We introduce the Uchuu suite of large high-resolution cosmological N-body simulations. The largest simulation, named Uchuu, consists of 2.1 trillion (12 800³) dark matter particles in a box of side-length 2.0 |$\, h^{-1} \, \rm Gpc$|⁠, with particle mass of 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 of 8.97 × 10⁵|$\, h^{-1}\, \rm M_{\odot }$|⁠. Combining these simulations, we can follow the evolution of dark matter haloes and subhaloes 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 haloes 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 haloes and of relaxed haloes 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.¹ Future releases will include gravitational lensing maps and mock galaxy, X-ray cluster, and active galactic nucleus catalogues.

In this paper, we describe the implementation and performance of GreeM, a massively parallel TreePM code for large-scale cosmological N-body simulations. GreeM uses a recursive multi-section algorithm for domain decomposition. The size of the domains are adjusted so that the total calculation time of the force becomes the same for all processes. The loss of performance due to non-optimal load balancing is around 4%, even for more than 10$^3$ CPU cores. GreeM runs efficiently on PC clusters and massively-parallel computers, such as a Cray XT4. The measured calculation speed on Cray XT4 is 5 $\times$ 10$^4$ particles per second per CPU core, for the case of an opening angle of $\theta$$=$ 0.5, if the number of particles per CPU core is larger than 10$^6$.

The core–cusp problem is one of the controversial issues in the standard paradigm of Λ cold dark matter (ΛCDM) theory. However, under the assumption of conventional spherical symmetry, the strong degeneracy among model parameters makes it unclear whether dwarf spheroidal (dSph) galaxies indeed have cored dark matter density profiles at their centers. In this work, we revisit this problem using nonspherical mass models, which have the advantage of being able to alleviate the degeneracy. Applying our mass models to the currently available kinematic data of the eight classical dSphs, we find that within finite uncertainties, most of these dSphs favor cusped central profiles rather than cored ones. In particular, Draco has a cusped dark matter halo with high probability even considering a prior bias. We also find the diversity of the inner slopes in their dark matter halos. To clarify the origin of this diversity, we investigate the relation between the inner dark matter density slope and stellar-to-halo mass ratio for the sample dSphs and find that this relation is generally in agreement with the predictions from recent ΛCDM and hydrodynamical simulations. We also find that the simulated subhalos have an anticorrelation between the dark matter density at 150 pc and pericenter distance, which is consistent with the observed one. We estimate their astrophysical factors for dark matter indirect searches and circular velocity profiles associated with huge uncertainties. To more precisely estimate their dark matter profiles, wide-field spectroscopic surveys for the dSphs are essential.

We study evolution of dark matter substructures, especially how they lose mass and change density profile after they fall in gravitational potential of larger host halos. We develop an analytical prescription that models the subhalo mass evolution and calibrate it to results of $N$-body numerical simulations of various scales from very small (Earth size) to large (galaxies to clusters) halos. We then combine the results with halo accretion histories and calculate the subhalo mass function that is physically motivated down to Earth-mass scales. Our results—valid for arbitrary host masses and redshifts—have reasonable agreement with those of numerical simulations at resolved scales. Our analytical model also enables self-consistent calculations of the boost factor of dark matter annihilation, which we find to increase from tens of percent at the smallest (Earth) and intermediate (dwarfs) masses to a factor of several at galaxy size, and to become as large as a factor of $\sim 10$ for the largest halos (clusters) at small redshifts. Our analytical approach can accommodate substructures in the subhalos (sub-subhalos) in a consistent framework, which we find to give up to a factor of a few enhancements to the annihilation boost. The presence of the subhalos enhances the intensity of the isotropic gamma-ray background by a factor of a few, and as the result, the measurement by the Fermi Large Area Telescope excludes the annihilation cross section greater than $\sim 4\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ for dark matter masses up to $\sim 200\mathrm{GeV}$.