Linear and non-linear bias: predictions vs. measurements
  We study the linear and non-linear bias parameters which determine the
mapping between the distributions of galaxies and the full matter density
fields, comparing different measurements and predictions. Associating galaxies
with dark matter haloes in the MICE Grand Challenge N-body simulation we
directly measure the bias parameters by comparing the smoothed density
fluctuations of haloes and matter in the same region at different positions as
a function of smoothing scale. Alternatively we measure the bias parameters by
matching the probability distributions of halo and matter density fluctuations,
which can be applied to observations. These direct bias measurements are
compared to corresponding measurements from two-point and different third-order
correlations, as well as predictions from the peak-background model, which we
presented in previous articles using the same data. We find an overall
variation of the linear bias measurements and predictions of $\sim 5 \%$ with
respect to results from two-point correlations for different halo samples with
masses between $\sim 10^{12} - 10^{15}$ $h^{-1}M_\odot$ at the redshifts
$z=0.0$ and $0.5$. Variations between the second- and third-order bias
parameters from the different methods show larger variations, but with
consistent trends in mass and redshift. The various bias measurements reveal a
tight relation between the linear and the quadratic bias parameters, which is
consistent with results from the literature based on simulations with different
cosmologies. Such a universal relation might improve constraints on
cosmological models, derived from second-order clustering statistics at small
scales or higher-order clustering statistics.
