Quasi Non-linear Evolution of Stochastic Bias

Abstract

It is generally believed that the spatial distribution of galaxies does not trace that of the total mass. The understanding of the bias effect is therefore necessary to determine the cosmological parameters and the primordial density fluctuation spectrum from the galaxy survey. The deterministic description of bias may not be appropriate because of the various stochasticity of galaxy formation process. In nature, the biasing is epoch dependent and recent deep survey of the galaxy shows the large biasing at high redshift. Hence, we investigate quasi non-linear evolution of the stochastic bias by using the tree level perturbation method. Especially, the influence of the initial cross correlation on the evolution of the skewness and the bi-spectrum is examined in detail. We find that the non-linear bias can be generated dynamically. The small value of the initial cross correlation can bend the $\dg$-$\dm$ relation effectively and easily lead to the negative curvature ($b_2<0$). We also propose a method to predict the bias, cross correlation and skewness at high redshift. As an illustration, the possibility of the large biasing at high redshift is discussed. Provided the present bias parameter as $b=1.5$ and $Ω=1.0$, we predict the large scale bias as $b=4.63$ at $z=3$ by fitting the bi-spectrum to the Lick catalog data. Our results will be important for the future deep sky survey.