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  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].
© Max Planck Society and the author(s)