rough_estimate_from_equilibrium_theory. [Online; accessed 29-April-2026]

    work page 2026

  60. [60]

    Statistics of cosmic microwave background polarization.Physical Review D, 55(12):7368, 1997

    Marc Kamionkowski, Arthur Kosowsky, and Albert Stebbins. Statistics of cosmic microwave background polarization.Physical Review D, 55(12):7368, 1997

    work page 1997

  61. [61]

    Cmb anisotropies: Total angular momentum method.Physical Review D, 56(2):596, 1997

    Wayne Hu and Martin White. Cmb anisotropies: Total angular momentum method.Physical Review D, 56(2):596, 1997

    work page 1997

  62. [62]

    Polarized spots in anisotropic open universes.Classical and Quantum Gravity, 26(17):172001, 2009

    Rockhee Sung and Peter Coles. Polarized spots in anisotropic open universes.Classical and Quantum Gravity, 26(17):172001, 2009

    work page 2009

  63. [63]

    Bianchi model cmb polarization and its implications for cmb anomalies.Monthly Notices of the Royal Astronomical Society, 380(4):1387–1398, 2007

    Andrew Pontzen and Anthony Challinor. Bianchi model cmb polarization and its implications for cmb anomalies.Monthly Notices of the Royal Astronomical Society, 380(4):1387–1398, 2007

    work page 2007

  64. [64]

    Rogues’ gallery: the full freedom of the bianchi cmb anomalies.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 79(10):103518, 2009

    Andrew Pontzen. Rogues’ gallery: the full freedom of the bianchi cmb anomalies.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 79(10):103518, 2009

    work page 2009

  65. [65]

    Linearization of homogeneous, nearly-isotropic cosmological models.Classical and Quantum Gravity, 28(18):185007, 2011

    Andrew Pontzen and Anthony Challinor. Linearization of homogeneous, nearly-isotropic cosmological models.Classical and Quantum Gravity, 28(18):185007, 2011

    work page 2011

  66. [66]

    Design, planning, and performance of the cmb-s4 experiment

    Robert W Besuner. Design, planning, and performance of the cmb-s4 experiment. InGround-based and Airborne Telescopes IX, volume 12182, pages 474–486. SPIE, 2022. 21

    work page 2022

  67. [67]

    Complementingtheground-basedcmb-s4experiment on large scales with the pixie satellite.Physical Review D, 95(6):063504, 2017

    ErminiaCalabrese, DavidAlonso, andJoDunkley. Complementingtheground-basedcmb-s4experiment on large scales with the pixie satellite.Physical Review D, 95(6):063504, 2017

    work page 2017

  68. [68]

    The simons observatory: Astro2020 decadal project whitepaper.arXiv preprint arXiv:1907.08284, 2019

    Maximilian H Abitbol, Shunsuke Adachi, Peter Ade, James Aguirre, Zeeshan Ahmed, Simone Aiola, Aamir Ali, David Alonso, Marcelo A Alvarez, Kam Arnold, et al. The simons observatory: Astro2020 decadal project whitepaper.arXiv preprint arXiv:1907.08284, 2019

    work page arXiv 1907

  69. [69]

    The simons observatory: science goals and forecasts.Journal of Cosmology and Astroparticle Physics, 2019(02):056–056, 2019

    Peter Ade, James Aguirre, Zeeshan Ahmed, Simone Aiola, Aamir Ali, David Alonso, Marcelo A Alvarez, Kam Arnold, Peter Ashton, Jason Austermann, et al. The simons observatory: science goals and forecasts.Journal of Cosmology and Astroparticle Physics, 2019(02):056–056, 2019

    work page 2019

  70. [70]

    The simons observatory: in- strument overview

    Nicholas Galitzki, Aamir Ali, Kam S Arnold, Peter C Ashton, Jason E Austermann, Carlo Baccigalupi, Taylor Baildon, Darcy Barron, James A Beall, Shawn Beckman, et al. The simons observatory: in- strument overview. InMillimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy IX, volume 10708, pages 40–52. SPIE, 2018

    work page 2018

  71. [71]

    Test of the gravitational force law on cosmological scales using the kinematic sunyaev-zeldovich effect.Physical Review Letters, 136(15):151002, 2026

    PA Gallardo, K Pardo, OHE Philcox, N Battaglia, ES Battistelli, R Bean, E Calabrese, SK Choi, M Devlin, J Dunkley, et al. Test of the gravitational force law on cosmological scales using the kinematic sunyaev-zeldovich effect.Physical Review Letters, 136(15):151002, 2026

    work page 2026

  72. [72]

    The Atacama Cosmology Telescope: A Test of the Gravitational Force Law on Cosmological Scales Using the Kinematic Sunyaev-Zeldovich Effect

    Patricio A Gallardo, Kris Pardo, Oliver HE Philcox, Nicholas Battaglia, Elia S Battistelli, Rachel Bean, Erminia Calabrese, Steve K Choi, Rolando Dünner, Mark Devlin, et al. The atacama cosmology telescope: A test of the gravitational force law on cosmological scales using the kinematic sunyaev- zeldovich effect.arXiv preprint arXiv:2604.14327, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  73. [73]

    Measurement of the galaxy-velocity power spectrum of DESI tracers with the kinematic Sunyaev-Zeldovich effect using DESI DR2 and ACT DR6

    Edmond Chaussidon, Selim C Hotinli, Simone Ferraro, Kendrick Smith, Xinyi Chen, J Aguilar, S Ahlen, D Bianchi, D Brooks, T Claybaugh, et al. Measurement of the galaxy-velocity power spectrum of desi tracers with the kinematic sunyaev-zeldovich effect using desi dr2 and act dr6.arXiv preprint arXiv:2604.04867, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  74. [74]

    Explaining Neural Networks on the Sky: Machine Learning Interpretability for Cosmic Microwave Background Maps

    IndiraOcampoandGuadalupeCañas-Herrera. Explainingneuralnetworksonthesky: Machinelearning interpretability for cosmic microwave background maps.arXiv preprint arXiv:2604.05290, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  75. [75]

    Recovering the cmb signal with neural

    Giuseppe Puglisi and Carlo Baccigalupi. Recovering the cmb signal with neural. InMachine Learning for Astrophysics 2024: Proceedings of the 2nd ML4ASTRO International Conference 8-12 July 2024, page 111. Springer Nature

    work page 2024

  76. [76]

    healpy: equal area pixelization and spherical harmonics transforms for data on the sphere in python.Journal of Open Source Software, 4(35):1298, 2019

    Andrea Zonca, Leo Singer, Daniel Lenz, Martin Reinecke, Cyrille Rosset, Eric Hivon, and Krzysztof Gorski. healpy: equal area pixelization and spherical harmonics transforms for data on the sphere in python.Journal of Open Source Software, 4(35):1298, 2019

    work page 2019

  77. [77]

    Healpix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere.The Astrophysical Journal, 622(2):759–771, 2005

    Krzysztof M Gorski, Eric Hivon, Anthony J Banday, Benjamin D Wandelt, Frode K Hansen, Mstvos Reinecke, and Matthia Bartelmann. Healpix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere.The Astrophysical Journal, 622(2):759–771, 2005

    work page 2005

  78. [78]

    HEALPix: Hierarchical Equal Area isoLatitude Pixelization of a sphere.https: //healpix.sourceforge.io/, 2026

    HEALPix Developers. HEALPix: Hierarchical Equal Area isoLatitude Pixelization of a sphere.https: //healpix.sourceforge.io/, 2026. Accessed: 2026-05-12. 22

    work page 2026