The Coyote Universe II: Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum

TL;DR

This paper addresses the need for 1% accurate predictions of the nonlinear matter power spectrum to enable precision cosmology with dark-energy probes. It introduces the Cosmic Calibration Framework, combining a space-filling simulation design, principal component analysis of a transformed power spectrum, and Gaussian-process emulation to predict $P(k)$ over a five-parameter cosmological space with only 37 training models, using HaloFit as a validation proxy. The emulator achieves sub-percent accuracy ($<1\\%$) for $k\lesssim 1\,h\,\mathrm{Mpc}^{-1}$ and $0\le z\le 1$, with sensitivity analyses highlighting the main active parameters and demonstrating robustness. This work paves the way for fast, precise predictions in upcoming surveys, enabling efficient parameter inference and narrowing the computational burden for cosmological analyses; a final paper will present the full simulation suite results and a public emulator release.

Abstract

The power spectrum of density fluctuations is a foundational source of cosmological information. Precision cosmological probes targeted primarily at investigations of dark energy require accurate theoretical determinations of the power spectrum in the nonlinear regime. To exploit the observational power of future cosmological surveys, accuracy demands on the theory are at the one percent level or better. Numerical simulations are currently the only way to produce sufficiently error-controlled predictions for the power spectrum. The very high computational cost of (precision) N-body simulations is a major obstacle to obtaining predictions in the nonlinear regime, while scanning over cosmological parameters. Near-future observations, however, are likely to provide a meaningful constraint only on constant dark energy equation of state 'wCDM' cosmologies. In this paper we demonstrate that a limited set of only 37 cosmological models -- the "Coyote Universe" suite -- can be used to predict the nonlinear matter power spectrum at the required accuracy over a prior parameter range set by cosmic microwave background observations. This paper is the second in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum for wCDM cosmologies.

Figures (14)

• Figure 1: Left panel: an orthogonal array (OA) based design for 3 parameters, $_1$, $_2$, $_3$ and nine sampling points. Right panel: the OA based design perturbed in such a way that the one-dimensional projection onto any parameter leads to an equally spaced distribution of sample points. The projection onto any two dimensions leads to a space filling design.
• Figure 2: Projections of the design shown in Figure \ref{['design_3d']} onto two dimensions. The lower triangle shows the projection of the OA design, the upper triangle of the OA-LH design. Note that when projected onto one dimension, the OA-LH design leads to an even coverage and no points lie on top of each other.
• Figure 3: Two-dimensional projections of the SLH design given in Eq. (\ref{['slh']}). The symmetric design points are connected to show the reflection through the center.
• Figure 4: Best-fit TT power spectra for each model in Table \ref{['tab:basic']} using the WMAP-5 results. The only parameter which has been optimized by minimizing $^2$ is the optical depth $$. The upper panel shows the resulting power spectra, the black points with error bars show WMAP-5 data points, and the thick black line the best-fit WMAP-5 model. The lower panel shows the residuals for each model with respect to the best-fit model. Some of our models are undernormalized, the best-fit $$ being smaller than $0.01$ which would lead to a reionization redshift of $z<2$ and $^2$ for these models is larger than 3000 (the $^2$ for the best-fit WMAP-5 model is at roughly 2650). We fixed $$ for those models at $=0.01$ and show them with dashed lines.
• Figure 5: Sweep through $h$ for model 32. The red circle marks the estimate for the Hubble parameter from assuming perfect knowledge of $_A$, in excellent agreement with the result from the WMAP-5 likelihood for the best-fit value of $h$ for this model.