Simulating the Universe with MICE: The abundance of massive clusters
  We introduce a new set of large N-body runs, the MICE simulations, that
provide a unique combination of very large cosmological volumes with good mass
resolution. They follow the gravitational evolution of ~ 8.5 billion particles
(2048^3) in volumes covering up to 450 (Gpc/h)^3. Our main goal is to
accurately model and calibrate basic cosmological probes that will be used by
upcoming astronomical surveys. Here we take advantage of the very large volumes
of MICE to make a robust sampling of the high-mass tail of the halo mass
function (MF). We discuss and avoid possible systematic effects in our study,
and do a detailed analysis of different error estimators. We find that
available fits to the local abundance of halos (Warren et al. (2006)) match
well the abundance in MICE up to M ~ 10^{14}\Msun, but significantly deviate
for larger masses, underestimating the mass function by 10% (30%) at M = 3.16 x
10^{14}\Msun (10^{15}\Msun). Similarly, the widely used Sheth & Tormen (1999)
fit, if extrapolated to high redshift assuming universality, leads to an
underestimation of the cluster abundance by 30%, 20% and 15% at z=0, 0.5, 1 for
M ~ [7 - 2.5 - 0.8] x 10^{14}\Msun respectively ($\nu = \delta_c/\sigma ~ 3$).
We provide a re-calibration of the halo MF valid over 5 orders of magnitude in
mass, 10^{10} < M/(\Msun) < 10^{15}, that accurately describes its redshift
evolution up to z=1. We explore the impact of this re-calibration on the
determination of dark-energy, and conclude that using available fits may
systematically bias the estimate of w by as much as 50% for medium-depth (z <=
1) surveys. MICE halo catalogues are publicly available at
http://www.ice.cat/mice
