Modelling large-scale halo bias using the bispectrum
  We study the relation between the halo and matter density fields -- commonly
termed bias -- in the LCDM framework. In particular, we examine the local model
of biasing at quadratic order in the matter density. This model is
characterized by parameters b_1 and b_2. Using an ensemble of N-body
simulations, we apply several statistical methods to estimate the parameters.
We measure halo and matter fluctuations smoothed on various scales and find
that the parameters vary with smoothing scale. We argue that, for real-space
measurements, owing to the mixing of wavemodes, no scale can be found for which
the parameters are independent of smoothing. However, this is not the case in
Fourier space. We measure halo power spectra and construct estimates for an
effective large-scale bias. We measure the configuration dependence of the halo
bispectra B_hhh and reduced bispectra Q_hhh for very large-scale k-space
triangles. From this we constrain b_1 and b_2. Using the lowest-order
perturbation theory, we find that for B_hhh the best-fit parameters are in
reasonable agreement with one another as the triangle scale is varied, but that
the fits become poor as smaller scales are included. The same is true for
Q_hhh. The best-fit parameters depend on the discreteness correction. This led
us to consider halo-mass cross-bispectra. The results from these statistics
support our earlier findings. We develop a test to explore the importance of
missing higher-order terms in the models. We prove that low-order expansions
are not able to correctly model the data, even on scales k_1~0.04 h/Mpc. If
robust inferences are to be drawn from galaxy surveys, then accurate models for
the full nonlinear matter bispectrum and trispectrum will be essential.
