We perform an ensemble of N-body simulations with 2048 3 particles for 101 flat wCDM cosmological models sampled based on a maximin-distance Sliced Latin Hypercube Design. By using the halo catalogs extracted at multiple redshifts in the range of z = [0, 1.48], we develop Dark Emulator, which enables fast and accurate computations of the halo mass function, halo-matter cross-correlation, and halo auto-correlation as a function of halo masses, redshift, separations and cosmological models, based on the Principal Component Analysis and the Gaussian Process Regression for the large-dimensional input and output data vector. We assess the performance of the emulator using a validation set of N-body simulations that are not used in training the emulator. We show that, for typical halos hosting CMASS galaxies in the Sloan Digital Sky Survey, the emulator predicts the halo-matter cross correlation, relevant for galaxy-galaxy weak lensing, with an accuracy better than 2% and the halo auto-correlation, relevant for galaxy clustering correlation, with an accuracy better than 4%. We give several demonstrations of the emulator. It can be used to study properties of halo mass density profiles such as the mass-concentration relation and splashback radius for different cosmologies. The emulator outputs can be combined with an analytical prescription of halo-galaxy connection such as the halo occupation distribution at the equation level, instead of using the mock catalogs, to make accurate predictions of galaxy clustering statistics such as the galaxy-galaxy weak lensing and the projected correlation function for any model within the wCDM cosmologies, in a few CPU seconds. Subject headings: large-scale structure of the universe -numerical simulations -machine learning

We present the evolution of dark matter halos in six large cosmological N-body simulations, called the ν 2 GC (New Numerical Galaxy Catalog) simulations on the basis of the ΛCDM cosmology consistent with observational results obtained by the Planck satellite. The largest simulation consists of 8192 3 (550 billion) dark matter particles in a box of 1.12 h −1 Gpc (a mass resolution of 2.20 × 10 8 h −1 M ⊙ ). Among simulations utilizing boxes larger than 1 h −1 Gpc, our simulation yields the highest resolution simulation that has ever been achieved. A ν 2 GC simulation with the smallest box consists of eight billions particles in a box of 70h −1 Mpc (a mass resolution of 3.44 × 10 6 h −1 M ⊙ ). These simulations can follow the evolution of halos over masses of eight orders of magnitude, from small dwarf galaxies to massive clusters. Using the unprecedentedly high resolution and powerful statistics of the ν 2 GC simulations, we provide statistical results of the halo mass function, mass accretion rate, formation redshift, and merger statistics, and present accurate fitting functions for the Planck cosmology. By combining the ν 2 GC simulations with our new semi-analytic galaxy formation model, we are able to prepare mock catalogs of galaxies and active galactic nuclei, which will be made publicly available in the near future.

We introduce the Uchuu suite of large high-resolution cosmological N-body simulations. The largest simulation, named Uchuu, consists of 2.1 trillion (128003) dark matter particles in a box of side-length 2.0$\, h^{-1} \rm Gpc$, with particle mass 3.27 × 108$\, h^{-1} \rm M_{\odot }$. The highest resolution simulation, Shin-Uchuu, consists of 262 billion (64003) particles in a box of side-length 140$\, h^{-1} \rm Mpc$, with particle mass 8.97 × 105$\, h^{-1} \rm M_{\odot }$. Combining these simulations we can follow the evolution of dark matter halos and subhalos spanning those hosting dwarf galaxies to massive galaxy clusters across an unprecedented volume. In this first paper, we present basic statistics, dark matter power spectra, and the halo and subhalo mass functions, which demonstrate the wide dynamic range and superb statistics of the Uchuu suite. From an analysis of the evolution of the power spectra we conclude that our simulations remain accurate from the Baryon Acoustic Oscillation scale down to the very small. We also provide parameters of a mass-concentration model, which describes the evolution of halo concentration and reproduces our simulation data to within 5 per cent for halos with masses spanning nearly eight orders of magnitude at redshift 0 ≤ z ≤ 14. There is an upturn in the mass-concentration relation for the population of all halos and of relaxed halos at z ≳ 0.5, whereas no upturn is detected at z < 0.5. We make publicly available various N-body products as part of Uchuu Data Release 1 on the Skies & Universes site†. Future releases will include gravitational lensing maps and mock galaxy, X-ray cluster, and active galactic nuclei catalogues.