We present two large cosmological N-body simulations, called Horizon Run 2 (HR2) and Horizon Run 3 (HR3), made using 60003 = 216 billions and 72103 = 374 billion particles, spanning a volume of (7.200 h-1Gpc)3 and (10.815 h-1Gpc)3, respectively. These simulations improve on our previous Horizon Run 1 (HR1) up to a factor of 4.4 in volume, and range from 2600 to over 8800 times the volume of the Millennium Run. In addition, they achieve a considerably finer mass resolution, down to 1.25 X 1011h-1M⊙, allowing to resolve galaxy-size halos with mean particle separations of 1.2h-1Mpc and 1.5h-1Mpc, respectively. We have measured the power spectrum, correlation function, mass function and basic halo properties with percent level accuracy, and verified that they correctly reproduce the CDM theoretical expectations, in excellent agreement with linear perturbation theory. Our unprecedentedly large-volume N-body simulations can be used for a variety of studies in cosmology and astrophysics, ranging from large-scale structure topology, baryon acoustic oscillations, dark energy and the characterization of the expansion history of the Universe, till galaxy formation science - in connection with the new SDSS-III. To this end, we made a total of 35 all-sky mock surveys along the past light cone out to z = 0.7 (8 from the HR2 and 27 from the HR3), to simulate the BOSS geometry. The simulations and mock surveys are already publicly available at http://astro.kias.re.kr/Horizon-Run23/.

We have developed a cosmological N-body code which can simulate unprecedently large number of massive particles. This code is based on the Particle-Mesh scheme, and utilize the recent fast I/O devices to swap all variables. Using the new code we have simulated the formation and evolution of structures at high redshifts in the standard Cold Dark Matter (CDM) cosmogony. A simulation evolving 1024^3 particles on a 2048^3 mesh with the initial standard CDM power spectrum is being made. This is the first billion particle cosmological simulation with initial conditions representing the theoretical model over the widest range of space. A smaller, but still very large CDM simulation with 512^3 particles on a 1024^3 mesh has been completed. We have found that the galaxy-scale CDM halos with diameters of tens of kpcs undergo complete collapse before redshift 10. Our results clearly indicate that galactic and subgalactic structures have formed far before redshift 5 which is the present upper limit to the epoch of observed structures. We emphasize that the non-linear evolution of the galactic and subgalactic-scale structures starts as early as z ~ 50, and that cosmological simulations must start at such high redshifts. A high mass resolution is also indispensable to accurately represent the theoretical model in the initial conditions down to subgalactic scales, and to correctly study the subsequent formation and evolution of structures through hierarchical clustering.