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We perform an ensemble of $N$-body simulations with $2048^3$ particles for101 flat $w$CDM cosmological models sampled based on a maximin-distance SlicedLatin Hypercube Design. By using the halo catalogs extracted at multipleredshifts in the range of $z=[0,1.48]$, we develop Dark Emulator, which enablesfast and accurate computations of the halo mass function, halo-mattercross-correlation, and halo auto-correlation as a function of halo masses,redshift, separations and cosmological models, based on the Principal ComponentAnalysis and the Gaussian Process Regression for the large-dimensional inputand output data vector. We assess the performance of the emulator using avalidation set of $N$-body simulations that are not used in training theemulator. We show that, for typical halos hosting CMASS galaxies in the SloanDigital Sky Survey, the emulator predicts the halo-matter cross correlation,relevant for galaxy-galaxy weak lensing, with an accuracy better than $2\%$ andthe halo auto-correlation, relevant for galaxy clustering correlation, with anaccuracy better than $4\%$. We give several demonstrations of the emulator. Itcan be used to study properties of halo mass density profiles such as themass-concentration relation and splashback radius for different cosmologies.The emulator outputs can be combined with an analytical prescription ofhalo-galaxy connection such as the halo occupation distribution at the equationlevel, instead of using the mock catalogs, to make accurate predictions ofgalaxy clustering statistics such as the galaxy-galaxy weak lensing and theprojected correlation function for any model within the $w$CDM cosmologies, ina few CPU seconds.

Dark Quest. I. Fast and Accurate Emulation of Halo Clustering Statistics and Its Application to Galaxy Clustering