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arxiv: 2503.16355 · v2 · pith:EBSXGDZXnew · submitted 2025-03-20 · 🌌 astro-ph.CO

DEMNUni: the Sunyaev-Zel'dovich effect in the presence of massive neutrinos and dynamical dark energy

Pith reviewed 2026-05-22 23:00 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords Sunyaev-Zel'dovich effectmassive neutrinosdynamical dark energyCompton-y parameterN-body simulationsgalaxy clustersPlanck data
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The pith

Massive neutrinos reduce the mean logarithmic Compton-y from clusters linearly with neutrino fraction, improving agreement with Planck tSZ data over massless models.

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

The paper uses lightcones from the DEMNUni N-body simulations to examine how neutrino mass and dynamical dark energy alter the thermal Sunyaev-Zel'dovich signal from galaxy clusters and groups. It establishes that the distribution of the logarithmic Compton parameter follows a skewed Gaussian whose mean decreases linearly with neutrino mass fraction at fixed dark energy model, with an approximate slope of 10. The tSZ angular power spectrum scales as a power law in sigma_8^cb when neutrino mass rises, with exponents from 7.3 to 8.1, and massless-neutrino models overpredict Planck Compton-y measurements while sums of 0.16 or 0.32 eV fit better. The work also provides forecasts for the cumulative signal-to-noise with the Simons Observatory LAT and a chi-squared estimator to test distinguishability from LambdaCDM.

Core claim

In the DEMNUni simulations, an increase in total neutrino mass produces a linear drop in the mean of the log Compton-y distribution with slope approximately 10 f_nu at fixed dark energy, while the tSZ power spectrum follows a power-law scaling in sigma_8^cb with indices 7.3-8.1; massless neutrino models overestimate Planck y-data, whereas sums m_nu = 0.16 or 0.32 eV yield improved agreement.

What carries the argument

Lightcone maps of the Compton-y parameter extracted from DEMNUni N-body simulations that incorporate neutrino free-streaming and dynamical dark energy, from which the skewed-Gaussian distribution and power-spectrum scaling are measured.

If this is right

  • The tSZ power spectrum can constrain neutrino mass through its power-law dependence on sigma_8^cb.
  • Models with sum m_nu around 0.16-0.32 eV are preferred by current Planck tSZ data over massless cases.
  • Simons Observatory LAT observations can achieve signal-to-noise sufficient to test these models against LambdaCDM using a tailored chi-squared estimator.

Where Pith is reading between the lines

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

  • The linear suppression offers a potential independent route to neutrino mass bounds from cluster statistics alone.
  • If the scaling persists at higher resolution, future tSZ surveys could tighten limits on both neutrino mass and dark energy simultaneously.

Load-bearing premise

The simulations and lightcone construction capture the non-linear effects of neutrino free-streaming and dark energy on hot gas in clusters without dominant resolution limits or missing baryonic physics.

What would settle it

A direct measurement showing the slope of mean log y versus f_nu deviates substantially from 10, or a power-spectrum scaling exponent outside the reported 7.3-8.1 range when neutrino mass is varied at fixed sigma_8^cb.

read the original abstract

In recent years, the study of secondary anisotropies in the Cosmic Microwave Background has become a fundamental instrument to test our understanding of the Universe. Using a set of lightcones produced with the ``Dark Energy and Massive Neutrino Universe'' $N$-body simulations, we study how different dark energy equations of state and neutrino masses impact the properties of the thermal Sunyaev-Zel'dovich (tSZ) effect, focusing on the signal arising from galaxy clusters and groups. We analyse the distribution of values for the Compton-$y$ parameter and study its angular power spectrum. We find that the distribution of the logarithmic Compton parameter can be fitted with a skewed Gaussian, with a mean that, at fixed dark energy model, decreases linearly with an approximate slope of $10 f_\nu$. Regarding the power spectrum of the thermal SZ effect, we find that an increase in $\sum {m_\nu}$ is observed as a power-law scaling with respect to $\sigma_8^{\mathrm{cb}}$, with exponents ranging from 7.3 to 8.1. We also find that models with massless neutrinos typically overestimate Compton-$y$ data extracted from Planck measurements; a better agreement with the simulations is obtained for $\sum m_\nu = 0.16$ or $\sum m_\nu=0.32$ eV. For all the \texttt{DEMNUni} models we forecast the cumulative signal-to-noise ratio for thermal SZ observations with the LAT instrument of the Simons Observatory; furthermore, we compute a tailored $\chi_\mathrm{SNR}^2$ estimator to infer if such models can be distinguished from the reference $\Lambda$CDM.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper analyzes the thermal Sunyaev-Zel'dovich (tSZ) effect using lightcones constructed from the DEMNUni N-body simulations that vary neutrino mass sum and dark energy equation of state. It reports that the distribution of log y is well-fit by a skewed Gaussian whose mean decreases linearly with neutrino fraction f_ν (slope ~10 at fixed DE model), that the tSZ angular power spectrum scales as a power law in σ8^cb with exponents 7.3–8.1 when ∑m_ν increases, and that massless-neutrino models overpredict Planck y measurements while ∑m_ν = 0.16 or 0.32 eV improve the fit. Forecasts for the cumulative SNR with Simons Observatory LAT and a tailored χ²_SNR estimator are also presented.

Significance. If the underlying gas modeling is shown to be robust, the work would provide a direct simulation-based quantification of how neutrino free-streaming and dynamical dark energy alter the tSZ signal from clusters, offering a complementary route to neutrino-mass constraints and a concrete forecast for near-term observations. The use of a single, internally consistent simulation suite spanning multiple cosmologies is a clear strength, enabling clean isolation of parameter effects without mixing different codes or initial conditions.

major comments (3)
  1. [Methods / lightcone construction and y-map computation (likely §3)] The central quantitative claims (linear slope of ~10 f_ν for <log y>, power-law exponents 7.3–8.1 for C_ℓ(σ8^cb), and improved Planck agreement at ∑m_ν = 0.16–0.32 eV) rest on the fidelity of the hot-gas pressure field extracted from pure N-body lightcones. The manuscript does not quantify the systematic uncertainty arising from the absence of hydrodynamics and baryonic feedback (cooling, star formation, AGN), which are known to suppress the tSZ power spectrum by 10–30 % on cluster scales; this uncertainty directly affects the reported slopes and the claimed preference for non-zero neutrino mass.
  2. [§2 (simulation description) and results sections reporting the fits] No information is supplied on simulation resolution, box size, particle number, or the precise halo-to-gas prescription used to generate the Compton-y maps. Without these details or convergence tests, it is impossible to assess whether the reported linear scaling with f_ν and the power-law exponents are numerically converged or sensitive to the sub-grid modeling choices.
  3. [Results section on Planck comparison] The comparison to Planck y data and the conclusion that massive-neutrino models fit better are presented without an explicit error budget that includes the modeling uncertainty from missing baryonic physics or from the choice of halo mass function / pressure profile. This makes the statistical significance of the preference for ∑m_ν = 0.16–0.32 eV difficult to evaluate.
minor comments (2)
  1. [Abstract] The abstract states quantitative results (slope, exponents) without any accompanying simulation parameters or uncertainty estimates; moving a brief methods summary or reference to the relevant table/figure into the abstract would improve readability.
  2. [Throughout] Notation for σ8^cb versus the usual σ8 should be defined at first use and used consistently; the distinction between cold+baryon and total-matter power spectrum is important for neutrino studies but is not always explicit.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive and detailed report. We address each major comment below, clarifying the scope of our N-body study and indicating revisions where details or caveats will be added.

read point-by-point responses
  1. Referee: [Methods / lightcone construction and y-map computation (likely §3)] The central quantitative claims (linear slope of ~10 f_ν for <log y>, power-law exponents 7.3–8.1 for C_ℓ(σ8^cb), and improved Planck agreement at ∑m_ν = 0.16–0.32 eV) rest on the fidelity of the hot-gas pressure field extracted from pure N-body lightcones. The manuscript does not quantify the systematic uncertainty arising from the absence of hydrodynamics and baryonic feedback (cooling, star formation, AGN), which are known to suppress the tSZ power spectrum by 10–30 % on cluster scales; this uncertainty directly affects the reported slopes and the claimed preference for non-zero neutrino mass.

    Authors: We agree that the DEMNUni simulations are dark-matter-only N-body runs and employ a halo-based prescription for the electron pressure without hydrodynamics or explicit baryonic feedback. This is a genuine limitation: the absolute tSZ amplitude is likely overestimated relative to reality by an amount comparable to the 10–30 % suppression cited. Because the identical prescription is used across all cosmologies, however, the differential trends (linear slope with f_ν and power-law scaling with σ_8^cb) are expected to be more robust than the absolute normalization. For the Planck comparison we will add an explicit caveat that the apparent preference for ∑m_ν = 0.16–0.32 eV is subject to this modeling uncertainty and should be regarded as indicative. A quantitative propagation of the baryonic systematic would require a separate hydrodynamical suite, which lies outside the present scope. revision: partial

  2. Referee: [§2 (simulation description) and results sections reporting the fits] No information is supplied on simulation resolution, box size, particle number, or the precise halo-to-gas prescription used to generate the Compton-y maps. Without these details or convergence tests, it is impossible to assess whether the reported linear scaling with f_ν and the power-law exponents are numerically converged or sensitive to the sub-grid modeling choices.

    Authors: We apologize for the omission in the main text. The DEMNUni suite uses 2048^3 particles in 2 Gpc/h boxes; the y-maps are constructed from light-cone halo catalogs by assigning a polytropic gas profile normalized to the halo mass and virial temperature (details in the original DEMNUni papers). We will insert a concise table and paragraph in §2 listing box size, particle number, force resolution, and the exact halo-to-gas mapping, together with references to convergence tests already performed in the simulation papers. This will allow readers to judge numerical robustness directly. revision: yes

  3. Referee: [Results section on Planck comparison] The comparison to Planck y data and the conclusion that massive-neutrino models fit better are presented without an explicit error budget that includes the modeling uncertainty from missing baryonic physics or from the choice of halo mass function / pressure profile. This makes the statistical significance of the preference for ∑m_ν = 0.16–0.32 eV difficult to evaluate.

    Authors: We concur that an explicit error budget is needed. In the revised manuscript we will add a dedicated paragraph enumerating the main uncertainty sources (baryonic feedback at the 10–30 % level, choice of pressure profile, and halo mass function) and will qualify the Planck comparison accordingly, stating that the improvement seen for massive-neutrino models is within the statistical errors of the data but remains subject to these systematics. A full Monte-Carlo propagation of all modeling choices would require additional simulations varying the sub-grid prescription, which is beyond the scope of this work. revision: partial

standing simulated objections not resolved
  • Quantitative assessment of the 10–30 % baryonic suppression on the reported slopes and on the statistical significance of the Planck preference, which cannot be performed without a dedicated hydrodynamical simulation campaign.

Circularity Check

0 steps flagged

No circularity: results are direct simulation outputs benchmarked externally

full rationale

The paper derives its claims (skewed-Gaussian fits to log-y distributions, linear slope ~10 f_ν, power-law C_ℓ scalings with exponents 7.3–8.1, and improved Planck agreement at ∑m_ν = 0.16–0.32 eV) solely from post-processing of the DEMNUni N-body lightcones. These quantities are measured outputs, not quantities that the paper's own equations or fits define in terms of themselves. No self-citation chain, uniqueness theorem, or ansatz is invoked to justify the central scalings; the simulations and external Planck comparison supply independent content. The analysis therefore contains no load-bearing step that reduces by construction to its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on standard cosmological simulation assumptions plus the specific DEMNUni runs; no new entities are postulated.

free parameters (1)
  • approximate slope 10 f_ν
    Linear fit coefficient to mean log Compton-y versus neutrino fraction at fixed dark energy model.
axioms (1)
  • domain assumption Standard LambdaCDM extended by massive neutrinos and dynamical dark energy governs structure formation in the simulations.
    Invoked throughout the abstract as the basis for the lightcone production and tSZ calculation.

pith-pipeline@v0.9.0 · 5858 in / 1470 out tokens · 80270 ms · 2026-05-22T23:00:37.921169+00:00 · methodology

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Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages · 45 internal anchors

  1. [1]

    First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters

    D.N. Spergel, L. Verde, H.V. Peiris, E. Komatsu, M.R. Nolta, C.L. Bennett et al.,First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters, The Astrophysical Journal Supplement Series148 (2003) 175 [astro-ph/0302209]

  2. [2]

    Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation

    E. Komatsu, K.M. Smith, J. Dunkley, C.L. Bennett, B. Gold, G. Hinshaw et al.,Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, The Astrophysical Journal Supplement192 (2011) 18 [1001.4538]

  3. [3]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown et al.,Planck 2013 results. XVI. Cosmological parameters, Astronomy & Astrophysics571 (2014) A16 [1303.5076]

  4. [4]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al., Planck 2015 results. XIII. Cosmological parameters, Astronomy & Astrophysics594 (2016) A13 [1502.01589]

  5. [5]

    Planck 2018 results. VI. Cosmological parameters

    Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. VI. Cosmological parameters, Astronomy & Astrophysics641 (2020) A6 [1807.06209]. – 21 –

  6. [6]

    The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters

    T. Louis, A. La Posta, Z. Atkins, H.T. Jense, I. Abril-Cabezas, G.E. Addison et al.,The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods andΛCDM Parameters, arXiv e-prints (2025) arXiv:2503.14452 [2503.14452]

  7. [7]

    The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

    E. Calabrese, J.C. Hill, H.T. Jense, A. La Posta, I. Abril-Cabezas, G.E. Addison et al.,The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models, arXiv e-prints (2025) arXiv:2503.14454 [2503.14454]

  8. [8]

    DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations

    A.G. Adame, J. Aguilar, S. Ahlen, S. Alam, D.M. Alexander, M. Alvarez et al.,DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations, Journal of Cosmology and Astroparticle Physics2025 (2025) 021 [2404.03002]

  9. [9]

    DEMNUni: ISW, Rees-Sciama, and weak-lensing in the presence of massive neutrinos

    C. Carbone, M. Petkova and K. Dolag,DEMNUni: ISW, Rees-Sciama, and weak-lensing in the presence of massive neutrinos, Journal of Cosmology and Astroparticle Physics2016 (2016) 034 [1605.02024]

  10. [10]

    Parimbelli, C

    G. Parimbelli, C. Carbone, J. Bel, B. Bose, M. Calabrese, E. Carella et al.,DEMNUni: comparing nonlinear power spectra prescriptions in the presence of massive neutrinos and dynamical dark energy, Journal of Cosmology and Astroparticle Physics2022 (2022) 041 [2207.13677]

  11. [11]

    Kugel, J

    R. Kugel, J. Schaye, M. Schaller, I.G. McCarthy, J. Braspenning, J.C. Helly et al.,The FLAMINGO project: a comparison of galaxy cluster samples selected on mass, X-ray luminosity, Compton-Y parameter, or galaxy richness, Monthly Notices of the Royal Astronomical Society 534 (2024) 2378 [2406.03180]

  12. [12]

    La Posta, D

    A. La Posta, D. Alonso, N.E. Chisari, T. Ferreira and C. García-García,X + y: insights on gas thermodynamics from the combination of X-ray and thermal Sunyaev-Zel’dovich data cross-correlated with cosmic shear, arXiv e-prints (2024) arXiv:2412.12081 [2412.12081]

  13. [13]

    Bigwood, A

    L. Bigwood, A. Amon, A. Schneider, J. Salcido, I.G. McCarthy, C. Preston et al.,Weak lensing combined with the kinetic Sunyaev-Zel’dovich effect: a study of baryonic feedback, Monthly Notices of the Royal Astronomical Society534 (2024) 655 [2404.06098]

  14. [14]

    R.H. Liu, S. Ferraro, E. Schaan, R. Zhou, J.N. Aguilar, S. Ahlen et al.,Measurements of the Thermal Sunyaev-Zel’dovich Effect with ACT and DESI Luminous Red Galaxies, arXiv e-prints (2025) arXiv:2502.08850 [2502.08850]

  15. [15]

    Schiappucci, S

    E. Schiappucci, S. Raghunathan, C. To, F. Bianchini, C.L. Reichardt, N. Battaglia et al., Constraining cosmological parameters using the pairwise kinematic Sunyaev-Zel’dovich effect with CMB-S4 and future galaxy cluster surveys, arXiv e-prints (2024) arXiv:2409.18368 [2409.18368]

  16. [16]

    Cosmology with the pairwise kinematic SZ effect: Calibration and validation using hydrodynamical simulations

    B. Soergel, A. Saro, T. Giannantonio, G. Efstathiou and K. Dolag,Cosmology with the pairwise kinematic SZ effect: calibration and validation using hydrodynamical simulations, Monthly Notices of the Royal Astronomical Society478 (2018) 5320 [1712.05714]

  17. [17]

    Chiang, R

    Y.-K. Chiang, R. Makiya, B. Ménard and E. Komatsu,The Cosmic Thermal History Probed by Sunyaev-Zeldovich Effect Tomography, The Astrophysical Journal902 (2020) 56 [2006.14650]

  18. [18]

    Evidence for oscillation of atmospheric neutrinos

    Y. Fukuda, T. Hayakawa, E. Ichihara, K. Inoue, K. Ishihara, H. Ishino et al.,Evidence for Oscillation of Atmospheric Neutrinos, Physical Review Letters81 (1998) 1562 [hep-ex/9807003]

  19. [19]

    The effect of massive neutrinos on the Sunyaev-Zeldovich and X-ray observables of galaxy clusters

    M. Roncarelli, C. Carbone and L. Moscardini,The effect of massive neutrinos on the Sunyaev-Zel’dovich and X-ray observables of galaxy clusters, Monthly Notices of the Royal Astronomical Society 447 (2015) 1761 [1409.4285]

  20. [20]

    The kinematic Sunyaev-Zel'dovich effect of the large-scale structure (I): dependence on neutrino mass

    M. Roncarelli, F. Villaescusa-Navarro and M. Baldi,The kinematic Sunyaev-Zel’dovich effect of the large-scale structure (I): dependence on neutrino mass, Monthly Notices of the Royal Astronomical Society 467 (2017) 985 [1702.00676]. – 22 –

  21. [21]

    S. Alam, M. Ata, S. Bailey, F. Beutler, D. Bizyaev, J.A. Blazek 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 Society470 (2017) 2617 [1607.03155]

  22. [22]

    Abbott, M

    T.M.C. Abbott, M. Aguena, A. Alarcon, O. Alves, A. Amon, F. Andrade-Oliveira et al.,Dark Energy Survey Year 3 results: Constraints on extensions toΛ CDM with weak lensing and galaxy clustering, Physical Review D107 (2023) 083504 [2207.05766]

  23. [23]

    Tishue, S.C

    A.J. Tishue, S.C. Hotinli, P. Adshead, E.D. Kovetz and M.S. Madhavacheril,Neutrino Mass Constraints from kSZ Tomography, arXiv e-prints (2025) arXiv:2502.05260 [2502.05260]

  24. [24]

    Massive neutrinos and cosmology

    J. Lesgourgues and S. Pastor,Massive neutrinos and cosmology, Physics Reports 429 (2006) 307 [astro-ph/0603494]

  25. [25]

    Lesgourgues, G

    J. Lesgourgues, G. Mangano, G. Miele and S. Pastor,Neutrino Cosmology, Cambridge University Press (2013)

  26. [26]

    Workman, V.D

    R.L. Workman, V.D. Burkert, V. Crede, E. Klempt, U. Thoma, L. Tiator et al.,Review of Particle Physics, Progress of Theoretical and Experimental Physics2022 (2022) 083C01

  27. [27]

    Accelerating Universes with Scaling Dark Matter

    M. Chevallier and D. Polarski,Accelerating Universes with Scaling Dark Matter, International Journal of Modern Physics D10 (2001) 213 [gr-qc/0009008]

  28. [28]

    Exploring the Expansion History of the Universe

    E.V. Linder,Exploring the Expansion History of the Universe, Physical Review Letters90 (2003) 091301 [astro-ph/0208512]

  29. [29]

    Springel,The cosmological simulation code gadget-2, Monthly Notices of the Royal Astronomical Society 364 (2005) 1105–1134

    V. Springel,The cosmological simulation code gadget-2, Monthly Notices of the Royal Astronomical Society 364 (2005) 1105–1134

  30. [30]

    Viel, M.G

    M. Viel, M.G. Haehnelt and V. Springel,The effect of neutrinos on the matter distribution as probed by the intergalactic medium, Journal of Cosmology and Astroparticle Physics2010 (2010) 015–015

  31. [31]

    Populating a cluster of galaxies - I. Results at z=0

    V. Springel, S.D.M. White, G. Tormen and G. Kauffmann,Populating a cluster of galaxies - I. Results at [formmu2]z=0, Monthly Notices of the Royal Astronomical Society328 (2001) 726 [astro-ph/0012055]

  32. [32]

    Substructures in hydrodynamical cluster simulations

    K. Dolag, S. Borgani, G. Murante and V. Springel,Substructures in hydrodynamical cluster simulations, Monthly Notices of the Royal Astronomical Society399 (2009) 497 [0808.3401]

  33. [33]

    Full-sky maps for gravitational lensing of the CMB

    C. Carbone, V. Springel, C. Baccigalupi, M. Bartelmann and S. Matarrese,Full-sky maps for gravitational lensing of the cosmic microwave background, Monthly Notices of the Royal Astronomical Society 388 (2008) 1618 [0711.2655]

  34. [34]

    Multiple Lensing of the Cosmic Microwave Background anisotropies

    M. Calabrese, C. Carbone, G. Fabbian, M. Baldi and C. Baccigalupi,Multiple lensing of the cosmic microwave background anisotropies, Journal of Cosmology and Astroparticle Physics3 (2015) 049 [1409.7680]

  35. [35]

    CMB weak-lensing beyond the Born approximation: a numerical approach

    G. Fabbian, M. Calabrese and C. Carbone,CMB weak-lensing beyond the Born approximation: a numerical approach, Journal of Cosmology and Astroparticle Physics2018 (2018) 050 [1702.03317]

  36. [36]

    Hilbert, A

    S. Hilbert, A. Barreira, G. Fabbian, P. Fosalba, C. Giocoli, S. Bose et al.,The accuracy of weak lensing simulations, Monthly Notices of the Royal Astronomical Society493 (2020) 305 [1910.10625]

  37. [37]

    Mellier et al

    Euclid Collaboration, Y. Mellier, Abdurro’uf, J.A. Acevedo Barroso, A. Achúcarro, J. Adamek et al.,Euclid. I. Overview of the Euclid mission, arXiv e-prints (2024) arXiv:2405.13491 [2405.13491]

  38. [38]

    Kompaneets,The Establishment of Thermal Equilibrium between Quanta and Electrons, Soviet Journal of Experimental and Theoretical Physics4 (1957) 730

    A.S. Kompaneets,The Establishment of Thermal Equilibrium between Quanta and Electrons, Soviet Journal of Experimental and Theoretical Physics4 (1957) 730. – 23 –

  39. [39]

    Zel’dovich and R.A

    Y.B. Zel’dovich and R.A. Sunyaev,The Interaction of Matter and Radiation in a Hot-Model Universe, Astrophysics and Space Science4 (1969) 301

  40. [40]

    Sunyaev and Y.B

    R.A. Sunyaev and Y.B. Zel’dovich,Small-Scale Fluctuations of Relic Radiation, Astrophysics and Space Science7 (1970) 3

  41. [41]

    Sunyaev,Fluctuations in microwave background radiation due to secondary ionization of the intergalactic gas in the universe., Pisma v Astronomicheskii Zhurnal3 (1977) 491

    R.A. Sunyaev,Fluctuations in microwave background radiation due to secondary ionization of the intergalactic gas in the universe., Pisma v Astronomicheskii Zhurnal3 (1977) 491

  42. [42]

    The kinematic Sunyaev-Zel'dovich effect of the large-scale structure (II): the effect of modified gravity

    M. Roncarelli, M. Baldi and F. Villaescusa-Navarro,The kinematic Sunyaev-Zel’dovich effect of the large-scale structure (II): the effect of modified gravity, Monthly Notices of the Royal Astronomical Society 481 (2018) 2497 [1805.11607]

  43. [43]

    On the Cluster Physics of Sunyaev-Zel'dovich Surveys II: Deconstructing the Thermal SZ Power Spectrum

    N. Battaglia, J.R. Bond, C. Pfrommer and J.L. Sievers,On the Cluster Physics of Sunyaev-Zel’dovich and X-Ray Surveys. II. Deconstructing the Thermal SZ Power Spectrum, The Astrophysical Journal758 (2012) 75 [1109.3711]

  44. [44]

    Statistical Imprints of SZ Effects in the Cosmic Microwave Background

    A. Cooray, D. Baumann and K. Sigurdson,Statistical imprints of SZ effects in the cosmic microwave background, inBackground Microwave Radiation and Intracluster Cosmology, F. Melchiorri and Y. Rephaeli, eds., p. 309, Jan., 2005, DOI [astro-ph/0410006]

  45. [45]

    Cosmology from the Thermal Sunyaev-Zel'dovich Power Spectrum: Primordial non-Gaussianity and Massive Neutrinos

    J.C. Hill and E. Pajer,Cosmology from the thermal Sunyaev-Zel’dovich power spectrum: Primordial non-Gaussianity and massive neutrinos, Physical Review D88 (2013) 063526 [1303.4726]

  46. [46]

    The Structure of Cold Dark Matter Halos

    J.F. Navarro, C.S. Frenk and S.D.M. White,The Structure of Cold Dark Matter Halos, The Astrophysical Journal 462 (1996) 563 [astro-ph/9508025]

  47. [47]

    Dark matter halo concentrations in the Wilkinson Microwave Anisotropy Probe year 5 cosmology

    A.R. Duffy, J. Schaye, S.T. Kay and C. Dalla Vecchia,Dark matter halo concentrations in the Wilkinson Microwave Anisotropy Probe year 5 cosmology, Monthly Notices of the Royal Astronomical Society 390 (2008) L64 [0804.2486]

  48. [48]

    Representations of celestial coordinates in FITS

    M.R. Calabretta and E.W. Greisen,Representations of celestial coordinates in FITS, Astronomy & Astrophysics395 (2002) 1077 [astro-ph/0207413]

  49. [49]

    Azzalini,A class of distributions which includes the normal ones, Scandinavian Journal of Statistics 12 (1985) 171

    A. Azzalini,A class of distributions which includes the normal ones, Scandinavian Journal of Statistics 12 (1985) 171

  50. [50]

    Bolliet, A

    B. Bolliet, A. Kusiak, F. McCarthy, A. Sabyr, K. Surrao, J.C. Hill et al.,class_sz I: Overview, arXiv e-prints (2023) arXiv:2310.18482 [2310.18482]

  51. [51]

    Bolliet, J

    B. Bolliet, J. Colin Hill, S. Ferraro, A. Kusiak and A. Krolewski,Projected-field kinetic Sunyaev-Zel’dovich Cross-correlations: halo model and forecasts, Journal of Cosmology and Astroparticle Physics 2023 (2023) 039 [2208.07847]

  52. [52]

    The Large Scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests

    J.L. Tinker, B.E. Robertson, A.V. Kravtsov, A. Klypin, M.S. Warren, G. Yepes et al.,The Large-scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests, The Astrophysical Journal 724 (2010) 878 [1001.3162]

  53. [53]

    Dark Energy from the Thermal Sunyaev Zeldovich Power Spectrum

    B. Bolliet, B. Comis, E. Komatsu and J.F. Macías-Pérez,Dark energy constraints from the thermal Sunyaev-Zeldovich power spectrum, Monthly Notices of the Royal Astronomical Society 477 (2018) 4957 [1712.00788]

  54. [54]

    Planck 2015 results. XXII. A map of the thermal Sunyaev-Zeldovich effect

    Planck Collaboration, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2015 results. XXII. A map of the thermal Sunyaev-Zeldovich effect, Astronomy & Astrophysics 594 (2016) A22 [1502.01596]

  55. [55]

    Efficient Computation of CMB anisotropies in closed FRW models

    A. Lewis, A. Challinor and A. Lasenby,Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann-Robertson-Walker Models, The Astrophysical Journal 538 (2000) 473 [astro-ph/9911177]

  56. [56]

    CAMB: Code for Anisotropies in the Microwave Background

    A. Lewis and A. Challinor, “CAMB: Code for Anisotropies in the Microwave Background.” Astrophysics Source Code Library, Feb, 2011. – 24 –

  57. [57]

    The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters

    E. Komatsu and U. Seljak,The Sunyaev-Zel’dovich angular power spectrum as a probe of cosmological parameters, Monthly Notices of the Royal Astronomical Society336 (2002) 1256 [astro-ph/0205468]

  58. [58]

    L.D. Shaw, D. Nagai, S. Bhattacharya and E.T. Lau,Impact of Cluster Physics on the Sunyaev-Zel’dovich Power Spectrum, The Astrophysical Journal725 (2010) 1452 [1006.1945]

  59. [59]

    H. Trac, P. Bode and J.P. Ostriker,Templates for the Sunyaev-Zel’dovich Angular Power Spectrum, The Astrophysical Journal727 (2011) 94 [1006.2828]

  60. [60]

    Bolliet, T

    B. Bolliet, T. Brinckmann, J. Chluba and J. Lesgourgues,Including massive neutrinos in thermal Sunyaev Zeldovich power spectrum and cluster counts analyses, Monthly Notices of the Royal Astronomical Society497 (2020) 1332 [1906.10359]

  61. [61]

    Cosmology with massive neutrinos II: on the universality of the halo mass function and bias

    E. Castorina, E. Sefusatti, R.K. Sheth, F. Villaescusa-Navarro and M. Viel,Cosmology with massive neutrinos II: on the universality of the halo mass function and bias, Journal of Cosmology and Astroparticle Physics2014 (2014) 049 [1311.1212]

  62. [62]

    Spherical collapse in $\nu \Lambda CDM$

    M. LoVerde,Spherical collapse inνΛCDM, Physical Review D90 (2014) 083518 [1405.4858]

  63. [63]

    Toward a halo mass function for precision cosmology: the limits of universality

    J. Tinker, A.V. Kravtsov, A. Klypin, K. Abazajian, M. Warren, G. Yepes et al.,Toward a Halo Mass Function for Precision Cosmology: The Limits of Universality, The Astrophysical Journal 688 (2008) 709 [0803.2706]

  64. [64]

    P. Ade, J. Aguirre, Z. Ahmed, S. Aiola, A. Ali, D. Alonso et al.,The Simons Observatory: science goals and forecasts, Journal of Cosmology and Astroparticle Physics2019 (2019) 056 [1808.07445]

  65. [65]

    CMB distortion from circumgalactic gas

    P. Singh, B.B. Nath, S. Majumdar and J. Silk,CMB distortion from circumgalactic gas, Monthly Notices of the Royal Astronomical Society448 (2015) 2384 [1408.4896]

  66. [66]

    Joint analysis of the thermal Sunyaev-Zeldovich effect and 2MASS galaxies: Probing gas physics in the local Universe and beyond

    R. Makiya, S. Ando and E. Komatsu,Joint analysis of the thermal Sunyaev-Zeldovich effect and 2MASS galaxies: probing gas physics in the local Universe and beyond, Monthly Notices of the Royal Astronomical Society480 (2018) 3928 [1804.05008]

  67. [67]

    Probing gravity at large scales through CMB lensing

    A.R. Pullen, S. Alam and S. Ho,Probing gravity at large scales through CMB lensing, Monthly Notices of the Royal Astronomical Society449 (2015) 4326 [1412.4454]

  68. [68]

    Deconstructing the kinetic SZ Power Spectrum

    L.D. Shaw, D.H. Rudd and D. Nagai,Deconstructing the Kinetic SZ Power Spectrum, The Astrophysical Journal 756 (2012) 15 [1109.0553]

  69. [69]

    S. Bird, M. Viel and M.G. Haehnelt,Massive neutrinos and the non-linear matter power spectrum, Monthly Notices of the Royal Astronomical Society420 (2012) 2551 [1109.4416]. – 25 –