The Primordial Large Scale Biasing

Using a modified Press-Schechter formalism we analytically derive two constrained mass distribution functions: n(M) for the regions where the primordial potential perturbations are negative and n+(M) for the regions where they are positive. We use the SCDM model with with Γ = 0.25 and σ8 = 1 as a fiducial one, which agrees with the COBE measurements. We show that n−(M) is systematically greater than n+(M) for the masses corresponding to galaxy clusters. In the range of masses 10 − 10hM⊙ the mass function n−(M) is 1.3 − 2 times greater than n+(M). The scale of the potential fluctuations is ≈ 120hMpc for the model in question while the rms density contrast is only about 0.03 on this scale. We conclude that galaxy clusters are strongly biased (bcl ≈ 5− 10, where bcl is defined by the relation ∆ncl/ncl = bcl∆ρm/ρm ) toward the regions of the negative primordial potential. This effect, in principle, allows us to use clusters as tracers of the primordial gravitational potential fluctuations. Subject headings: cosmology: theory — large-scale structure of universe