The Large Scale Biasing and the Primordial Gravitational Potential

Abstract

We modified the Press-Schechter (PS) formalism and then analytically derived a constrained mass distribution function n(M|varphi) for the regions having some specified value of the primordial gravitational potential, varphi. 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 Gamma = Omega h = 0.25 normalized to sigma_{8} = 1. In particular, we show that the probability of finding a clump of mass 10^{14} - 10^{15}h^{-1}M_{odot} in the region of negative initial potential is 1.3 - 3 times greater (depending on the mass) than that in the region of positiveinitial potential. The scale of the potential fluctuations R_{varphi}=sqrt{3} sigma_{varphi}/sigma_{varphi'} is shown to be approx 120 h^{-1} Mpc for the spectrum in question. The rms mass density contrast on this scale is only about sigma_{delta}(R_{varphi}) approx 0.03. Assuming that the modified PS theory is statistically correct, we conclude that clusters are significantly biased (b ge 10, b is a bias factor defined by Delta n_{cl}/ n_{cl} = b Delta rho_m/rho_m) toward the regions having negative initial potential.

Latex file,15 pages,2 postscript figures, accepted by ApJ Letter

References in corpus (4)

• The Most Massive Distant Clusters: Determining Omega and sigma_8
• Constraints on the fluctuation amplitude and density parameter from X-ray cluster number counts
• The Cosmological Mass Distribution Function in the Zel'dovich Approximation
• Determining the Amplitude of Mass Fluctuations in the Universe

Cited by in corpus (9)

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• Formation of caustics in Dirac-Born-Infeld type scalar field systems
• Formation and clustering of primordial black holes in Brans-Dicke theory
• The Effect of Primordial Anti-Biasing on the Local Measurement of the Key Cosmological Parameters
• The Cosmological Mass Function in the Zel'dovich Approximation