In order to confront theoretical model
predictions for the mass distribution
against observational data, one needs a relation of density fields
of mass and luminous objects. The biasing of density peaks in a
Gaussian random field is well formulated [37, 4
], and it provides
the first theoretical framework for the origin of galaxy density
biasing. In this scheme, the galaxy-galaxy and mass-mass
correlation functions are related in the linear regime via
The above deterministic linear biasing is not
based on a reasonable physical motivation. If , it must break down in deep voids because values of
below
are forbidden by definition.
Even in the simple case of no evolution in comoving galaxy number
density, the linear biasing relation is not preserved during the
course of fluctuation growth. Non-linear biasing, where
varies with
, is inevitable.
Indeed, an analytical model for biasing of halos
on the basis of the extended Press-Schechter
approximation [59] predicts that the
biasing is nonlinear and provides a useful approximation for its
behavior as a function of scale, time, and mass threshold.
-body simulations provide a more accurate description
of the nonlinearity of the halo biasing confirming the validity of
the Mo and White model [35, 103
].