We study the evolution of the halo-halo correlation function and small-scale (≈0.2-7 h-1 Mpc) bias in four cosmological models (ΛCDM, OCDM, τCDM, and SCDM) using very high resolution n-body simulations with a dynamical range of ~10,000-32,000 (force resolution of ≈2-4 h-1 kpc and particle mass of ≈109 h-1 M☉). The high force and mass resolution allows dark matter halos to survive in the tidal fields of high-density regions and thus prevents the ambiguities related with the "overmerging problem." This allows us to estimate for the first time the evolution of the correlation function and bias at small (down to ~100 h-1 kpc) scales. We find that at all epochs the two-point correlation function of galaxy-size halos ξhh is well approximated by a power law with slope ≈1.6-1.8. The difference between the shape of ξhh and the shape of the correlation function of matter results in the scale-dependent bias at scales 7 h-1 Mpc, which we find to be a generic prediction of the hierarchical models, independent of the epoch and of the model details. The bias evolves rapidly from a high value of ~2-5 at z ~ 3-7 to the antibias of b ~ 0.5-1 at small 5 h-1 Mpc scales at z = 0. Another generic prediction is that the comoving amplitude of the correlation function for halos above a certain mass evolves nonmonotonically: it decreases from an initially high value at z ~ 3-7, and very slowly increases at z 1. We find that our results agree well with existing clustering data at different redshifts, indicating the general success of the hierarchical models of structure formation in which galaxies form inside the host DM halos. Particularly, we find an excellent agreement in both slope and the amplitude between ξhh(z = 0) in our ΛCDM60 simulation and the galaxy correlation function measured using the Automatic Plate Measuring Facility galaxy survey. At high redshifts, the observed clustering of the Lyman-break galaxies is also well reproduced by the models. We find good agreement at z 2 between our results and predictions of the analytical models of bias evolution. This indicates that we have a solid understanding of the nature of the bias and of the processes that drive its evolution at these epochs. We argue, however, that at lower redshifts the evolution of the bias is driven by dynamical processes inside the nonlinear high-density regions such as galaxy clusters and groups. These processes do not depend on cosmology and tend to erase the differences in clustering properties of halos that exist between cosmological models at high z.
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