  We present the first results from the new Bolshoi N-body cosmological LCDM
simulation that uses cosmological parameters favored by current observations.
The Bolshoi simulation was done in a volume 250Mpc on a side using 8billion
particles with mass and force resolution adequate to follow subhalos down to a
completeness limit of Vcirc=50km/ s circular velocity. Using excellent
statistics of halos and subhalos (10M at every moment and 50M over the whole
history) we present accurate approximations for statistics such as the halo
mass function, the concentrations for distinct halos and subhalos, abundance of
halos as function of their circular velocity, the abundance and the spatial
distribution of subhalos. We find that at high redshifts the concentration
falls to a minimum of about 3.8 and then rises slightly for higher values of
halo mass. We find that while the Sheth-Tormen approximation for the mass
function of halos found by spherical overdensity is accurate at low redshifts,
it over-predicts the abundance of halos by nearly an order of magnitude by
z=10. We find that the number of subhalos scales with the circular velocity of
the host halo as Vhost**0.5, and that subhalos have nearly the same radial
distribution as dark matter particles at radii 0.3-2 times the host halo virial
radius. The subhalo velocity function n(>V) behaves as V**(-3). We give
normalization of this relation for different masses and redshifts. Finally, we
use an abundance-matching procedure to assign r-band luminosities to dark
matter halos as a function of halo Vcirc, and find that the luminosity-velocity
relation is in remarkably good agreement with the observed Tully-Fisher
relation for galaxies in the range 50-200km/s.
