The Coyote Universe Extended: Precision Emulation of the Matter Power Spectrum

TL;DR

This paper extends the Coyote Universe power-spectrum emulator to higher wavenumbers and redshifts by employing a nested-box simulation strategy and leveraging renormalized perturbation theory for large scales. It introduces an $h$-extension method that avoids re-running N-body simulations, using a nine-basis PCA-Gaussian-process framework to fuse linear and nonlinear information across scales. The resulting emulator achieves better than 5% accuracy across a broad $k$–$z$ domain, with ~1% accuracy for $k\lesssim1\,\mathrm{Mpc}^{-1}$ when $h$ is fixed and modest degradation when $h$ is free, and it includes a smooth power-spectrum generation scheme to stitch results from different box sizes. While baryonic physics remains a major source of uncertainty at small scales, the approach provides a robust gravity-only calibration and a practical tool for interpreting current and upcoming surveys (e.g., DES, LSST). The public code and planned extensions to dynamical dark energy and weak-lensing predictions position this work as a key enabling technology for cosmological inference from nonlinear structure formation.

Abstract

Modern sky surveys are returning precision measurements of cosmological statistics such as weak lensing shear correlations, the distribution of galaxies, and cluster abundance. To fully exploit these observations, theorists must provide predictions that are at least as accurate as the measurements, as well as robust estimates of systematic errors that are inherent to the modeling process. In the nonlinear regime of structure formation, this challenge can only be overcome by developing a large-scale, multi-physics simulation capability covering a range of cosmological models and astrophysical processes. As a first step to achieving this goal, we have recently developed a prediction scheme for the matter power spectrum (a so-called emulator), accurate at the 1% level out to k~1/Mpc and z=1 for wCDM cosmologies based on a set of high-accuracy N-body simulations. It is highly desirable to increase the range in both redshift and wavenumber and to extend the reach in cosmological parameter space. To make progress in this direction, while minimizing computational cost, we present a strategy that maximally re-uses the original simulations. We demonstrate improvement over the original spatial dynamic range by an order of magnitude, reaching k~10 h/Mpc, a four-fold increase in redshift coverage, to z=4, and now include the Hubble parameter as a new independent variable. To further the range in k and z, a new set of nested simulations run at modest cost is added to the original set. The extension in h is performed by including perturbation theory results within a multi-scale procedure for building the emulator. This economical methodology still gives excellent error control, ~5% near the edges of the domain of applicability of the emulator. A public domain code for the new emulator is released as part of the work presented in this paper.

Figures (14)

• Figure 1: Comparison of the simulations with renormalized perturbation theory for M037 (averaged over 20 realizations) at three redshifts. The black horizontal lines show the 1% error limits. The red lines show the matching points we choose for connecting perturbation theory to the simulation results. For $1.0\le a \le 0.5$ the matching value is at $k=0.03~$Mpc$^{-1}$ and for $0.4\le a\le 0.2$ it is at $k=0.1~$Mpc$^{-1}$.
• Figure 2: Two examples of how nested simulation volumes are used to cover a large range in $k$. Models shown have the most extreme values of $_8$, M019 with $_8=0.6159$ (right column) and M037 with $_8=0.9$ (left column). The upper row shows the full power spectra from the different simulations as well as the corresponding Nyquist limit (vertical line) and the shot noise limit (horizontal line). The lower row shows the different power spectra matched up (without any additional smoothing) at the $k$-values described in Tables \ref{['tab:assem1']} -- \ref{['tab:assem3']}. The power spectra results are shown at $z=0$ and $z=4$. In all cases the matching leads to a relatively smooth power spectrum covering the full $k$ range of interest. In the lower panel, at $z=0$, we show the good agreement between the 365 Mpc and 180 Mpc boxes at high $k$ by overlaying the two power spectra (see text for details). Note that in the lower plots at $z=0$ we used the original emulator predictions for the intermediate $k$ range shown in red.
• Figure 3: Variations in power spectra due to different realizations from 127 simulations, each for a 325 Mpc box size. The upper panel shows the ratio of each of the 127 results at $z=0$ with respect to the average power spectrum. The lower panel shows an attempt to correct the results -- here we adjust the amplitude of each power spectrum so that it matches the average power spectrum at the largest $k$-value. While at large $k$ this reduces the error somewhat, the procedure is not satisfactory overall and we do not use it in the final results. The scatter is roughly at the few percent level.
• Figure 4: Test of realization scatter on small scales. Shown are the results from six simulations that have the same realization on large scales but different realizations on small scales divided by the average of all six power spectra. The red line indicates the transition between the two regimes. Note that some of the realization noise from the small scales leaks back to larger scales.
• Figure 5: Accuracy of the linear power spectrum emulator of the full six-dimensional parameter space. Shown is the ratio of the emulator to the linear power spectra for ten extra models not used for constructing the emulator itself. The error overall is within 1%. Note that we only included information on the Hubble parameter $h$ on large scales, with an upper cutoff at $k=0.03~$Mpc$^{-1}$.