ar X iv : a st ro - p h / 98 03 22 1 v 2 2 5 Ju l 1 99 8 LARGE SCALE BIASING AND THE PRIMORDIAL GRAVITATIONAL POTENTIAL

We modified the Press-Schechter (PS) formalism and then analytically derived a constrained mass distribution function n(M |φ) for the regions having some specified value of the primordial gravitational potential, φ. The resulting modified PS theory predicts that gravitationally bound clumps with masses corresponding to rich clusters are significantly biased toward the regions of negative primordial potential the troughs of the potential. The prediction is quantitative, depending on the mass and the depth of the troughs, which can be tested in large N-body simulations. As an illustration of the magnitude of the effect we calculate the constrained mass function for the CDM model with Γ = Ωh = 0.25 normalized to σ8 = 1. In particular, we show that the probability of finding a clump of mass 10 − 10hM⊙ in the region of negative initial potential is 1.3 − 3 times greater (depending on the mass) than that in the region of positive initial potential. The scale of the potential fluctuations Rφ = √ 3σφ/σφ′ is shown to be ≈ 120hMpc for the spectrum in question. The rms mass density contrast on this scale is only about σδ(Rφ) ≈ 0.03. Assuming that the modified PS theory is statistically correct, we conclude that clusters are significantly biased (b ≥ 10, b is a bias factor defined by ∆ncl/ncl = b∆ρm/ρm) toward the regions having negative initial potential. Subject headings: cosmology: theory — large-scale structure of universe