Integrated Sachs-Wolfe maps from the Gower Street $w$CDM simulations

TL;DR

The paper tackles the challenge of predicting the late-time ISW signal across a broad $w$CDM parameter space by extending the pyGenISW pipeline and TheoryCL framework to the Gower Street simulations. It generates full-sky ISW maps for $791$ $w$CDM cosmologies using the GS light-cone data, and validates the maps against linear-theory predictions and pyCCL benchmarks, finding strong agreement in the regime where ISW dominates. The results reveal that quintessence-like models ($w>-1$) tend to produce stronger ISW imprints than phantom models ($w<-1$), consistent with more rapid late-time decay of gravitational potentials, and quantify the variability of ISW amplitudes via power-ratio statistics. The authors provide public code and ISW data, and discuss the maps’ utility for covariance estimation, stacking analyses, and simulation-based inference in upcoming surveys such as Euclid, DESI, Rubin-LSST, and Roman. These maps constitute a robust tool for theoretical and observational ISW–LSS studies across a wide dark-energy landscape, extending capabilities beyond the standard $\Lambda$CDM paradigm.

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 $Λ$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 $Λ$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.

Figures (9)

• Figure 1: Distribution of the 791 GS simulations in an $\Omega_{\mathrm{m}}-\sigma_8$ parameter space, color-coded by $w$, and marker sizes illustrate relative differences in neutrino mass. These parameters are the most relevant for ISW calculations, and the three representative simulations are highlighted with unfilled black markers.
• Figure 2: Top panel: Comparison of the ISW kernel, defined as the product 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 parameter space. In the bottom panel, we compare our results from the fiducial TheoryCL pipeline and pyCCL, as well as alternative computations using CAMB and approximate $f(z)$ formulae described in \ref{['sec:ISW']}. This panel highlights the excellent agreement between our pipeline and pyCCL.
• 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.
• 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 $\mu K$. The quintessence model shows the most pronounced colors, indicating the strongest ISW signal, followed by the $\Lambda$CDM, while the phantom model shows the weakest signal (see also \ref{['fig:hist_3_ISWmaps']} for comparison).
• 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.