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arxiv: 2512.24369 · v1 · submitted 2025-12-30 · 🌌 astro-ph.CO

Integrated Sachs-Wolfe maps from the Gower Street wCDM simulations

Mina Ghodsi Yengejeh , Andr\'as Kov\'acs , Istv\'an Szapudi , Istv\'an Csabai This is my paper

Pith reviewed 2026-05-16 18:49 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords Integrated Sachs-Wolfe effectwCDM cosmologyN-body simulationsCMB temperature mapsdark energy equation of stategravitational potential evolutionlarge-scale structure
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The pith

Full-sky ISW maps are generated for 791 wCDM cosmologies from N-body simulations and validated against linear theory.

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

The paper extends an existing code package to produce full-sky Integrated Sachs-Wolfe temperature maps across a wide range of dark energy models using large N-body simulations. It computes the signals by following changes in the gravitational potential over time for equation of state values from phantom to quintessence regimes. The resulting maps are checked against linear theory predictions for their power spectra and cross-correlations with density fields, showing close agreement where the ISW contribution dominates. These maps and the code are released publicly to support further studies of dark energy through its effect on the cosmic microwave background.

Core claim

By tracing the time evolution of the gravitational potential across large-volume simulations that span dark energy equation of state parameters from -1.79 to -0.34, full-sky ISW maps are produced and projected onto the sphere using HEALPix. Validation against linear theory expectations shows excellent agreement in the angular power spectra and ISW-density cross-correlations for multipoles from 2 to 200. Quintessence-like models with w greater than -1 exhibit higher ISW amplitudes than phantom models with w less than -1, consistent with enhanced late-time decay of gravitational potentials.

What carries the argument

The extended pyGenISW pipeline that follows gravitational potential evolution in Gower Street N-body simulations and projects the resulting ISW signals onto HEALPix full-sky temperature maps.

If this is right

  • The maps enable ISW analyses across a much broader range of dark energy models than was previously possible with LambdaCDM-only tools.
  • Quintessence models produce stronger ISW signals than phantom models because their gravitational potentials decay more rapidly at late times.
  • Public release of the maps and code allows direct use in theoretical predictions and comparisons with observational large-scale structure data.
  • The close match to linear theory across the full suite confirms that the simulations track potential evolution correctly on the relevant scales.

Where Pith is reading between the lines

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

  • These maps could be used as templates to search for the ISW effect in upcoming galaxy surveys and CMB data.
  • The systematic difference in signal strength between model classes offers a possible route to distinguish dark energy behaviors observationally.
  • Applying the same pipeline to simulations that include baryonic physics or smaller scales might extend the maps' usefulness beyond linear regimes.

Load-bearing premise

The N-body simulations must accurately capture the time evolution of the gravitational potential on the large scales that drive the ISW effect.

What would settle it

A clear mismatch between the measured ISW angular power spectra or density cross-correlations from the maps and the linear theory benchmarks in the multipole range 2 to 200 would show the maps do not reliably model the effect.

Figures

Figures reproduced from arXiv: 2512.24369 by Andr\'as Kov\'acs, Istv\'an Csabai, Istv\'an Szapudi, Mina Ghodsi Yengejeh.

Figure 1
Figure 1. Figure 1: Distribution of the 791 GS simulations in an Ωm − σ8 parameter space, color-coded by w, and marker sizes illustrate relative differences in neutrino mass. These parameters are the most relevant for ISW cal￾culations, and the three representative simulations are highlighted with unfilled black markers. In [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top panel: Comparison of the ISW kernel, defined as the prod￾uct of cosmic expansion and growth, for all the 791 GS simulations (gray). We again highlight simulations 401 (yellow), 742 (green), and 127 (dark blue), as representatives of different w values in the GS pa￾rameter space. In the bottom panel, we compare our results from the fiducial TheoryCL pipeline and pyCCL, as well as alternative compu￾tatio… view at source ↗
Figure 3
Figure 3. Figure 3: Simulation-based ISW map construction. Density contrast maps and cosmological parameters from the Gower Street simulation are propagated through a unified model (extended TheoryCL) and a spherical-Bessel ISW pipeline (extended pyGenISW), yielding fully consistent ISW power spectrum predictions and corresponding ISW temperature maps. Sim 401 -20 K 20 Sim 742 -20 K 20 Sim 127 -20 K 20 [PITH_FULL_IMAGE:figur… view at source ↗
Figure 4
Figure 4. Figure 4: Sky-maps of ISW signal, showing half of the sky in an orthographic projection. Three representatives correspond to simulations 401 (w = −0.34), 742 (w = −1), and 127 (w = −1.79), highlighting different dark energy EOS. The maps are color-coded based on the ISW temperature anisotropies in µK. The quintessence model shows the most pronounced colors, indicating the strongest ISW signal, followed by the ΛCDM, … view at source ↗
Figure 5
Figure 5. Figure 5: Histograms of ISW temperature maps for the three characteristic examples: Sim 127 (w = −1.79), Sim 742 (w = −1), and Sim 401 (w = −0.34). Different panels show redshift-binned ISW temperature statistics, using HEALPix pixel values. Clear trends are visible with varying w parameters, and also with redshift. The bottom panel in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Theoretical vs. map-based power spectra for ISW auto-correlations (left) and galaxy auto-correlations (right). The top panels again display the three characteristic models with different w parameters, comparing the measured value from pyGenISW and anafast (solid) with the theoretical expectations from TheoryCL (dashed). We mark the limitations due to cosmic variance (shaded about dashed lines), and also th… view at source ↗
Figure 7
Figure 7. Figure 7: Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Mean ∆TISW temperatures in percentiles of the δm projected mat￾ter density field. The impact of varying the input cosmological parame￾ters is shown here in the most extreme parts of the density field, where the ISW signals differ most (in blue and red shaded areas). troughs and peaks where the ISW is expected to be maximal (see e.g., Gruen et al. 2016). To reduce small-scale fluctuations in the map, we app… view at source ↗
Figure 9
Figure 9. Figure 9: shows the resulting ISW amplitudes, A Tg ISW as a function of the matter density parameter, Ωm, for all 777 valid GS simu￾lations. The points are colour-coded by the dark energy EOS pa￾rameter, w, and three representative simulations are highlighted with different markers. We made the following observations: – The horizontal dashed line indicates the fiducial ΛCDM ex￾pectation at A Tg ISW = 1, among a set … view at source ↗
read the original abstract

The late-time linear Integrated Sachs-Wolfe (ISW) effect directly probes the dynamics of cosmic acceleration and the nature of dark energy. Detecting these weak, secondary temperature anisotropy signals of the CMB requires accurate theoretical predictions of their amplitude across cosmological models. By extending the pyGenISW package, previously limited to $\Lambda$CDM, we aim to generate full-sky ISW maps for a suite of 791 $w$CDM cosmologies using the Gower Street N-body simulations, thereby enabling ISW analyses across a broader dark-energy parameter space. We make our code and ISW data publicly available. We compute the ISW signals by tracing the time evolution of the gravitational potential across large-volume simulations that span dark energy equation of state parameters from phantom to quintessence, $-1.79 \lesssim w \lesssim -0.34$. These data are projected onto the sphere using HEALPix to obtain full-sky temperature maps. We validate our pipeline by comparing the measured ISW angular power spectra and ISW-density cross-correlations against linear theory expectations ($2 \leq \ell \leq 200$) computed with benchmarks from the pyCCL library. The agreement is excellent across the multipole range where the ISW contribution is expected to dominate, confirming the reliability of our modelling of gravitational-potential evolution. With additional tests of the ISW signal's strength in density extrema, as well as comparing all models to a reference $\Lambda$CDM cosmology, we found that quintessence-like models ($w > -1$) show higher ISW amplitudes than phantom models ($w < -1$), consistent with enhanced late-time decay of gravitational potentials. The consistency of our $w$CDM ISW maps and their agreement with theory predictions confirm the robustness of our methodology, establishing it as a reliable tool for theoretical and observational ISW-LSS analyses.

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

0 major / 3 minor

Summary. The paper extends the pyGenISW package to produce full-sky ISW temperature maps from the Gower Street N-body simulations for 791 wCDM cosmologies with dark-energy equation-of-state values spanning -1.79 ≲ w ≲ -0.34. Gravitational-potential evolution is traced through the simulations, projected onto the sphere with HEALPix, and validated by comparing the resulting angular power spectra and ISW-density cross-correlations to linear-theory predictions from the pyCCL library over 2 ≤ ℓ ≤ 200. Excellent agreement is reported on these scales; additional tests show higher ISW amplitudes for quintessence-like models (w > -1) than for phantom models (w < -1). The code and maps are released publicly.

Significance. If the reported agreement with linear theory holds, the work supplies a valuable, publicly available suite of ISW maps spanning a broad w range. This resource directly supports theoretical modeling and observational ISW-LSS cross-correlation studies beyond ΛCDM. The public release of both code and data, together with the direct comparison to an independent linear-theory library, constitutes a clear strength for reproducibility and community use.

minor comments (3)
  1. The abstract and main text state that the maps are validated for 2 ≤ ℓ ≤ 200 but do not report quantitative measures (e.g., fractional residuals, χ² per degree of freedom, or maximum deviation) of the agreement; adding such metrics would allow readers to assess the precision of the match more objectively.
  2. The manuscript does not specify the exact sampling strategy or spacing of the 791 w values (e.g., whether they are uniformly spaced in w or drawn from a prior); this detail is needed for users who wish to interpolate or re-weight the maps.
  3. Figure captions should explicitly note the multipole range and the reference cosmology used for the amplitude comparisons shown in the results section.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for recommending minor revision. We are pleased that the referee recognizes the value of the publicly released ISW maps and code for wCDM cosmologies, as well as the validation against linear theory. No specific major comments were provided in the report, so we have no points to address point-by-point at this time.

Circularity Check

0 steps flagged

No significant circularity; validation uses independent external benchmark

full rationale

The paper's core derivation consists of running N-body simulations to trace gravitational potential evolution and projecting the resulting ISW signals onto HEALPix maps. These maps are then compared directly to linear-theory angular power spectra and cross-correlations computed by the independent pyCCL library over 2 ≤ ℓ ≤ 200. Because the benchmark is external, parameter-free, and not derived from the same simulation outputs or fitted quantities, the agreement constitutes genuine validation rather than a self-referential reduction. No equations define a quantity in terms of itself, no fitted parameters are relabeled as predictions, and the extension of pyGenISW is a straightforward code development whose correctness is tested against the external library. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of pre-existing N-body simulations and standard linear perturbation theory without introducing new fitted parameters or postulated entities.

axioms (2)
  • domain assumption Linear perturbation theory accurately describes the ISW effect on scales 2 ≤ ℓ ≤ 200
    Invoked when comparing simulated power spectra to pyCCL benchmarks.
  • domain assumption The Gower Street N-body simulations correctly evolve the gravitational potential under wCDM cosmologies
    Underlying assumption for tracing potential time evolution across the 791 models.

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