  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.
