Pith. sign in

REVIEW 2 major objections 5 minor 44 references

Predictions for the diffuse cosmic dipole at radio frequencies from reionization imprints

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read The paper predicts that the kinematic dipole spectrum of a diffuse radio background is set entirely by that background's own frequency spectrum, so reionization-era imprints (free-free plus Comptonization distortions, the redshifted 21-cm…

desk verdict Solid kinematic-dipole predictions; the missing treatment of intrinsic cosmic dipoles keeps the observability claim from landing. read the letter →

arxiv 1908.07496 v3 pith:JSIYISK4 submitted 2019-08-20 astro-ph.CO

T. Trombetti , C. Burigana This is my paper · ORCID
classification astro-ph.CO
keywords cosmicdipolekinematicCompton–Gettingeffectredshifted21-cmlinefree-freedistortionComptonizationextragalacticradiobackgroundreionization
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 attempts to establish that the dipole anisotropy of any diffuse radio background is not a nuisance but a spectral diagnostic: when the observer moves relative to the CMB rest frame, the frequency spectrum of the induced dipole is fully determined by the frequency dependence of that background's monopole spectrum. The authors compute those dipole spectra for four reionization-linked signals—diffuse free-free emission combined with Comptonization distortion, the redshifted 21-cm line, the residual extragalactic radio background, and their combinations—and find recognizable signatures: power-law dipole tails whose slopes mirror the monopole spectral indices, sign changes where one component dominates, and a 60–200 MHz modulation from the 21-cm line. If these predictions are right, reionization and cosmic thermal history can be probed through dipole measurements alone, using only relative and interfrequency calibration and bypassing the demanding absolute calibration of radio instruments. The approach connects monopole and anisotropy analyses and could be applied to wide-sky surveys or to collections of sky patches.

What carries the argument

The load-bearing object is the kinematic (Compton–Getting) dipole of a diffuse background, obtained by Lorentz-boosting the photon occupation number according to $\nu' = \nu(1-\hat n\cdot\beta)/(1-\beta^2)^{1/2}$ and converting back to thermodynamic temperature with $T_{\rm th}(\nu) = h\nu/[k\ln(1+1/\eta(\nu))]$. The specific identity that carries the whole argument is Eq. (17), which expresses the first-order dipole as $-\beta T_0$ times the logarithmic derivative of $\eta$ with respect to frequency; it translates any monopole spectral shape into a dipole spectrum, so every prediction in the paper follows from inserting the monopole models of Section 2 into this relation.

What would settle it

Measure the dipole of the residual extragalactic radio background at several frequencies (e.g., 0.15–8 GHz) on a wide-sky survey after subtracting detected sources: if the dipole direction does not match the CMB dipole direction, or the dipole amplitude is not described by $\beta T_{\rm ant}(1+\alpha)$ with $\alpha$ the monopole spectral index, the kinematic-only isotropy assumption is falsified.

Watch

Extended reading notes

Core claim

The central claim is that the spectral shape of the cosmic dipole generated by the observer's peculiar motion is fixed by the logarithmic frequency derivative of the photon occupation number $\eta(\nu)$ of the monopole background, via the first-order relation $\Delta T_{\rm th} \simeq - x \beta T_0\, [(1+\eta)\ln^2(1+1/\eta)]^{-1}\, d\ln\eta/d\ln x$ (Eq. 17). Using this identity on representative monopole models, the paper predicts that the free-free plus Comptonization dipole rises as a positive power law at low frequencies and then crosses to the negative Comptonization regime; the redshifted 21-cm line produces sign-changing dipole features whose amplitude tracks the steepness of the monopole, with the deep absorption-profile model yielding a dipole about an order of magnitude larger than milder models; and the residual extragalactic background yields a dipole with nearly the same power-law index as its monopole. In combined spectra, the 21-cm line shows up as a modulation between roughly 60 and 200 MHz over the smoother extragalactic and free-free dipoles. The paper argues that these spectral fingerprints require only relative calibration and can therefore be extracted from wide surveys or sky patches.

Load-bearing premise

The predictions assume that each diffuse radio background is isotropic on large angular scales in the CMB rest frame, so that the only dipole is the kinematic one induced by the observer's motion; the intrinsic dipoles from source clustering and patchy reionization are not modeled.

Editorial extensions

If this is right

  • A measurement of the dipole spectrum of the residual extragalactic background, with only relative calibration, can constrain the amplitude and spectral index of that background after source subtraction.
  • The predicted 60–200 MHz modulation and the sign inversions in the combined dipole spectrum can serve as diagnostics to distinguish global 21-cm reionization models, including the deep absorption profile observed near 78 MHz.
  • The frequency where the free-free dipole gives way to the Comptonization dipole shifts with the residual background level, so wide-frequency radio-to-microwave observations can separate the components.
  • Because the dipoles are two to three orders of magnitude smaller than the corresponding monopoles, precise dipole corrections are required when measuring weak monopole components such as the 21-cm line, while the dipole measurement itself avoids absolute calibration.
  • Comparing dipoles measured for different backgrounds tests whether the observer's motion is the same with respect to each background frame, which bears on the cosmological principle.

Reading between the lines

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

  • (Editorial inference) A wide-area radio survey that measures both the monopole and dipole of the residual background after source subtraction could directly test the kinematic-only assumption: if intrinsic source-clustering dipoles dominate, the dipole direction would not align with the CMB dipole direction.
  • (Editorial inference) The same boosting formalism applies to other monopole components such as the cosmic infrared background, so the differential approach could become a general consistency check on foreground subtraction in CMB spectral-distortion experiments.
  • (Editorial inference) Because the 21-cm line is tomographic, a future analysis might attempt to reconstruct the dipole per redshift shell rather than for the integrated global signal; this would require modeling the intrinsic dipole from density gradients and patchy reionization that the paper leaves out.
  • (Editorial inference) The strongest test of the relative-calibration advantage would be a joint measurement of the dipole pattern's direction and frequency shape across the 60–200 MHz range on many independent sky patches, separating the coherent kinematic pattern from intrinsic fluctuations.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper computes the kinematic dipole induced by the observer's peculiar motion on four diffuse radio backgrounds: the free-free plus Comptonization distortion, the redshifted 21cm line, the residual extragalactic background, and their combinations. The dipole is obtained by Lorentz-boosting an isotropic occupation number via Eq. (16), with the first-order approximation Eq. (17), and the monopole models are taken from the literature. Analytic approximations in Eqs. (21)-(27) are validated against the exact computation in Figs. 4 and 7. The central claims are that each background leaves a characteristic dipole spectrum (power-law slopes, sign changes, and a 60-200 MHz modulation from the 21cm line) and that these signatures can be measured with relative calibration alone.

Significance. If the predictions correspond to observable sky signals, the paper provides a useful link between monopole and anisotropy analyses and offers falsifiable spectral signatures. The derivation of the kinematic dipole from the monopole is parameter-free given isotropy, and the analytic approximations are checked against the exact numerical computation. The paper is strongest as a calculation of the kinematic dipole component of reionization-related backgrounds, identifying frequency ranges and spectral shapes that could be searched for; the observability claim, however, rests on an unstated isotropy assumption that requires substantial additional support.

major comments (2)
  1. [Section 3, Eqs. (15)-(17); Figs. 5-7] The computation assumes that each background is isotropic in the CMB rest frame, so that the only dipole is the kinematic one induced by the observer's motion. This premise is never stated or justified. For the redshifted 21cm line, the intrinsic dipole from large-scale density and ionization fluctuations during reionization is expected to be of order the brightness-temperature fluctuations themselves, tens of mK at 50-200 MHz, whereas the kinematic dipole from a monopole of 10-100 mK is only beta times that, i.e. roughly 0.01-0.1 mK. The 60-200 MHz modulation emphasized in Fig. 7 would therefore be completely dominated by the intrinsic term unless that term is separately removed. For the residual extragalactic background, source clustering produces a dipole that is known to be comparable to or larger than the kinematic dipole for the same source populations. Section 6 discusses Galactic foreground subtraction but does not propose any strategy for separating or removing intrinsic cosmic dipoles, and the sentence in Section 6 stating that all patch variations from cosmic diffuse dipoles should follow the observer-motion pattern is exactly the unproven assumption. The abstract's claim that these signatures can be observed relying only on relative calibration is therefore not supported for the 21cm and residual-background components.
  2. [Section 2.3, Eq. (14) and Fig. 6] The residual extragalactic background is treated as a smooth power-law monopole, and its dipole is computed by boosting that monopole. Radio source populations, however, carry an intrinsic dipole from clustering and from the source-count dipole, which is comparable to or larger than the kinematic dipole; the paper itself cites Colin et al. (2017) and Bengaly et al. (2018, 2019), where such radio dipoles are reported. The predicted power-law dipole spectrum in Fig. 6 is thus not the observable sky dipole unless the intrinsic dipole is modeled or shown to be subdominant. A concrete test would be to evaluate the dipole spectrum of simulated EoR light-cones or of the residual source population and compare with Eqs. (26)-(27); until this is done, the predictions should be framed as predictions for the kinematic component only.
minor comments (5)
  1. [Eq. (18)] As printed, Eq. (18) appears to read "eta = 1 - 3u x + ...", but the first two terms should be (1 - 3u)/x to be consistent with Eq. (5); the missing division by x makes the formula confusing.
  2. [Eq. (15)] The notation in Eq. (15) would be clearer as T_th = x T0 / ln(1 + 1/eta(nu,n,beta)); the current placement of "BB/dist" inside the logarithm is hard to parse.
  3. [Section 2.1] There is a typo in the phrase "two pairs of different FF and Componization distortion models": "Componization" should be "Comptonization".
  4. [Section 2.2] The phrase "The CMB is assumed as a back light" should read "The CMB is assumed as a background light".
  5. [Section 5] There are small formatting issues in the text, such as "The conditionF2+F3+F4 = 0" missing a space, and references to "Fig. (7)" and "Figs. (4) and (6)" where the parentheses are unnecessary.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the dipole spectra follow from a standard Lorentz-boost formula applied to independently chosen monopole models, and the dipole results are never used to fit a parameter.

full rationale

The paper's central derivation is the mapping from a monopole occupancy eta(nu) to a kinematic dipole via Eqs. (16)-(17), a standard Compton-Getting/Lorentz-invariance result (Forman 1970; Danese & de Zotti 1981). The monopole models in Sect. 2 are taken from prior literature or fitted to source counts, optical depth, and absolute-temperature data, not to dipole data; the dipole spectra in Figs. 4-7 are therefore genuinely derivative predictions. The approximate analytic expressions in Eqs. (21)-(27) are Taylor expansions of the same differential relation and recover the known (1+alpha) boost factors, which is a consistency check rather than a repackaging of the inputs. Self-citations (Trombetti & Burigana 2014; Burigana et al. 2018) supply the FF model and the map-level form of the boost, but the underlying physics is standard and the cited FF model is validated against numerical simulations, so the self-citations are not load-bearing for the dipole claim. The implicit isotropy assumption (kinematic dipole only) is a physical limitation, not a circular reduction: the paper does not define the predicted dipole in terms of the observed dipole, and no parameter is fitted to the predicted quantity. Hence no significant circularity is present.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its predictions are monopole-to-dipole mappings applied to literature models and to power-law fits of those models. The explicit free parameters are the reionization free-free and Comptonization amplitudes and the fitted residual background amplitudes; the unstated isotropy axiom (item 3) is the principal risk.

free parameters (6)
  • Comptonization parameter u = 1e-7 and 2e-6
    Two representative values set the amplitude of the Comptonization distortion and control the free-free to Comptonization transition frequency (Eq. 28). Values are within FIRAS constraints |u| <= 1.5e-5 (95% CL).
  • Free-free amplitude yB(2 GHz) for Oh halo model = 1.5e-6
    Rescaled to match Oh (1999) prediction for the global free-free signal from ionized halos; defines the extreme free-free monopole model.
  • Free-free amplitude AFF for Gnedin-based model = 7.012e-9 at 1 GHz, with yB ~ AFF (nu/GHz)^-zeta, zeta ~ 0.15
    Output of the Trombetti & Burigana (2014) free-free model with kmax = 100; defines the minimal free-free case.
  • Residual extragalactic background amplitude A = 2.35 mK and 1.51 mK (Eq. 14), plus 4.7 mK and 0.151 mK variants
    Fitted to the integrated number-count model of Gervasi et al. (2008a) for Smax = 50 nJy and 15 nJy; sets the level of the subtracted radio background.
  • Power-law slope of extragalactic background alpha = 2.57 to 2.707, plus 2.65 for residuals
    Adopted slopes from Seiffert et al. (2011), Gervasi et al. (2008a), and the paper's own fit; enters the dipole scaling (1+alpha) in Eq. (26).
  • Clumping factor cutoff kmax = 100
    Chosen for the Gnedin (2000)-based free-free model to compute the baryon variance sigma^2(z); affects the free-free monopole amplitude via (1+sigma^2).
assumptions (5)
  • standard math Lorentz invariance of the photon distribution function under the observer boost (Forman 1970; Danese & de Zotti 1981)
    Basis for Eqs. (15)-(17); standard physics, not disputed.
  • domain assumption The CMB dipole is entirely kinematic, with beta = A_dip/T0 = 1.2345e-3 (Planck 2015)
    Section 3. If a significant intrinsic CMB dipole exists, the reference blackbody dipole subtracted in Figs. 4-7 would be mis-set, shifting all residual predictions.
  • domain assumption Each diffuse radio background is isotropic in the CMB frame on dipole scales; the only dipole is the kinematic one
    Implicit in Section 3 and Figs. 5-6; not stated or justified. Intrinsic dipoles from source clustering or patchy reionization are not modeled.
  • domain assumption The free-free plus Comptonization occupation number in Eq. (4) is accurate over the observable radio range
    Appendix A argues the yB-based approximation holds above about 10 MHz for typical reionization histories; deviations only at nu_B below about 3-10 MHz.
  • domain assumption The selected monopole models are representative of the plausible range of reionization and radio background scenarios
    Section 2: models span from minimal (Planck-compatible) to extreme (Oh halos; EDGES absorption) cases.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Predictions for the diffuse cosmic dipole at radio frequencies from reionization imprints." pith.science (2026). https://pith.science/paper/JSIYISK4

@misc{pith2026190807496,
  author       = {Pith},
  title        = {Pith review of: Predictions for the diffuse cosmic dipole at radio frequencies from reionization imprints},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JSIYISK4}},
  note         = {Machine review of arXiv:1908.07496}
}
read the original abstract

The cosmological reionization can be studied in the radio through the tomographic view offered by the redshifted 21-cm line and the integrated information carried out by the diffuse free-free emission, coupled to the Comptonization distortion, relevant at higher frequencies. Current predictions span a wide range of possibilities, while the recent EDGES observations disagree with the standard models and call, if confirmed, for non-standard physical processes and/or for an early population of extragalactic sources producing a remarkable background at high redshifts almost consistent with the ARCADE 2 claim of a significant excess of CMB absolute temperature at low frequency. These signatures can be observed in global signal and fluctuations, from very large to small angular scales. The observer peculiar motion with respect to a reference frame in rest with respect to the CMB produces boosting effects in various observable quantities, remarkable at low multipoles, and particularly in the dipole, with frequency spectral behaviours depending on the monopole emission spectrum. We present a novel investigation at radio frequencies, aimed at predicting the imprints expected in the redshifted 21-cm line signal and in the diffuse free-free emission plus the Comptonization distortion for several models. Furthermore, we consider the same type of signal but expected from the cosmological radio background determining the offset for 21-cm line. The combination of these signals and their relevance in the various frequency ranges are studied. This approach, linking monopole and anisotropy analyses, can be applied on wide sky coverage surveys as well as to sets of sky patches. Relying only on the quality of interfrequency and relative data calibration, it in principle by-passes the need for precise absolute calibration, a critical point of current and future radio interferometric facilities.

Figures

Figures reproduced from arXiv: 1908.07496 by the authors.

Figure 1
Figure 1. Monopole signal for the considered combined Comptonization and diffuse FF distortion models after subtracting the current CMB spectrum in the blackbody approximation at the effective temperature T0. Solid and three dots-dashed lines refer to positive and negative values, respectively. Free-free distortions are evaluated for a reionization model compatible with Planck results and for an extreme model involving a popu… view at source ↗
Figure 2
Figure 2. Monopole signal in terms of antenna temperature for the models of redshifted 21cm line. The depth of the EDGES profile is greater by a factor of ' 3 than that of the standard case model in Cohen et al. (2017). See also the legend and the text. sically diffuse. An important extragalactic background signal is expected from the integrated contribution of discrete sources. A large fraction of it can be resolved through … view at source ↗
Figure 3
Figure 3. Monopole signal in terms of antenna temperature for the two considered extragalactic background models and various estimates of extragalactic source background signal for different assumptions of source contribution subtraction. The labels "Res Back" and "Res Back P(D)" refer to the choice of A = 2.35 and 1.51 mK in Eq. (14), while the additional label "Uncer" includes a reduction by factor of 10. The dashed lines r… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Dipole spectrum (in equivalent thermodynamic, or CMB, tem￾perature) expressed as the difference between the dipole spectrum pro￾duced in the presence of an FF distortion (dominant at low frequencies) plus a Comptonization distortion (dominant at high frequencies) with …
Figure 6
Figure 6. Figure 6: Dipole spectrum (in equivalent thermodynamic, or CMB, tem￾perature) expressed as the difference between the dipole spectrum pro￾duced by the radio signals of the extragalactic background (summed in intensity with the CMB blackbody) for the monopole models in [PITH_FUL…
Figure 7
Figure 7. Figure 7: Dipole spectrum (in equivalent thermodynamic, or CMB, temperature) expressed as the difference between the dipole spectrum produced by the combinations of signals and the dipole spectrum corresponding to the blackbody at the current temperature T0. Thick solid lines (o…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 33 canonical work pages

  1. [1]

    On a possible nonequilibrium imprint in the cosmic background at low frequencies

    Baiesi, M., Burigana, C., Conti, L., et al. 2019, arXiv e-prints, arXiv:1908.08876

    work page Pith review arXiv 2019

  2. [2]

    A., Kholupenko, E

    Balashev, S. A., Kholupenko, E. E., Chluba, J., Ivanchik, A. V ., & Varshalovich, D. A. 2015, ApJ, 810, 131

    work page 2015

  3. [3]

    2018, Nature, 555, 71

    Barkana, R. 2018, Nature, 555, 71

    2018

  4. [4]

    Bengaly, C. A. P., Maartens, R., & Santos, M. G. 2018, J. Cosmology Astropart. Phys., 2018, 031

    work page 2018

  5. [5]

    Bengaly, C. A. P., Siewert, T. M., Schwarz, D. J., & Maartens, R. 2019, MNRAS, 486, 1350

    work page 2019

  6. [6]

    Bernardi, G., Zwart, J. T. L., Price, D., et al. 2016, MNRAS, 461, 2847

    work page 2016

  7. [7]

    D., Rogers, A

    Bowman, J. D., Rogers, A. E. E., Monsalve, R. A., Mozdzen, T. J., & Mahesh, N. 2018, Nature, 555, 67

    2018

  8. [8]

    S., Trombetti, T., et al

    Burigana, C., Carvalho, C. S., Trombetti, T., et al. 2018, J. Cosmology Astropart. Phys., 4, 021

    work page 2018

Show all 44 references
  1. [9]

    1995, A&A, 303, 323

    Burigana, C., de Zotti, G., & Danese, L. 1995, A&A, 303, 323

    1995

  2. [10]

    A., Salvaterra, R., et al

    Burigana, C., Popa, L. A., Salvaterra, R., et al. 2008, MNRAS, 385, 404

    2008

  3. [11]

    O., Lazio, J., Bale, S., et al

    Burns, J. O., Lazio, J., Bale, S., et al. 2012, Advances in Space Research, 49, 433

    2012

  4. [12]

    2017, MNRAS, 472, 1915

    Cohen, A., Fialkov, A., Barkana, R., & Lotem, M. 2017, MNRAS, 472, 1915

    2017

  5. [13]

    2017, MNRAS, 471, 1045

    Colin, J., Mohayaee, R., Rameez, M., & Sarkar, S. 2017, MNRAS, 471, 1045

    2017

  6. [14]

    & de Zotti, G

    Danese, L. & de Zotti, G. 1981, A&A, 94, L33 De Zotti, G., González-Nuevo, J., Lopez-Caniego, M., et al. 2018, J. Cosmology Astropart. Phys., 4, 020 De Zotti, G., Negrello, M., Castex, G., Lapi, A., & Bonato, M. 2016, J. Cosmol- ogy Astropart. Phys., 3, 047

    1981

  7. [15]

    Deshpande, A. A. 2018, ApJ, 866, L7

    2018

  8. [16]

    E., Turner, W., Millenaar, R., et al

    Dewdney, P. E., Turner, W., Millenaar, R., et al. 2013, SKA Program Develop- ment Office, SKA-TEL-SKO-DD-001, Revision: 1

    2013

  9. [17]

    & Taylor, G

    Dowell, J. & Taylor, G. B. 2018, ApJ, 858, L9

    2018

  10. [18]

    2018, ApJ, 868, 63

    Ewall-Wice, A., Chang, T.-C., Lazio, J., et al. 2018, ApJ, 868, 63

    2018

  11. [19]

    & Holder, G

    Feng, C. & Holder, G. 2018, ApJ, 858, L17

    2018

  12. [20]

    Fixsen, D. J. 2009, ApJ, 707, 916

    2009

  13. [21]

    J., Cheng, E

    Fixsen, D. J., Cheng, E. S., Gales, J. M., et al. 1996, ApJ, 473, 576

    1996

  14. [22]

    Forman, M. A. 1970, Planet. Space Sci., 18, 25

    1970

  15. [23]

    R., Oh, S

    Furlanetto, S. R., Oh, S. P., & Briggs, F. H. 2006, Phys. Rep., 433, 181

    2006

  16. [24]

    & Theuns, T

    Gao, L. & Theuns, T. 2007, Science, 317, 1527

    2007

  17. [25]

    Gnedin, N. Y . 2000, ApJ, 542, 535

    2000

  18. [26]

    D., & Puchwein, E

    Hills, R., Kulkarni, G., Meerburg, P. D., & Puchwein, E. 2018, Nature, 564, E32

    2018

  19. [27]

    Mirabel, I. F. 2019, arXiv e-prints [arXiv:1902.00511] Muñoz, J. B. & Loeb, A. 2018, Nature, 557, 684

    2019 arXiv

  20. [28]

    Oh, S. P. 1999, ApJ, 527, 16 Planck Collaboration. 2016a, A&A, 594, A1 Planck Collaboration. 2016b, A&A, 594, A5 Planck Collaboration. 2016c, A&A, 594, A8 Planck Collaboration, Aghanim, N., Akrami, Y ., et al. 2018a, arXiv e-prints [arXiv:1807.06209] Planck Collaboration, Agha...

    1999 arXiv

  21. [29]

    P., Diego, J

    Ponente, P. P., Diego, J. M., Sheth, R. K., et al. 2011, MNRAS, 410, 2353

    2011

  22. [30]

    2018, MNRAS, 481, 4548

    Prandoni, I., Guglielmino, G., Morganti, R., et al. 2018, MNRAS, 481, 4548

    2018

  23. [31]

    & Seymour, N

    Prandoni, I. & Seymour, N. 2015, Advancing Astrophysics with the Square Kilo- metre Array (AASKA14), 67

    2015

  24. [32]

    Pritchard, J. R. & Loeb, A. 2010, Phys. Rev. D, 82, 023006

    2010

  25. [33]

    Retana-Montenegro, E., Röttgering, H. J. A., Shimwell, T. W., et al. 2018, A&A, 620, A74

    2018

  26. [34]

    & Burigana, C

    Salvaterra, R. & Burigana, C. 2002, MNRAS, 336, 592

    2002

  27. [35]

    R., et al

    Schneider, R., Salvaterra, R., Choudhury, T. R., et al. 2008, MNRAS, 384, 1525 Seiffert, M., Fixsen, D. J., Kogut, A., et al. 2011, ApJ, 734, 6

    2008

  28. [36]

    2018, MNRAS, 481, L6

    Sharma, P. 2018, MNRAS, 481, L6

    2018

  29. [37]

    J., Kogut, A., et al

    Singal, J., Fixsen, D. J., Kogut, A., et al. 2011, ApJ, 730, 138

    2011

  30. [38]

    2017, Physical Review Letters, 118, 151301

    Slosar, A. 2017, Physical Review Letters, 118, 151301

    2017

  31. [39]

    & Cowsik, R

    Subrahmanyan, R. & Cowsik, R. 2013, ApJ, 776, 42

    2013

  32. [40]

    N., Pritchard, J., & Vedantham, H

    Subrahmanyan, R., Shankar, U. N., Pritchard, J., & Vedantham, H. K. 2015, Advancing Astrophysics with the Square Kilometre Array (AASKA14), 14

    2015

  33. [41]

    & Burigana, C

    Trombetti, T. & Burigana, C. 2014, MNRAS, 437, 2507

    2014

  34. [42]

    V ., et al

    Vernstrom, T., Scott, D., Wall, J. V ., et al. 2014, MNRAS, 440, 2791

    2014

  35. [43]

    V ., et al

    Vernstrom, T., Scott, D., Wall, J. V ., et al. 2016, MNRAS, 462, 2934

    2016

  36. [44]

    G., Matarrese, S., & Riotto, A

    Viel, M., Lesgourgues, J., Haehnelt, M. G., Matarrese, S., & Riotto, A. 2005, Phys. Rev. D, 71, 063534 Zel’dovich, Y . B., Illarionov, A. F., & Sunyaev, R. A. 1972, Soviet Journal of Experimental and Theoretical Physics, 35, 643 Article number, page 11 of 12 A&A proofs: manusc...

    1995

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.